Yearning for the Infinite — Aleph 2

Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).

▲ Yearning for the Infinite, Max Cooper at the Barbican Hall, London. Track Aleph 2. Video by Martin Krzywinski. Photo by Michal Augustini. (more)

I discuss the math behind the video and the system I built to create the video.

Hidden Markov Models

Everything we see hides another thing, we always want to see what is hidden by what we see.
—Rene Magritte

A Hidden Markov Model extends a Markov chain to have hidden states. Hidden states are used to model aspects of the system that cannot be directly observed and themselves form a Markov chain and each state may emit one or more observed values.

Hidden states in HMMs do not have to have meaning—they can be used to account for measurement errors, compress multi-modal observational data, or to detect unobservable events.

▲ Nature Methods Points of Significance column: Hidden Markov Models. (read)

In this column, we extend the cell growth model from our Markov Chain column to include two hidden states: normal and sedentary.

We show how to calculate forward probabilities that can predict the most likely path through the HMM given an observed sequence.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Hidden Markov Models. Nature Methods 16:795–796.

Background reading

Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

Hola Mundo Cover

My cover design for Hola Mundo by Hannah Fry. Published by Blackie Books.

▲ Hola Mundo by Hannah Fry. Cover design is based on my 2013 `\pi` day art. (read)

Curious how the design was created? Read the full details.

Markov Chains

You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts

A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.

▲ Nature Methods Points of Significance column: Markov Chains. (read)

Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current state—the future is independent of the past if the present is known.

Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.

This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. Nature Methods 16:663–664.

1-bit zoomable gigapixel maps of Moon, Solar System and Sky

Places to go and nobody to see.

Exquisitely detailed maps of places on the Moon, comets and asteroids in the Solar System and stars, deep-sky objects and exoplanets in the northern and southern sky. All maps are zoomable.

▲ 3.6 gigapixel map of the near side of the Moon, annotated with 6,733. (details)

▲ 100 megapixel and 10 gigapixel map of the Solar System on 20 July 2019, annotated with 758k asteroids, 1.3k comets and all planets and satellites. (details)

▲ 100 megapixle and 10 gigapixel map of the Northern Celestial Hemisphere, annotated with 44 million stars, 74,000 deep-sky objects and 3,000 exoplanets. (details)

▲ 100 megapixle and 10 gigapixel map of the Southern Celestial Hemisphere, annotated with 69 million stars, 88,000 deep-sky objects and 1000 exoplanets. (details)

Quantile regression

Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"

▲ Nature Methods Points of Significance column: Quantile regression. (read)

Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.

Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.

Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nature Methods 16:451–452.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nature Methods 12:999–1000.

Analyzing outliers: Robust methods to the rescue

Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.

▲ Nature Methods Points of Significance column: Analyzing outliers: Robust methods to the rescue. (read)

We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.

Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.

Background reading

Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.

Two-level factorial experiments

Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.

They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.

▲ Nature Methods Points of Significance column: Two-level factorial experiments. (read)

Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).

Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.

Background reading

Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.

Happy 2019 `\pi` Day—
Digits, internationally

Celebrate `\pi` Day (March 14th) and set out on an exploration explore accents unknown (to you)!

This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.

A special kids' edition merges math with color and fat fonts.

▲ 116 digits in 64 languages. (details)

▲ 223 digits in 102 languages. (details)

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day and 2018 `\pi` Day.

Tree of Emotional Life

One moment you're :) and the next you're :-.

Make sense of it all with my Tree of Emotional life—a hierarchical account of how we feel.

▲ A section of the Tree of Emotional Life.

Find and snap to colors in an image

One of my color tools, the colorsnap application snaps colors in an image to a set of reference colors and reports their proportion.

Below is Times Square rendered using the colors of the MTA subway lines.

▲ Times Square in New York City.

▲ Times Square in New York City rendered using colors of the MTA subway lines.

▲ Granger rainbow snapped to subway lines colors from four cities. (zoom)

Take your medicine ... now

Drugs could be more effective if taken when the genetic proteins they target are most active.

Design tip: rediscover CMYK primaries.

More of my American Scientific Graphic Science designs

Ruben et al. A database of tissue-specific rhythmically expressed human genes has potential applications in circadian medicine Science Translational Medicine 10 Issue 458, eaat8806.

Predicting with confidence and tolerance

We focus on the important distinction between confidence intervals, typically used to express uncertainty of a sampling statistic such as the mean and, prediction and tolerance intervals, used to make statements about the next value to be drawn from the population.

Confidence intervals provide coverage of a single point—the population mean—with the assurance that the probability of non-coverage is some acceptable value (e.g. 0.05). On the other hand, prediction and tolerance intervals both give information about typical values from the population and the percentage of the population expected to be in the interval. For example, a tolerance interval can be configured to tell us what fraction of sampled values (e.g. 95%) will fall into an interval some fraction of the time (e.g. 95%).

▲ Nature Methods Points of Significance column: Predicting with confidence and tolerance. (read)

Altman, N. & Krzywinski, M. (2018) Points of significance: Predicting with confidence and tolerance Nature Methods 15:843–844.

Background reading

Krzywinski, M. & Altman, N. (2013) Points of significance: Importance of being uncertain. Nature Methods 10:809–810.

4-day Circos course

A 4-day introductory course on genome data parsing and visualization using Circos. Prepared for the Bioinformatics and Genome Analysis course in Institut Pasteur Tunis, Tunis, Tunisia.

▲ Composite of the kinds of images you will learn to make in this course.

Oryza longistaminata genome cake

Data visualization should be informative and, where possible, tasty.

Stefan Reuscher from Bioscience and Biotechnology Center at Nagoya University celebrates a publication with a Circos cake.

The cake shows an overview of a de-novo assembled genome of a wild rice species Oryza longistaminata.

▲ Circos cake celebrating Reuscher et al. 2018 publication of the Oryza longistaminata genome.

Optimal experimental design

The presence of constraints in experiments, such as sample size restrictions, awkward blocking or disallowed treatment combinations may make using classical designs very difficult or impossible.

Optimal design is a powerful, general purpose alternative for high quality, statistically grounded designs under nonstandard conditions.

▲ Nature Methods Points of Significance column: Optimal experimental design. (read)

We discuss two types of optimal designs (D-optimal and I-optimal) and show how it can be applied to a scenario with sample size and blocking constraints.

Smucker, B., Krzywinski, M. & Altman, N. (2018) Points of significance: Optimal experimental design Nature Methods 15:599–600.

Background reading

Krzywinski, M., Altman, N. (2014) Points of significance: Two factor designs. Nature Methods 11:1187–1188.

Krzywinski, M. & Altman, N. (2014) Points of significance: Analysis of variance (ANOVA) and blocking. Nature Methods 11:699–700.

Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments. Nature Methods 11:597–598.

The Whole Earth Cataloguer

An illustration of the Tree of Life, showing some of the key branches.

The tree is drawn as a DNA double helix, with bases colored to encode ribosomal RNA genes from various organisms on the tree.

▲ The circle of life. (read, zoom)

All living things on earth descended from a single organism called LUCA (last universal common ancestor) and inherited LUCA’s genetic code for basic biological functions, such as translating DNA and creating proteins. Constant genetic mutations shuffled and altered this inheritance and added new genetic material—a process that created the diversity of life we see today. The “tree of life” organizes all organisms based on the extent of shuffling and alteration between them. The full tree has millions of branches and every living organism has its own place at one of the leaves in the tree. The simplified tree shown here depicts all three kingdoms of life: bacteria, archaebacteria and eukaryota. For some organisms a grey bar shows when they first appeared in the tree in millions of years (Ma). The double helix winding around the tree encodes highly conserved ribosomal RNA genes from various organisms.

Johnson, H.L. (2018) The Whole Earth Cataloguer, Sactown, Jun/Jul, p. 89

Why we can't give up this odd way of typing

An article about keyboard layouts and the history and persistence of QWERTY.

My Carpalx keyboard optimization software is mentioned along with my World's Most Difficult Layout: TNWMLC. True typing hell.

▲ TNWMLC requires seriously flexible digits. It’s 87% more difficult than using a standard Qwerty keyboard, according to Martin Krzywinski, who created it (Credit: Ben Nelms). (read)

McDonald, T. (2018) Why we can't give up this odd way of typing, BBC, 25 May 2018.

Molecular Case Studies Cover

The theme of the April issue of Molecular Case Studies is precision oncogenomics. We have three papers in the issue based on work done in our Personalized Oncogenomics Program (POG).

The covers of Molecular Case Studies typically show microscopy images, with some shown in a more abstract fashion. There's also the occasional Circos plot.

I've previously taken a more fine-art approach to cover design, such for those of Nature, Genome Research and Trends in Genetics. I've used microscopy images to create a cover for PNAS—the one that made biology look like astrophysics—and thought that this is kind of material I'd start with for the MCS cover.

▲ Cover design for Apr 2018 issue of Molecular Case Studies. (details)

Happy 2018 `\tau` Day—Art for everyone

▲ You know what day it is. (details)

Universe Superclusters and Voids

A map of the nearby superclusters and voids in the Unvierse.

By "nearby" I mean within 6,000 million light-years.

▲ The Universe — Superclustesr and Voids. The two supergalactic hemispheres showing Abell clusters, superclusters and voids within a distance of 6,000 million light-years from the Milky Way. (details)

Datavis for your feet—the 178.75 lb socks

In the past, I've been tangentially involved in fashion design. I've also been more directly involved in fashion photography.

It was now time to design my first ... pair of socks.

▲ Some datavis for your feet: the 178.75 lb socks. (get some)

In collaboration with Flux Socks, the design features the colors and relative thicknesses of Rogue olympic weightlifting plates. The first four plates in the stack are the 55, 45, 35, and 25 competition plates. The top 4 plates are the 10, 5, 2.5 and 1.25 lb change plates.

The perceived weight of each sock is 178.75 lb and 357.5 lb for the pair.

The actual weight is much less.

Genes Behind Psychiatric Disorders

Find patterns behind gene expression and disease.

Expression, correlation and network module membership of 11,000+ genes and 5 psychiatric disorders in about 6" x 7" on a single page.

Design tip: Stay calm.

▲ An analysis of dust reveals how the presence of men, women, dogs and cats affects the variety of bacteria in a household. Appears on Graphic Science page in December 2015 issue of Scientific American.

More of my American Scientific Graphic Science designs

Gandal M.J. et al. Shared Molecular Neuropathology Across Major Psychiatric Disorders Parallels Polygenic Overlap Science 359 693–697 (2018)

Curse(s) of dimensionality

We discuss the many ways in which analysis can be confounded when data has a large number of dimensions (variables). Collectively, these are called the "curses of dimensionality".

▲ Nature Methods Points of Significance column: Curse(s) of dimensionality. (read)

Some of these are unintuitive, such as the fact that the volume of the hypersphere increases and then shrinks beyond about 7 dimensions, while the volume of the hypercube always increases. This means that high-dimensional space is "mostly corners" and the distance between points increases greatly with dimension. This has consequences on correlation and classification.

Statistics vs Machine Learning

Inference creates a mathematical model of the datageneration process to formalize understanding or test a hypothesis about how the system behaves. Prediction aims at forecasting unobserved outcomes or future behavior. Typically we want to do both and know how biological processes work and what will happen next. Inference and ML are complementary in pointing us to biologically meaningful conclusions.

▲ Nature Methods Points of Significance column: Statistics vs machine learning. (read)

Statistics asks us to choose a model that incorporates our knowledge of the system, and ML requires us to choose a predictive algorithm by relying on its empirical capabilities. Justification for an inference model typically rests on whether we feel it adequately captures the essence of the system. The choice of pattern-learning algorithms often depends on measures of past performance in similar scenarios.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Statistics vs machine learning. Nature Methods 15:233–234.

Background reading

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: supervised methods. Nature Methods 15:5–6.

...more about the Points of Significance column

Happy 2018 `\pi` Day—Boonies, burbs and boutiques of `\pi`

Celebrate `\pi` Day (March 14th) and go to brand new places. Together with Jake Lever, this year we shrink the world and play with road maps.

Streets are seamlessly streets from across the world. Finally, a halva shop on the same block!

▲ A great 10 km run loop between Istanbul, Copenhagen, San Francisco and Dublin. Stop off for halva, smørrebrød, espresso and a Guinness on the way. (details)

Intriguing and personal patterns of urban development for each city appear in the Boonies, Burbs and Boutiques series.

▲ In the Boonies, Burbs and Boutiques of `\pi` we draw progressively denser patches using the digit sequence 159 to inform density. (details)

No color—just lines. Lines from Marrakesh, Prague, Istanbul, Nice and other destinations for the mind and the heart.

▲ Roads from cities rearranged according to the digits of `\pi`. (details)

The art is featured in the Pi City on the Scientific American SA Visual blog.

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day and 2017 `\pi` Day.

Machine learning: supervised methods (SVM & kNN)

We examine two very common supervised machine learning methods: linear support vector machines (SVM) and k-nearest neighbors (kNN).

SVM is often less computationally demanding than kNN and is easier to interpret, but it can identify only a limited set of patterns. On the other hand, kNN can find very complex patterns, but its output is more challenging to interpret.

▲ Nature Methods Points of Significance column: Machine learning: supervised methods (SVM & kNN). (read)

We illustrate SVM using a data set in which points fall into two categories, which are separated in SVM by a straight line "margin". SVM can be tuned using a parameter that influences the width and location of the margin, permitting points to fall within the margin or on the wrong side of the margin. We then show how kNN relaxes explicit boundary definitions, such as the straight line in SVM, and how kNN too can be tuned to create more robust classification.

Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Machine learning: a primer. Nature Methods 15:5–6.

Background reading

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

...more about the Points of Significance column

Human Versus Machine

In a Nature graphics blog article, I present my process behind designing the stark black-and-white Nature 10 cover.

Nature 10, 18 December 2017

Machine learning: a primer

In this primer, we focus on essential ML principles— a modeling strategy to let the data speak for themselves, to the extent possible.

The benefits of ML arise from its use of a large number of tuning parameters or weights, which control the algorithm’s complexity and are estimated from the data using numerical optimization. Often ML algorithms are motivated by heuristics such as models of interacting neurons or natural evolution—even if the underlying mechanism of the biological system being studied is substantially different. The utility of ML algorithms is typically assessed empirically by how well extracted patterns generalize to new observations.

▲ Nature Methods Points of Significance column: Machine learning: a primer. (read)

We present a data scenario in which we fit to a model with 5 predictors using polynomials and show what to expect from ML when noise and sample size vary. We also demonstrate the consequences of excluding an important predictor or including a spurious one.

Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.

...more about the Points of Significance column

Snowflake simulation

Just in time for the season, I've simulated a snow-pile of snowflakes based on the Gravner-Griffeath model.

▲ A few of the beautiful snowflakes generated by the Gravner-Griffeath model. (explore)

The work is described as a wintertime tale in In Silico Flurries: Computing a world of snow and co-authored with Jake Lever in the Scientific American SA Blog.

Gravner, J. & Griffeath, D. (2007) Modeling Snow Crystal Growth II: A mesoscopic lattice map with plausible dynamics.

Genes that make us sick

My illustration of the location of genes in the human genome that are implicated in disease appears in The Objects that Power the Global Economy, a book by Quartz.

▲ The location of genes implicated in disease in the human genome, shown here as a spiral. (more...)

Ensemble methods: Bagging and random forests

We introduce two common ensemble methods: bagging and random forests. Both of these methods repeat a statistical analysis on a bootstrap sample to improve the accuracy of the predictor. Our column shows these methods as applied to Classification and Regression Trees.

▲ Nature Methods Points of Significance column: Ensemble methods: Bagging and random forests. (read)

For example, we can sample the space of values more finely when using bagging with regression trees because each sample has potentially different boundaries at which the tree splits.

Random forests generate a large number of trees by not only generating bootstrap samples but also randomly choosing which predictor variables are considered at each split in the tree.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Ensemble methods: bagging and random forests. Nature Methods 14:933–934.

Background reading

Krzywinski, M. & Altman, N. (2017) Points of Significance: Classification and regression trees. Nature Methods 14:757–758.

...more about the Points of Significance column

Classification and regression trees

Decision trees classify data by splitting it along the predictor axes into partitions with homogeneous values of the dependent variable. Unlike logistic or linear regression, CART does not develop a prediction equation. Instead, data are predicted by a series of binary decisions based on the boundaries of the splits. Decision trees are very effective and the resulting rules are readily interpreted.

Trees can be built using different metrics that measure how well the splits divide up the data classes: Gini index, entropy or misclassification error.

▲ Nature Methods Points of Significance column: Classification and decision trees. (read)

When the predictor variable is quantitative and not categorical, regression trees are used. Here, the data are still split but now the predictor variable is estimated by the average within the split boundaries. Tree growth can be controlled using the complexity parameter, a measure of the relative improvement of each new split.

Individual trees can be very sensitive to minor changes in the data and even better prediction can be achieved by exploiting this variability. Using ensemble methods, we can grow multiple trees from the same data.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Classification and regression trees. Nature Methods 14:757–758.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Regularization. Nature Methods 13:803-804.

...more about the Points of Significance column

Personal Oncogenomics Program 5 Year Anniversary Art

The artwork was created in collaboration with my colleagues at the Genome Sciences Center to celebrate the 5 year anniversary of the Personalized Oncogenomics Program (POG).

▲ 5 Years of Personalized Oncogenomics Program at Canada's Michael Smith Genome Sciences Centre. The poster shows 545 cancer cases. (left) Cases ordered chronologically by case number. (right) Cases grouped by diagnosis (tissue type) and then by similarity within group.

The Personal Oncogenomics Program (POG) is a collaborative research study including many BC Cancer Agency oncologists, pathologists and other clinicians along with Canada's Michael Smith Genome Sciences Centre with support from BC Cancer Foundation.

The aim of the program is to sequence, analyze and compare the genome of each patient's cancer—the entire DNA and RNA inside tumor cells— in order to understand what is enabling it to identify less toxic and more effective treatment options.

Principal component analysis

Principal component analysis (PCA) simplifies the complexity in high-dimensional data by reducing its number of dimensions.

▲ Nature Methods Points of Significance column: Principal component analysis. (read)

To retain trend and patterns in the reduced representation, PCA finds linear combinations of canonical dimensions that maximize the variance of the projection of the data.

PCA is helpful in visualizing high-dimensional data and scatter plots based on 2-dimensional PCA can reveal clusters.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Principal component analysis. Nature Methods 14:641–642.

Background reading

Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. Nature Methods 14:545–546.

...more about the Points of Significance column

`k` index: a weightlighting and Crossfit performance measure

Similar to the `h` index in publishing, the `k` index is a measure of fitness performance.

To achieve a `k` index for a movement you must perform `k` unbroken reps at `k`% 1RM.

The expected value for the `k` index is probably somewhere in the range of `k = 26` to `k=35`, with higher values progressively more difficult to achieve.

In my `k` index introduction article I provide detailed explanation, rep scheme table and WOD example.

Dark Matter of the English Language—the unwords

I've applied the char-rnn recurrent neural network to generate new words, names of drugs and countries.

The effect is intriguing and facetious—yes, those are real words.

But these are not: necronology, abobionalism, gabdologist, and nonerify.

These places only exist in the mind: Conchar and Pobacia, Hzuuland, New Kain, Rabibus and Megee Islands, Sentip and Sitina, Sinistan and Urzenia.

And these are the imaginary afflictions of the imagination: ictophobia, myconomascophobia, and talmatomania.

And these, of the body: ophalosis, icabulosis, mediatopathy and bellotalgia.

Want to name your baby? Or someone else's baby? Try Ginavietta Xilly Anganelel or Ferandulde Hommanloco Kictortick.

When taking new therapeutics, never mix salivac and labromine. And don't forget that abadarone is best taken on an empty stomach.

And nothing increases the chance of getting that grant funded than proposing the study of a new –ome! We really need someone to looking into the femome and manome.

Dark Matter of the Genome—the nullomers

An exploration of things that are missing in the human genome. The nullomers.

Julia Herold, Stefan Kurtz and Robert Giegerich. Efficient computation of absent words in genomic sequences. BMC Bioinformatics (2008) 9:167

Clustering

We've already seen how data can be grouped into classes in our series on classifiers. In this column, we look at how data can be grouped by similarity in an unsupervised way.

▲ Nature Methods Points of Significance column: Clustering. (read)

We look at two common clustering approaches: `k`-means and hierarchical clustering. All clustering methods share the same approach: they first calculate similarity and then use it to group objects into clusters. The details of the methods, and outputs, vary widely.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. Nature Methods 14:545–546.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

...more about the Points of Significance column

What's wrong with pie charts?

In this redesign of a pie chart figure from a Nature Medicine article [1], I look at how to organize and present a large number of categories.

I first discuss some of the benefits of a pie chart—there are few and specific—and its shortcomings—there are few but fundamental.

I then walk through the redesign process by showing how the tumor categories can be shown more clearly if they are first aggregated into a small number groups.

(bottom left) Figure 2b from Zehir et al. Mutational landscape of metastatic cancer revealed from prospective clinical sequencing of 10,000 patients. (2017) Nature Medicine doi:10.1038/nm.4333

Tabular Data

After 30 columns, this is our first one without a single figure. Sometimes a table is all you need.

In this column, we discuss nominal categorical data, in which data points are assigned to categories in which there is no implied order. We introduce one-way and two-way tables and the `\chi^2` and Fisher's exact tests.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Tabular data. Nature Methods 14:329–330.

...more about the Points of Significance column

Happy 2017 `\pi` Day—Star Charts, Creatures Once Living and a Poem

on a brim of echo,

capsized chamber
drawn into our constellation, and cooling.
—Paolo Marcazzan

Celebrate `\pi` Day (March 14th) with star chart of the digits. The charts draw 40,000 stars generated from the first 12 million digits.

▲ 12,000,000 digits of `\pi` interpreted as a star catalogue. (details)

The 80 constellations are extinct animals and plants. Here you'll find old friends and new stories. Read about how Desmodus is always trying to escape or how Megalodon terrorizes the poor Tecopa! Most constellations have a story.

▲ Find friends and stories among the 80 constellations of extinct animals and plants. Oh look, a Dodo guardings his eggs! (details)

This year I collaborate with Paolo Marcazzan, a Canadian poet, who contributes a poem, Of Black Body, about space and things we might find and lose there.

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day and and 2016 `\pi` Day.

Data in New Dimensions: convergence of art, genomics and bioinformatics

Art is science in love.
— E.F. Weisslitz

A behind-the-scenes look at the making of our stereoscopic images which were at display at the AGBT 2017 Conference in February. The art is a creative collaboration with Becton Dickinson and The Linus Group.

Its creation began with the concept of differences and my writeup of the creative and design process focuses on storytelling and how concept of differences is incorporated into the art.

Oh, and this might be a good time to pick up some red-blue 3D glasses.

▲ A stereoscopic image and its interpretive panel of single-cell transcriptomes of blood cells: diseased versus healthy control.

Interpreting P values

This month we continue our discussion about `P` values and focus on the fact that `P` value is a probability statement about the observed sample in the context of a hypothesis, not about the hypothesis being tested.

▲ Nature Methods Points of Significance column: Interpreting P values. (read)

Given that we are always interested in making inferences about hypotheses, we discuss how `P` values can be used to do this by way of the Benjamin-Berger bound, `\bar{B}` on the Bayes factor, `B`.

Heuristics such as these are valuable in helping to interpret `P` values, though we stress that `P` values vary from sample to sample and hence many sources of evidence need to be examined before drawing scientific conclusions.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Interpreting P values. Nature Methods 14:213–214.

Background reading

Krzywinski, M. & Altman, N. (2017) Points of significance: P values and the search for significance. Nature Methods 14:3–4.

Krzywinski, M. & Altman, N. (2013) Points of significance: Significance, P values and t–tests. Nature Methods 10:1041–1042.

...more about the Points of Significance column

Snellen Charts—Typography to Really Look at

Another collection of typographical posters. These ones really ask you to look.

▲ Snellen charts designed using physical constants, Braille and elemental abundances in the universe and human body.

The charts show a variety of interesting symbols and operators found in science and math. The design is in the style of a Snellen chart and typset with the Rockwell font.

Essentials of Data Visualization—8-part video series

In collaboration with the Phil Poronnik and Kim Bell-Anderson at the University of Sydney, I'm delighted to share with you our 8-part video series project about thinking about drawing data and communicating science.

▲ Essentials of Data Visualization: Thinking about drawing data and communicating science.

We've created 8 videos, each focusing on a different essential idea in data visualization: encoding, shapes, color, uncertainty, design, drawing missing or unobserved data, labels and process.

The videos were designed as teaching materials. Each video comes with a slide deck and exercises.

P values and the search for significance

We've written about P values before and warned readers about common misconceptions about them, which are so rife that the American Statistical Association itself has a long statement about them.

This month is our first of a two-part article about P values. Here we look at 'P value hacking' and 'data dredging', which are questionable practices that invalidate the correct interpretation of P values.

▲ Nature Methods Points of Significance column: P values and the search for significance. (read)

We also illustrate how P values can lead us astray by asking "What is the smallest P value we can expect if the null hypothesis is true but we have done many tests, either explicitly or implicitly?"

Incidentally, this is our first column in which the standfirst is a haiku.

Altman, N. & Krzywinski, M. (2017) Points of Significance: P values and the search for significance. Nature Methods 14:3–4.

Background reading

Krzywinski, M. & Altman, N. (2013) Points of significance: Significance, P values and t–tests. Nature Methods 10:1041–1042.

...more about the Points of Significance column

Intuitive Design

Appeal to intuition when designing with value judgments in mind.

Figure clarity and concision are improved when the selection of shapes and colors is grounded in the Gestalt principles, which describe how we visually perceive and organize information.

▲ One of the Gestalt principles tells us that the magenta and green shapes will be perceived as as two groups, overriding the fact that the shapes within the group might be different. What the principle does not tell us is how the reader is likely to value each group. (read)

The Gestalt principles are value free. For example, they tell us how we group objects but do not speak to any meaning that we might intuitively infer from visual characteristics.

▲ Nature Methods Points of View column: Intuitive Design. (read)

This month, we discuss how appealing to such intuitions—related to shapes, colors and spatial orientation— can help us add information to a figure as well as anticipate and encourage useful interpretations.

Krzywinski, M. (2016) Points of View: Intuitive Design. Nature Methods 13:895.

...more about the Points of View column

Regularization

Constraining the magnitude of parameters of a model can control its complexity.

This month we continue our discussion about model selection and evaluation and address how to choose a model that avoids both overfitting and underfitting.

Ideally, we want to avoid having either an underfitted model, which is usually a poor fit to the training data, or an overfitted model, which is a good fit to the training data but not to new data.

▲ Nature Methods Points of Significance column: Regularization (read)

Regularization is a process that penalizes the magnitude of model parameters. This is done by not only minimizing the SSE, `\mathrm{SSE} = \sum_i (y_i - \hat{y}_i)^2 `, as is done normally in a fit, but adding to this minimized quantity the sum of the mode's squared parameters, `\mathrm{SSE} + \lambda \sum_i \hat{\beta}^2_i`.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Regularization. Nature Methods 13:803-804.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

...more about the Points of Significance column

Model Selection and Overfitting

With four parameters I can fit an elephant and with five I can make him wiggle his trunk. —John von Neumann.

By increasing the complexity of a model, it is easy to make it fit to data perfectly. Does this mean that the model is perfectly suitable? No.

When a model has a relatively large number of parameters, it is likely to be influenced by the noise in the data, which varies across observations, as much as any underlying trend, which remains the same. Such a model is overfitted—it matches training data well but does not generalize to new observations.

▲ Nature Methods Points of Significance column: Model Selection and Overfitting (read)

We discuss the use of training, validation and testing data sets and how they can be used, with methods such as cross-validation, to avoid overfitting.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

...more about the Points of Significance column

Classifier Evaluation

It is important to understand both what a classification metric expresses and what it hides.

We examine various metrics use to assess the performance of a classifier. We show that a single metric is insufficient to capture performance—for any metric, a variety of scenarios yield the same value.

▲ Nature Methods Points of Significance column: Classifier Evaluation (read)

We also discuss ROC and AUC curves and how their interpretation changes based on class balance.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

...more about the Points of Significance column

Happy 2016 `\pi` Approximation, roughly speaking

Today is the day and it's hardly an approximation. In fact, `22/7` is 20% more accurate of a representation of `\pi` than `3.14`!

Time to celebrate, graphically. This year I do so with perfect packing of circles that embody the approximation.

buy artwork

By warping the circle by 8% along one axis, we can create a shape whose ratio of circumference to diameter, taken as twice the average radius, is 22/7.

If you prefer something more accurate, check out art from previous `\pi` days: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, and 2016 `\pi` Day.

Logistic Regression

Regression can be used on categorical responses to estimate probabilities and to classify.

The next column in our series on regression deals with how to classify categorical data.

We show how linear regression can be used for classification and demonstrate that it can be unreliable in the presence of outliers. Using a logistic regression, which fits a linear model to the log odds ratio, improves robustness.

▲ Nature Methods Points of Significance column: Logistic regression? (read)

Logistic regression is solved numerically and in most cases, the maximum-likelihood estimates are unique and optimal. However, when the classes are perfectly separable, the numerical approach fails because there is an infinite number of solutions.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

Background reading

Altman, N. & Krzywinski, M. (2016) Points of Significance: Regression diagnostics? Nature Methods 13:385-386.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression Nature Methods 12:999-1000.

...more about the Points of Significance column

Visualizing Clonal Evolution in Cancer

Genomic instability is one of the defining characteristics of cancer and within a tumor, which is an ever-evolving population of cells, there are many genomes. Mutations accumulate and propagate to create subpopulations and these groups of cells, called clones, may respond differently to treatment.

It is now possible to sequence individual cells within a tumor to create a profile of genomes. This profile changes with time, both in the kinds of mutation that are found and in their proportion in the overall population.

▲ Ways to present temporal and phylogenetic evolution of clones in cancer. M Krzywinski (2016) Molecular Cell 62:652-656. (read)

Clone evolution diagrams visualize these data. These diagrams can be qualitative, showing only trends, or quantitative, showing temporal and population changes to scale. In this Molecular Cell forum article I provide guidelines for drawing these diagrams, focusing with how to use color and navigational elements, such as grids, to clarify the relationships between clones.

▲ How to draw clone evolution diagrams better. M Krzywinski (2016) Molecular Cell xxx:xxx-xxx. (read)

I'd like to thank Maia Smith and Cydney Nielsen for assistance in preparing some of the figures in the paper.

Krzywinski, M. (2016) Visualizing Clonal Evolution in Cancer. Mol Cell 62:652-656.

Binning High-Resolution Data

Limitations in print resolution and visual acuity impose limits on data density and detail.

Your printer can print at 1,200 or 2,400 dots per inch. At reading distance, your reader can resolve about 200–300 lines per inch. This large gap—how finely we can print and how well we can see—can create problems when we don't take visual acuity into account.

▲ Nature Methods Points of View column: Binning high-resolution data. (read)

The column provides some guidelines—particularly relevant when showing whole-genome data, where the scale of elements of interest such as genes is below the visual acuity limit—for binning data so that they are represented by elements that can be comfortably discerned.

Krzywinski, M. (2016) Points of view: Binning high-resolution data. Nature Methods 13:463.

...more about the Points of View column

Regression diagnostics

Residual plots can be used to validate assumptions about the regression model.

Continuing with our series on regression, we look at how you can identify issues in your regression model.

The difference between the observed value and the model's predicted value is the residual, `r = y_i - \hat{y}_i`, a very useful quantity to identify the effects of outliers and trends in the data that might suggest your model is inadequate.

▲ Nature Methods Points of Significance column: Regression diagnostics? (read)

We also discuss normal probability plots (or Q-Q plots) and show how these can be used to check that the residuals are normally distributed, which is one of the assumptions of regression (constant variance being another).

Background reading

Altman, N. & Krzywinski, M. (2016) Points of Significance: Analyzing outliers: Influential or nuisance? Nature Methods 13:281-282.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression Nature Methods 12:999-1000.

...more about the Points of Significance column

Analyzing Outliers: Influential or Nuisance?

Some outliers influence the regression fit more than others.

This month our column addresses the effect that outliers have on linear regression.

You may be surprised, but not all outliers have the same influence on the fit (e.g. regression slope) or inference (e.g. confidence or prediction intervals). Outliers with large leverage—points that are far from the sample average—can have a very large effect. On the other hand, if the outlier is close to the sample average, it may not influence the regression slope at all.

▲ Nature Methods Points of Significance column: Analyzing Outliers: Influential or Nuisance? (read)

Quantities such as Cook's distance and the so-called hat matrix, which defines leverage, are useful in assessing the effect of outliers.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression Nature Methods 12:999-1000.

...more about the Points of Significance column

Typographical posters of bird songs

Chirp, chirp, chirp but much better looking.

▲ The song of the Northern Flicker, Black-capped Chickadee, Olive-sided Flycatcher and Red-eyed Vireo. Sweet to the eye and ear. (details)

If you like these, check out my other typographical art posters.

Happy 2016 Pi Day—gravity of `\pi`

Celebrate `\\pi` Day (March 14th) with colliding digits in space. This year, I celebrate the detection of gravitational waves at the LIGO lab and simulate the effect of gravity on masses created from the digits of `\\pi`.

▲ 1,000 digits of `\pi` under the influence of gravity. (details)

Some strange things can happen.

▲ 44 digits of `\pi` under the influence of gravity. (details)

The art is featured in the Gravity of Pi article on the Scientific American SA Visual blog.

Check out art from previous years: 2013 `\\pi` Day and 2014 `\\pi` Day and 2015 `\\pi` Day.

Neural Circuit Diagrams

Use alignment and consistency to untangle complex circuit diagrams.

This month we apply the ideas presented in our column about drawing pathways to neural circuit diagrams. Neural circuits are networks of cells or regions, typically with a large number of variables, such as cell and neurotransmitter type.

▲ Nature Methods Points of View column: Neural circuit diagrams. (read)

We discuss how to effectively route arrows, how to avoid pitfalls of redundant encoding and suggest ways to encorporate emphasis in the layout.

Hunnicutt, B.J. & Krzywinski, M. (2016) Points of View: Neural circuit diagrams. Nature Methods 13:189.

background reading

Hunnicutt, B.J. & Krzywinski, M. (2016) Points of Viev: Pathways. Nature Methods 13:5.

Wong, B. (2010) Points of Viev: Gestalt principles (part 1). Nature Methods 7:863.

Wong, B. (2010) Points of Viev: Gestalt principles (part 2). Nature Methods 7:941.

...more about the Points of View column

Pathways

Apply visual grouping principles to add clarity to information flow in pathway diagrams.

We draw on the Gestalt principles of connection, grouping and enclosure to construct practical guidelines for drawing pathways with a clear layout that maintains hierarchy.

▲ Nature Methods Points of View column: Pathways. (read)

We include tips about how to use negative space and align nodes to emphasizxe groups and how to effectively draw curved arrows to clearly show paths.

Hunnicutt, B.J. & Krzywinski, M. (2016) Points of Viev: Pathways. Nature Methods 13:5.

background reading

Wong, B. (2010) Points of Viev: Gestalt principles (part 1). Nature Methods 7:863.

Wong, B. (2010) Points of Viev: Gestalt principles (part 2). Nature Methods 7:941.

...more about the Points of View column

Multiple Linear Regression

When multiple variables are associated with a response, the interpretation of a prediction equation is seldom simple.

This month we continue with the topic of regression and expand the discussion of simple linear regression to include more than one variable. As it turns out, although the analysis and presentation of results builds naturally on the case with a single variable, the interpretation of the results is confounded by the presence of correlation between the variables.

By extending the example of the relationship of weight and height—we now include jump height as a second variable that influences weight—we show that the regression coefficient estimates can be very inaccurate and even have the wrong sign when the predictors are correlated and only one is considered in the model.

▲ Nature Methods Points of Significance column: Multiple Linear Regression. (read)

Care must be taken! Accurate prediction of the response is not an indication that regression slopes reflect the true relationship between the predictors and the response.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression Nature Methods 12:999-1000.

...more about the Points of Significance column

Circos and Hive Workshop Workshop—Poznan, Poland

Taught how Circos and hive plots can be used to show sequence relationships at Biotalent Functional Annotation of Genome Sequences Workshop at the Institute for Plant Genetics in Poznan, Poland.

Students generated images published in Fast Diploidization in Close Mesopolyploid Relatives of Arabidopsis.

Workshop materials: slides, handout, Circos and hive plot files.

▲ Drawing synteny between modern and ancient genomes with Circos.

Students also learned how to use hive plots to show synteny.

▲ Hive plots are great at showing 3-way sequence comparisons. Here three modern species of Australian Brassicaceae (S. nutans, S. lineare, B. antipoda) are compared based on their common relationships to the ancestral karotype.

Mandakova, T. et al. Fast Diploidization in Close Mesopolyploid Relatives of Arabidopsis The Plant Cell, Vol. 22: 2277-2290, July 2010

Play the Bacteria Game

Choose your own dust adventure!

Nobody likes dusting but everyone should find dust interesting.

Working with Jeannie Hunnicutt and with Jen Christiansen's art direction, I created this month's Scientific American Graphic Science visualization based on a recent paper The Ecology of microscopic life in household dust.

▲ An analysis of dust reveals how the presence of men, women, dogs and cats affects the variety of bacteria in a household. Appears on Graphic Science page in December 2015 issue of Scientific American.

We have also written about the making of the graphic, for those interested in how these things come together.

This was my third information graphic for the Graphic Science page. Unlike the previous ones, it's visually simple and ... interactive. Or, at least, as interactive as a printed page can be.

More of my American Scientific Graphic Science designs

Barberan A et al. (2015) The ecology of microscopic life in household dust. Proc. R. Soc. B 282: 20151139.

Names for 5,092 colors

A very large list of named colors generated from combining some of the many lists that already exist (X11, Crayola, Raveling, Resene, wikipedia, xkcd, etc).

▲ Confused? So am I. That's why I made a list.

For each color, coordinates in RGB, HSV, XYZ, Lab and LCH space are given along with the 5 nearest, as measured with ΔE, named neighbours.

I also provide a web service. Simply call this URL with an RGB string.

Simple Linear Regression

It is possible to predict the values of unsampled data by using linear regression on correlated sample data.

This month, we begin our column with a quote, shown here in its full context from Box's paper Science and Statistics.

In applying mathematics to subjects such as physics or statistics we make tentative assumptions about the real world which we know are false but which we believe may be useful nonetheless. The physicist knows that particles have mass and yet certain results, approximating what really happens, may be derived from the assumption that they do not. Equally, the statistician knows, for example, that in nature there never was a normal distribution, there never was a straight line, yet with normal and linear assumptions, known to be false, he can often derive results which match, to a useful approximation, those found in the real world.
—Box, G. J. Am. Stat. Assoc. 71, 791–799 (1976).

▲ Nature Methods Points of Significance column: Simple Linear Regression. (read)

This column is our first in the series about regression. We show that regression and correlation are related concepts—they both quantify trends—and that the calculations for simple linear regression are essentially the same as for one-way ANOVA.

While correlation provides a measure of a specific kind of association between variables, regression allows us to fit correlated sample data to a model, which can be used to predict the values of unsampled data.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Simple Linear Regression Nature Methods 12:999-1000.

Background reading

Altman, N. & Krzywinski, M. (2015) Points of significance: Association, correlation and causation Nature Methods 12:899-900.

Krzywinski, M. & Altman, N. (2014) Points of significance: Analysis of variance (ANOVA) and blocking. Nature Methods 11:699-700.

...more about the Points of Significance column

Association, correlation and causation

Correlation implies association, but not causation. Conversely, causation implies association, but not correlation.

This month, we distinguish between association, correlation and causation.

Association, also called dependence, is a very general relationship: one variable provides information about the other. Correlation, on the other hand, is a specific kind of association: an increasing or decreasing trend. Not all associations are correlations. Moreover, causality can be connected only to association.

▲ Nature Methods Points of Significance column: Association, correlation and causation. (read)

We discuss how correlation can be quantified using correlation coefficients (Pearson, Spearman) and show how spurious corrlations can arise in random data as well as very large independent data sets. For example, per capita cheese consumption is correlated with the number of people who died by becoming tangled in bedsheets.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Association, correlation and causation Nature Methods 12:899-900.

...more about the Points of Significance column

Bayesian networks

For making probabilistic inferences, a graph is worth a thousand words.

This month we continue with the theme of Bayesian statistics and look at Bayesian networks, which combine network analysis with Bayesian statistics.

In a Bayesian network, nodes represent entities, such as genes, and the influence that one gene has over another is represented by a edge and probability table (or function). Bayes' Theorem is used to calculate the probability of a state for any entity.

▲ Nature Methods Points of Significance column: Bayesian networks. (read)

In our previous columns about Bayesian statistics, we saw how new information (likelihood) can be incorporated into the probability model (prior) to update our belief of the state of the system (posterior). In the context of a Bayesian network, relationships called conditional dependencies can arise between nodes when information is added to the network. Using a small gene regulation network we show how these dependencies may connect nodes along different paths.

Background reading

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayesian Statistics Nature Methods 12:277-278.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem Nature Methods 12:277-278.

...more about the Points of Significance column

Unentangling complex plots

The Points of Significance column is on vacation this month.

Meanwhile, we're showing you how to manage small multiple plots in the Points of View column Unentangling Complex Plots.

▲ Nature Methods Points of View column: Unentangling complex plots. (download, more about Points of View)

Data in small multiples can vary in range, noise level and trend. Gregor McInerny and myself show you how you can deal with this by cropped and scaling the multiples to a different range to emphasize relative changes while preserving the context of the full data range to show absolute changes.

McInerny, G. & Krzywinski, M. (2015) Points of View: Unentangling complex plots. Nature Methods 12:591.

...more about the Points of View column

Fixing Jurassic World science visualizations

The Jurassic World Creation Lab webpage shows you how one might create a dinosaur from a sample of DNA. First extract, sequence, assemble and fill in the gaps in the DNA and then incubate in an egg and wait.

▲ We can't get dinosaur genomics right, but we can get it less wrong. (a) Corn genome used in Jurassic World Creation Lab website. Image is from the Science publication B73 Maize Genome: Complexity, Diversity, and Dynamics. Photo and composite by Universal Studios and Amblin Entertainment. (b) Random data on 8 chromosomes from chicken genome resized to triceratops genome size (3.2 Gb). Image by Martin Krzywinski. (c) Actual genome data for lizard genome, UCSC anoCar2.0, May 2010. Image by Martin Krzywinski. Triceratops outline in (b,c) from wikipedia.

With enough time, you'll grow your own brand new dinosaur. Or a stalk of corn ... with more teeth.

What went wrong? Let me explain.

▲ Corn World: Teeth on the Cob.

Printing Genomes

You've seen bound volumes of printouts of the human reference genome. But what if at the Genome Sciences Center we wanted to print everything we sequence today?

▲ Curiously, printing is 44 times as expensive as sequencing. (details)

Gene Volume Control

I was commissioned by Scientific American to create an information graphic based on Figure 9 in the landmark Nature Integrative analysis of 111 reference human epigenomes paper.

The original figure details the relationships between more than 100 sequenced epigenomes and genetic traits, including disease like Crohn's and Alzheimer's. These relationships were shown as a heatmap in which the epigenome-trait cell depicted the P value associated with tissue-specific H3K4me1 epigenetic modification in regions of the genome associated with the trait.

▲ Figure 9 from Integrative analysis of 111 reference human epigenomes (Nature (2015) 518 317–330). (details)

As much as I distrust network diagrams, in this case this was the right way to show the data. The network was meticulously laid out by hand to draw attention to the layered groups of diseases of traits.

▲ Network diagram redesign of the heatmap for a select set of traits. Only relationships with –log P > 3.9 are displayed. Appears on Graphic Science page in June 2015 issue of Scientific American. (details)

This was my second information graphic for the Graphic Science page. Last year, I illustrated the extent of differences in the gene sequence of humans, Denisovans, chimps and gorillas.

Sampling distributions and the bootstrap

The bootstrap is a computational method that simulates new sample from observed data. These simulated samples can be used to determine how estimates from replicate experiments might be distributed and answer questions about precision and bias.

▲ Nature Methods Points of Significance column: Sampling distributions and the bootstrap. (read)

We discuss both parametric and non-parametric bootstrap. In the former, observed data are fit to a model and then new samples are drawn using the model. In the latter, no model assumption is made and simulated samples are drawn with replacement from the observed data.

Kulesa, A., Krzywinski, M., Blainey, P. & Altman, N (2015) Points of Significance: Sampling distributions and the bootstrap Nature Methods 12:477-478.

Background reading

Krzywinski, M. & Altman, N. (2013) Points of Significance: Importance of being uncertain. Nature Methods 10:809-810.

...more about the Points of Significance column

Bayesian statistics

Building on last month's column about Bayes' Theorem, we introduce Bayesian inference and contrast it to frequentist inference.

Given a hypothesis and a model, the frequentist calculates the probability of different data generated by the model, P(data|model). When this probability to obtain the observed data from the model is small (e.g. `alpha` = 0.05), the frequentist rejects the hypothesis.

▲ Nature Methods Points of Significance column: Bayesian Statistics. (read)

In contrast, the Bayesian makes direct probability statements about the model by calculating P(model|data). In other words, given the observed data, the probability that the model is correct. With this approach it is possible to relate the probability of different models to identify one that is most compatible with the data.

The Bayesian approach is actually more intuitive. From the frequentist point of view, the probability used to assess the veracity of a hypothesis, P(data|model), commonly referred to as the P value, does not help us determine the probability that the model is correct. In fact, the P value is commonly misinterpreted as the probability that the hypothesis is right. This is the so-called "prosecutor's fallacy", which confuses the two conditional probabilities P(data|model) for P(model|data). It is the latter quantity that is more directly useful and calculated by the Bayesian.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem Nature Methods 12:277-278.

Background reading

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem Nature Methods 12:277-278.

...more about the Points of Significance column

Bayes' Theorem

In our first column on Bayesian statistics, we introduce conditional probabilities and Bayes' theorem

P(B|A) = P(A|B) × P(B) / P(A)

This relationship between conditional probabilities P(B|A) and P(A|B) is central in Bayesian statistics. We illustrate how Bayes' theorem can be used to quickly calculate useful probabilities that are more difficult to conceptualize within a frequentist framework.

▲ Nature Methods Points of Significance column: Bayes' Theorem. (read)

Using Bayes' theorem, we can incorporate our beliefs and prior experience about a system and update it when data are collected.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem Nature Methods 12:277-278.

Background reading

Oldford, R.W. & Cherry, W.H. Picturing probability: the poverty of Venn diagrams, the richness of eikosograms. (University of Waterloo, 2006)

...more about the Points of Significance column

Happy 2015 Pi Day—can you see `pi` through the treemap?

Celebrate `pi` Day (March 14th) with splitting its digit endlessly. This year I use a treemap approach to encode the digits in the style of Piet Mondrian.

▲ Digits of `pi`, `phi` and `e`. (details)

The art has been featured in Ana Swanson's Wonkblog article at the Washington Post—10 Stunning Images Show The Beauty Hidden in `pi`.

I also have art from 2013 `pi` Day and 2014 `pi` Day.

Split Plot Design

The split plot design originated in agriculture, where applying some factors on a small scale is more difficult than others. For example, it's harder to cost-effectively irrigate a small piece of land than a large one. These differences are also present in biological experiments. For example, temperature and housing conditions are easier to vary for groups of animals than for individuals.

▲ Nature Methods Points of Significance column: Split plot design. (read)

The split plot design is an expansion on the concept of blocking—all split plot designs include at least one randomized complete block design. The split plot design is also useful for cases where one wants to increase the sensitivity in one factor (sub-plot) more than another (whole plot).

Altman, N. & Krzywinski, M. (2015) Points of Significance: Split Plot Design Nature Methods 12:165-166.

Background reading

1. Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

2. Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.

3. Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

...more about the Points of Significance column

Color palettes for color blindness

In an audience of 8 men and 8 women, chances are 50% that at least one has some degree of color blindness¹. When encoding information or designing content, use colors that is color-blind safe.

▲ A 12-color palette safe for color blindness

Points of Significance Column Now Open Access

Nature Methods has announced the launch of a new statistics collection for biologists.

▲ Nature Methods Points of Significance column is now open access. (column archive)

As part of that collection, announced that the entire Points of Significance collection is now open access.

This is great news for educators—the column can now be freely distributed in classrooms.

...more about the Points of Significance column

Before and After—Designing Tiny Figures for Nature Methods

I've posted a writeup about the design and redesign process behind the figures in our Nature Methods Points of Significance column.

I have selected several figures from our past columns and show how they evolved from their draft to published versions.

▲ Fig 2 from Points of Significance: Nested designs. (Krzywinski, M. & Altman, N. (2014) Nature Methods 11:977-978.) (...more)

Clarity, concision and space constraints—we have only 3.4" of horizontal space— all have to be balanced for a figure to be effective.

▲ Fig 2c (excerpt) from Points of Significance: Designing comparative experiments. (Krzywinski, M. & Altman, N. (2014) Nature Methods 11:597-598.) (...more)

It's nearly impossible to find case studies of scientific articles (or figures) through the editing and review process. Nobody wants to show their drafts. With this writeup I hope to add to this space and encourage others to reveal their process. Students love this. See whether you agree with my decisions!

Sources of Variation

Past columns have described experimental designs that mitigate the effect of variation: random assignment, blocking and replication.

The goal of these designs is to observe a reproducible effect that can be due only to the treatment, avoiding confounding and bias. Simultaneously, to sample enough variability to estimate how much we expect the effect to differ if the measurements are repeated with similar but not identical samples (replicates).

▲ Nature Methods Points of Significance column: Sources of Variation. (read)

We need to distinguish between sources of variation that are nuisance factors in our goal to measure mean biological effects from those that are required to assess how much effects vary in the population.

Altman, N. & Krzywinski, M. (2014) Points of Significance: Two Factor Designs Nature Methods 11:5-6.

Background reading

1. Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

2. Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.

3. Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

...more about the Points of Significance column

Two Factor Designs

We've previously written about how to analyze the impact of one variable in our ANOVA column. Complex biological systems are rarely so obliging—multiple experimental factors interact and producing effects.

ANOVA is a natural way to analyze multiple factors. It can incorporate the possibility that the factors interact—the effect of one factor depends on the level of another factor. For example, the potency of a drug may depend on the subject's diet.

▲ Nature Methods Points of Significance column: Two Factor Designs. (read)

We can increase the power of the analysis by allowing for interaction, as well as by blocking.

Krzywinski, M., Altman, (2014) Points of Significance: Two Factor Designs Nature Methods 11:1187-1188.

Background reading

Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

...more about the Points of Significance column

Nested Designs—Assessing Sources of Noise

Sources of noise in experiments can be mitigated and assessed by nested designs. This kind of experimental design naturally models replication, which was the topic of last month's column.

▲ Nature Methods Points of Significance column: Nested designs. (read)

Nested designs are appropriate when we want to use the data derived from experimental subjects to make general statements about populations. In this case, the subjects are random factors in the experiment, in contrast to fixed factors, such as we've seen previously.

In ANOVA analysis, random factors provide information about the amount of noise contributed by each factor. This is different from inferences made about fixed factors, which typically deal with a change in mean. Using the F-test, we can determine whether each layer of replication (e.g. animal, tissue, cell) contributes additional variation to the overall measurement.

Krzywinski, M., Altman, N. & Blainey, P. (2014) Points of Significance: Nested designs Nature Methods 11:977-978.

Background reading

Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

...more about the Points of Significance column

Replication—Quality over Quantity

It's fitting that the column published just before Labor day weekend is all about how to best allocate labor.

Replication is used to decrease the impact of variability from parts of the experiment that contribute noise. For example, we might measure data from more than one mouse to attempt to generalize over all mice.

▲ Nature Methods Points of Significance column: Replication. (read)

It's important to distinguish technical replicates, which attempt to capture the noise in our measuring apparatus, from biological replicates, which capture biological variation. The former give us no information about biological variation and cannot be used to directly make biological inferences. To do so is to commit pseudoreplication. Technical replicates are useful to reduce the noise so that we have a better chance to detect a biologically meaningful signal.

Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication Nature Methods 11:879-880.

Background reading

Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking Nature Methods 11:699-700.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

...more about the Points of Significance column

Monkeys on a Hilbert Curve—Scientific American Graphic

I was commissioned by Scientific American to create an information graphic that showed how our genomes are more similar to those of the chimp and bonobo than to the gorilla.

I had about 5 x 5 inches of print space to work with. For 4 genomes? No problem. Bring out the Hilbert curve!

▲ Our genomes are much more similar to the chimp and bonobo than to the gorilla. And, we're practically still Denisovans. (details)

To accompany the piece, I will be posting to the Scientific American blog about the process of creating the figure. And to emphasize that the genome is not a blueprint!

As part of this project, I created some Hilbert curve art pieces. And while exploring, found thousands of Hilbertonians!

Happy Pi Approximation Day— π, roughly speaking 10,000 times

Celebrate Pi Approximation Day (July 22nd) with the art of arm waving. This year I take the first 10,000 most accurate approximations (m/n, m=1..10,000) and look at their accuracy.

▲ Accuracy of the first 10,000 m/n approximations of Pi. (details)

I turned to the spiral again after applying it to stack stacked ring plots of frequency distributions in Pi for the 2014 Pi Day.

▲ Frequency distribution of digits of Pi in groups of 4 up to digit 4,988. (details)

Analysis of Variance (ANOVA) and Blocking—Accounting for Variability in Multi-factor Experiments

Our 10th Points of Significance column! Continuing with our previous discussion about comparative experiments, we introduce ANOVA and blocking. Although this column appears to introduce two new concepts (ANOVA and blocking), you've seen both before, though under a different guise.

▲ Nature Methods Points of Significance column: Analysis of variance (ANOVA) and blocking. (read)

If you know the t-test you've already applied analysis of variance (ANOVA), though you probably didn't realize it. In ANOVA we ask whether the variation within our samples is compatible with the variation between our samples (sample means). If the samples don't all have the same mean then we expect the latter to be larger. The ANOVA test statistic (F) assigns significance to the ratio of these two quantities. When we only have two-samples and apply the t-test, t² = F.

ANOVA naturally incorporates and partitions sources of variation—the effects of variables on the system are determined based on the amount of variation they contribute to the total variation in the data. If this contribution is large, we say that the variation can be "explained" by the variable and infer an effect.

We discuss how data collection can be organized using a randomized complete block design to account for sources of uncertainty in the experiment. This process is called blocking because we are blocking the variation from a known source of uncertainty from interfering with our measurements. You've already seen blocking in the paired t-test example, in which the subject (or experimental unit) was the block.

We've worked hard to bring you 20 pages of statistics primers (though it feels more like 200!). The column is taking a month off in August, as we shrink our error bars.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of Variance (ANOVA) and Blocking Nature Methods 11:699-700.

Background reading

Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — t-tests Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.

...more about the Points of Significance column

Designing Experiments—Coping with Biological and Experimental Variation

This month, Points of Significance begins a series of articles about experimental design. We start by returning to the two-sample and paired t-tests for a discussion of biological and experimental variability.

▲ Nature Methods Points of Significance column: Designing Comparative Experiments. (read)

We introduce the concept of blocking using the paired t-test as an example and show how biological and experimental variability can be related using the correlation coefficient, ρ, and how its value imapacts the relative performance of the paired and two-sample t-tests.

We also emphasize that when reporting data analyzed with the paired t-test, differences in sample means (and their associated 95% CI error bars) should be shown—not the original samples—because the correlation in the samples (and its benefits) cannot be gleaned directly from the sample data.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments Nature Methods 11:597-598.

Background reading

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — t-tests Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.

Have skew, will test

Our May Points of Significance Nature Methods column jumps straight into dealing with skewed data with Non Parametric Tests.

▲ Nature Methods Points of Significance column: Non Parametric Testing. (read)

We introduce non-parametric tests and simulate data scenarios to compare their performance to the t-test. You might be surprised—the t-test is extraordinarily robust to distribution shape, as we've discussed before. When data is highly skewed, non-parametric tests perform better and with higher power. However, if sample sizes are small they are limited to a small number of possible P values, of which none may be less than 0.05!

Krzywinski, M. & Altman, N. (2014) Points of Significance: Non Parametric Testing Nature Methods 11:467-468.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — t-tests Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.

Mind your p's and q's

In the April Points of Significance Nature Methods column, we continue our and consider what happens when we run a large number of tests.

▲ Nature Methods Points of Significance column: Comparing Samples — Part II — Multiple Testing. (read)

Observing statistically rare test outcomes is expected if we run enough tests. These are statistically, not biologically, significant. For example, if we run N tests, the smallest P value that we have a 50% chance of observing is 1–exp(–ln2/N). For N = 10^k this P value is P_k=10^–kln2 (e.g. for 10⁴=10,000 tests, P₄=6.9×10^–5).

We discuss common correction schemes such as Bonferroni, Holm, Benjamini & Hochberg and Storey's q and show how they impact the false positive rate (FPR), false discovery rate (FDR) and power of a batch of tests.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part II — Multiple Testing Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — t-tests Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.

Happy Pi Day— go to planet π

Celebrate Pi Day (March 14th) with the art of folding numbers. This year I take the number up to the Feynman Point and apply a protein folding algorithm to render it as a path.

▲ Digits of Pi form landmass and shoreline. (details)

For those of you who liked the minimalist and colorful digit grid, I've expanded on the concept to show stacked ring plots of frequency distributions.

▲ Frequency distribution of digits of Pi in groups of 6 up to the Feynman Point. (details)

And if spirals are your thing...

▲ Frequency distribution of digits of Pi in groups of 4 up to digit 4,988. (details)

Have data, will compare

In the March Points of Significance Nature Methods column, we continue our discussion of t-tests from November (Significance, P values and t-tests).

We look at what happens how uncertainty of two variables combines and how this impacts the increased uncertainty when two samples are compared and highlight the differences between the two-sample and paired t-tests.

▲ Nature Methods Points of Significance column: Comparing Samples — Part I. (read)

When performing any statistical test, it's important to understand and satisfy its requirements. The t-test is very robust with respect to some of its assumptions, but not others. We explore which.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I Nature Methods 11:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.

Circos at British Library Beautiful Science Exhibit

Beautiful Science explores how our understanding of ourselves and our planet has evolved alongside our ability to represent, graph and map the mass data of the time. The exhibit runs 20 February — 26 May 2014 and is free to the public. There is a good Nature blog writeup about it, a piece in The Guardian, and a great video that explains the the exhibit narrated by Johanna Kieniewicz, the curator.

▲ Circos at the British Library Beautiful Science exhibit. (about exhibit)

▲ Mailed invitation to the exhibit features my science art. (zoom)

I am privileged to contribute an information graphic to the exhibit in the Tree of Life section. The piece shows how sequence similarity varies across species as a function of evolutionary distance. The installation is a set of 6 30x30 cm backlit panels. They look terrific.

▲ Circos Circles of Life installation at Beautiful Science exhibit at the British Library. (zoom)

Think outside the bar—box plots

Quick, name three chart types. Line, bar and scatter come to mind. Perhaps you said pie too—tsk tsk. Nobody ever thinks of the box plot.

Box plots reveal details about data without overloading a figure with a full frequency distribution histogram. They're easy to compare and now easy to make with BoxPlotR (try it). In our fifth Points of Significance column, we take a break from the theory to explain this plot type and—I hope— convince you that they're worth thinking about.

▲ Nature Methods Points of Significance column: Visualizing samples with box plots. (read)

The February issue of Nature Methods kicks the bar chart two more times: Dan Evanko's Kick the Bar Chart Habit editorial and a Points of View: Bar charts and box plots column by Mark Streit and Nils Gehlenborg.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Visualizing samples with box plots Nature Methods 11:119-120.

Wired Data|Life 2013 talk

I recently presented at the Wired Data|Life 2013 conference, sharing my thoughts on The Art and Science of Data Visualization.

For specialists, visualizations should expose detail to allow for exploration and inspiration. For enthusiasts, they should provide context, integrate facts and inform. For the layperson, they should capture the essence of the topic, narrate a story and deligt.

Wired's Brandon Keim wrote up a short article about me and some of my work—Circle of Life: The Beautiful New Way to Visualize Biological Data.

▲ The Art and Science of Data Visualization (PDF)

Power and Sample Size

Experimental designs that lack power cannot reliably detect real effects. Power of statistical tests is largely unappreciated and many underpowered studies continue to be published.

This month, Naomi and I explain what power is, how it relates to Type I and Type II errors and sample size. By understanding the relationship between these quantities you can design a study that has both low false positive rate and high power.

▲ Nature Methods Points of Significance column: Power and Sample Size. (read)

Krzywinski, M. & Altman, N. (2013) Points of Significance: Power and Sample Size Nature Methods 10:1139-1140.

20 imperatives of science—limits of evidence

20 Tips for Interpreting Scientific Claims is a wonderful comment in Nature warning us about the limits of evidence.

I've made a poster (download hires PDF, PNG) of this list, grouping them into categories that are my own. Thrust this into everyone's hands, including your own.

▲ 20 tips for interpreting scientific claims. From Sutherland et al, Nature 2013. (PDF, PNG, read article)

Sutherland WJ, Spiegelhalter D & Burgman M (2013) Policy: Twenty tips for interpreting scientific claims. Nature 503:335–337.

Significance, P values and t-tests

Have you wondered how statistical tests work? Why does everyone want such a small P value?

This month, Naomi and I explain how significance is measured in statistics and remind you that it does not imply biological significance. You'll also learn why the t-distribution is so important and why its shape is similar to that of a normal distribution, but not quite.

▲ Nature Methods Points of Significance column: Significance, P values and t-tests. (read)

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, P values and t-tests Nature Methods 10:1041-1042.

Drinks & Science Workshop: Effective Presentations and Slides

Your slides are not your presentation. They are a representation of your presentation.

Effective presentations require that you have a clear narrative—control detail and emphasis to deliver your message. Engage the audience early. Don't dump on them.

Effective slides are visual cues. Show only what you can't easily say. Text should acts as emphasis. Don't read.

▲ Drinks & Science Workshop: Effective Presentations and Slides. Science Online Vancouver. (workshop slides)

A workshop I gave on Oct 8th at Science Online Vancouver at Science World.

Error Bars

Error bar overlap does not imply significance. Error bar gap does not imply lack of significance. Chances are you find these statements surprising.

You've seen and used error bars. But do you understand how to interpret them in the context of statistical signifiance? This month we address the most common (and commonly misunderstood) method of visualizing uncertainty.

▲ Nature Methods Points of Significance column: Error Bars. (read)

We discuss error bars based on standard deviation, standard error of the mean and confidence intervals. It turns out that none of these behave as our intuition would wish.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Error Bars Nature Methods 10:921-922.

Launch of Nature Methods Statistics Column

This month, Nature Method is launching Points of Significance a new column to educate, enlighten and, if possible, entertaining bench scientists about statistics.

I will be working closely with with Naomi Altman from The Pennsylvania State University and Dan Evanko, the Chief Editor at Nature Methods, to make the column engaging and useful.

▲ Nature Methods Points of Significance column: Importance of Being Uncertain. (read)

Our first publication — The Importance of Being Uncertain — acknowledges not only the imperative of being right about how we're wrong, but also our appreciation for Oscar Wilde.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Importance of Being Uncertain Nature Methods 10:809-810.

Points of View — The Collection

Interested in data visualization? The Points of View columns are an excellent way to learn practical tips and design principles that help you communicate clearly. All the columns are now available as a collection, and open access during August 2013.

▲ The full collection of Nature Methods Points of View columns is now available for free for the month of August. (collection, more about Points of View)

The columns were written by Bang Wong, Martin Krzywinski, Nils Gehlenborg, Cydney Nielsen, Noam Shoresh, Rikke Schmidt Kjærgaard, Erica Savig and Alberto Cairo.

Storytelling with Graphics

This month, Alberto Cairo and I examine the importance of storytelling in presenting data. A strong narrative captures the reader's attention, informs and inspires.

▲ Nature Methods Points of View column: Storytelling. (download, more about Points of View)

Instead of "explain, not merely show," seek to "narrate, not merely explain."

Analyze as a specialist, present as a communicator

The distinction between the specialist and the communicator was made by Albert Cairo at 2013 Bloomberg Design Conference. I have used this principle to structure my talk to the UBC Tableau Users Group.

Design is algorithmics for the page. Use its principles to inform how to choose from among the options offered by your software. Recognize the limitations of your tool, as well as those features that are ineffective.

Don't practise visual intuitics—use shapes whose size and proportion can be well judged.

▲ What we see isn't always what it is. The luminance effect powerfully affects our interpretation of tone and color. (download talk)

Real Human Genome Art

A collaboration of science and art with Joanna Rudnick and Aaron De La Cruz.

The science of cancer genomics will be interpreted by individuals whose lives are affected by genomic mutations using the art style of Aaron De La Cruz.

Beautiful, meaningful and personal.

▲ A day of collaboration between science, art and people affected with cancer-causing mutations. (...more)

Multidimensional data

This month, Erica Savig and I look at the design process for a figure from her paper Multiplexed mass cytometry profiling of cellular states perturbed by small-molecule regulators. The underlying data set has 1.2 billion individual observations, categorized by drug, cell line, protein and stimulation condition.

▲ Nature Methods Points of View column: Multidimensional data. (download, more about Points of View)

Bodenmiller B, Zunder ER, Finck R et al. 2012 Multiplexed mass cytometry profiling of cellular states perturbed by small-molecule regulators Nature Biotechnology 30:858-867.

Although spatial encoding is the most perceptually accurate, in this case it's not the best channel to display quantitative information. Instead, the x/y position on the page is used to organize small multiples of the network of affected proteins.

▲ Data meets pointilism. The full data set was used to create the cover of the September 2012 issue of Nature Biotechnology. (about the cover)

Choosing Plotting Symbols

In this months column, Bang and I consider how to choose effective plotting symbols in the Points of View column Plotting Symbols.

▲ Nature Methods Points of View column: Plotting Symbols. (download, more about Points of View)

Choose symbols that overlap without ambiguity and communicate relationships in data.

Figure Design and Writing — Two Goals, One Process

This month I look at how creating effective figures is similar to the process of writing well in the Points of View column Elements of Visual Style.

▲ Nature Methods Points of View column: Elements of Visual Style. (download, more about Points of View)

Using Strunk's Elements of Style as an example of writing guidelines, I look how these can be translated to creating figures.

VIZBI 2013 Keynote—Visual Design Principles

When we create figures, we must communicate and design. In my talk I discuss some of the rules that turn graphical improvisation into a structured and reproducible process.

▲ Try to focus on a spot in these posters that celebrate Pi day. (download talk)

The fractal tree was created with OneZoom, which received the best poster award at the conference.

Happy Pi Day— 3.14

Celebrate Pi Day (March 14th) with a funky modern posters. Transcend, don't repeat, yourself and watch the dots shimmer.

▲ Try to focus on a spot in these posters that celebrate Pi day. (download posters)

The posters were inspired by the beautiful AIDS posters by Elena Miska.

For the Love of Type

I am always drawn to type and periodically I must do something about it.

If you were a type, what type would you be? Me, Gill Sans on weekdays and Perpetua on the weekend.

▲ Finding intrigue and consensus within and among letters. (typography posters)

Return of Nature Methods Points of View

I take over from Bang Wong as primary contributor to the Points of View column, a monthly advice and opinion piece about data visualization and information and figure design in molecular biology.

▲ Nature Methods Points of View column returns. (read more, Nature Methods blog)

Nature Encode Explorer

▲ Nature uses Circos motif on cover and interactive ENCODE data explorer. (read more)

Nature's special issue dedicated to the Encode Project uses the Circos motif on its cover as well as the interactive Encode Explorer, which is available as an app at iTunes.

Bloomberg Businessweek Design Conference

Together with Alberto Cairo, and then in conversation with Sam Grobart, I presented about science and design at Bloomberg's Businessweek Design Conference in San Francisco.

▲ Science loves design, but doesn't always know it. (download talk)

ICDM2012 Keynote — Needles in Stacks of Needles

My ICDM2012 keynote on genomics and data mining: Needles in Stacks of Needles.

▲ Computers compute but humans are ultimately responsible for identifying what is relevant and useful. (abstract, download talk, ICDM2012)

Genome Research cover

Creating strings of genome jewelery. Read about how it was done.

▲ Cover image accompanying Spark: A navigational paradigm for genomic data exploration. Genome Research 22 (11). (details, Genome Research)

The design accompanies Cydney Nielsen's Spark manuscript, which appeared in Genome Research.

Biovis 2012 — Getting into Visualization of Large Biological Data Sets

Guidelines for data encoding and visualization in biology, presented presented at Biovis 2012 (Visweek 2012).

▲ 20 imperatives of information design. (Krzywinski et al biovis2012)

2012 Presidential Debates — a Lexical Analysis

Building on the method I used to analyze the 2008 debates, I look at the 2012 Debates between Obama and Romney, lexically speaking. Obama speaks to "folks", while Romney fearmongers with "kill" and "hurt".

▲ Analysis of word usage by parts of speech for Obama and Romney reveals insight into each candidate.

Trends in Genetics cover

Making things round, not square. Read about how it was done.

▲ Nature and human life are as various as our several constitutions. Who shall say what prospect life offers to another? —Henry David Thoreau

A Circos-based design for the cover of the human genetics special issue of Trends in Genetics (Trends in Genetics October 2012, 28 (10)).

Schloss Dagstuhl - Visualization: communicating, clearly

My talk — Visualization: communicating, clearly from the Biological Data Visualization seminar at Schloss Dagstuhl.

Science needs words

And usually, really long and funny ones.

▲ Scientists love new words, when the old ones aren't long enough.

My neologisms were picked up by James Gorman of the New York Times in an article Ome, the sound of the scientific universe expanding.

PNAS cover

Biology or astrophysics? Read about how it was done.

▲ Hint: biology.

The image was published on the cover of PNAS (PNAS 1 May 2012; 109 (18))

the art of numbers

Numerology is bogus but art based on numbers has a beautiful random quality. Oh, and none of the metaphysical baggage.

▲ Distribution of the first 3,422, 13,689 and 123,201 digits of π.

▲ Progression and transition probabilities of digits in e, φ and π.

accidental similarity number

The quantity formed by the overlap of two or more numbers.

▲ The accidental similarity number of π, φ and e.

the 4ness of pi

How much 4ness does π have?

▲ The iness of each digit of π generalizes 4ness. It measures the similarity of the digit to its neighbours.

Compare the iness of π to that of the other famous transcendental number, e, and the mysterious but attractive Golden Ratio, φ.

▲ The iness of e and φ.

ASCII Illustration—Outer Space, Sequence and Typography

I have found a way to combine my curiosity about space, fear of large sequence assemblies and love of typography in a single illustration. Inspired by typographical portraits, I wanted to automate representing an image with multiple font weights, while sampling characters from a quote or debate transcripts.

▲ Part of the Pioneer plaque rendered with the sequence of human chromosome 1, using 4 layers of sizes (17pt, 33pt, 59pt and 93pt) and 8 weights of Gotham.

Tangering Tango—Color of 2012

If you made widgets, you could be justified in campaigning a widget of the year. Business acumen suggests it should be one of your widgets. Pantone has done exactly that, naming their 17-1463 color (tangerine tango), as color of the year 2012.

▲ Tangerine Tango - Pantone's color of the year.

I prefer green—green jive.

▲ Green Jive - My own color of the year.

World's Most Expensive Photograph

I really like the world's most expensive photograph, Rhein II by Andreas Gursky. Cautious use of the word "expensive" should be practised — in this case, merely meaning that only one person saw the $4.3 million price tag. Others saw lower prices, or no price tag at all.

▲ Rhein II by Andreas Gursky. $4.3 million.

Here's my own attempt at such compositions.

▲ Near Jokulsarlon on the way to Hofn, Iceland.

Adobe Swatches for Brewer Palettes

I could not find Illustrator swatch files for this awesome color resource, so I created them myself.

▲ Brewer palettes are ideal for information design. Download Illustrator swatch files (.ase .ai).

If you're interested in color and design and don't know about Brewer palettes, see my presentation.

Global Visualization of Google Searches by Language

World-wide Google searches, categorized by one of 21 languages, are visualized with WebGL, available from Chrome Experiments. The data offers some fascinating insights such as (a) in what two places in the US are Google searches in Chinese are performed? (b) what are the most remote locations are from which Google searches were detected? (c) Why is Istanbul the 3rd top location for searches? Why is Miami in the top 10?

▲ Global visualization of google searches by language reveals English dominates (42% searches) with Spanish a distant second (14%) and German and French third (7% each).

Download geotagged data.

PSA Genomics Workshop Slides

Designing effective visualizations in the biological sciences.

▲ Neither communication nor design are purely subjective.

Circos and Hive Plots: Challenging visualization paradigms in genomics and network analysis.

▲ Neither communication nor design are purely subjective.

Tor tor & Loa Loa — 546 Organisms with Same Genus and Species

In a recent conversation, I was challenged to name as many organisms with the same genus and species as I could. Neither a biologist, and especially not a taxonomist, my responses were limited to organisms with sequenced genomes I had come across in the literature. Immediately to mind sprung Gallus gallus (chicken) and ... nothing else. Well, that was embarrassing.

I was suddently taken up by the urge to find all instances of this occurrence. Using resources at the NCBI Taxonomy Browser I downloaded the NCBI taxonomy table which contains 1,097,405 entries in the names.dmp file (not all of these are unique genus/species combinations).

To my suprise I discovered that my performance in this challenge was beyond dysmal. In fact, there are 380 genuses which contain organisms that have the same genus and species name. Most of them (317) include a single organism, but some have many. For example the genus Salamandra has 14 organisms with the species salamandra, including Salamandra salamandra, Salamandra salamandra crespoi and Salamandra salamandra morenica. The genus Regulus has 13 organisms, including Regulus regulus azoricus, Regulus regulus japonensis and Regulus regulus regulus (these are all Goldcrests).

In total, there are 546 unique entries, when organisms with a unique subspecies name are considered distinct. If subspecies is not considered, the number of organisms with the same genus as species (i.e., regardless of subspecies) is 383. Here are organisms whose genus/species name is shorter than 6 letters (82 entries).

Shortest Species/Genus Duplicates (82, 5 letters or less)

Longest Species/Genus Duplicates (5, 14 letters or more)

Coccothraustes coccothraustes

Labiostrongylus labiostrongylus

Macrobilharzia macrobilharzia

Macropostrongylus macropostrongylus

Xanthocephalus xanthocephalus

The nematode worm Macropostrongylus macropostrongylus has the honour of being the longest genus/species duplicate organism. Given this distinction, it is surprising that Pubmed returns only 2 papers that refer to it.

Dataset

Download the full list. The number next to each ENTRY field is the NCBI Taxonomy ID for the organism. In a small number of cases there are ambiguities in parsing the data file (e.g. Troglodytes cf. troglodytes PS-2, Troglodytes sp. troglodytes PS-1). I left these in.

Visual Acuity and Sequence Visualization

Visual acuity limits of the human eye restrict the resolution at which we can comfortably visualize data.

In this short guide, I explain why dividing a scale into no more than 500 divisions is a good idea.

▲ Visualizing 1.5 Mb (S. cerevisiae chrIV) in a 183 mm wide figure (size limit in Nature for double column figures) restricts scale division to 2.9 kb to ensure comfortable reading.

2011 EMBO Journal Cover Contest

For the EMBO Journal 2011 Cover Contest, I prepared two entries, one for the scientific category and one for the non-scientific category.

▲ The non-scientific entry is abstract photo of fiber optics. The scientific entry was an information graphic showing a hive panel of genomic annotations in human, mouse and dog genomes. The hive panel is based on the use of the newly introduced hive plot.

The 2011 winners have been announced. My non-scientific entry (photo of fiber optics) received honourable mention and was included in the Favourites of the Jury gallery.

New Circos Domains

Until now, Circos did not have its own domain name, having been served from the lengthy and boring http://mkweb.bcgsc.ca/circos.

Recently, I was surprised to find out that the following domains were available

• circos.ca
• genomevisualization.com
• genomevisualization.org
• genomevisualization.net

All these now point to the Circos site.

ee spammings - beautiful language of spam poetry

ee spammings are spam edited into a format reminiscent of the poetry of ee cummings. Unwanted solicitations for questionable endeavours and products suddenly turn into heady words of the new literature. Art suddenly freed from the husk of spam.

Literature 2.0 — from unlikely origins.

Here's one example that emphasizes that today is ok.

i got 
to touch you

i like us 
and know the more. 

believe
       recontact 
me

today ok!
but matters

waiting for
           happy

I now have over 20 ee spammings — enjoy them all.

Neologisms - New Words, Much Needed

What do inconversible, mystific, postpetizer, prenopsis and suscitate have in common?

They are words that don't exist, but should. Learn new words.

Hive Plot Ads

Download large ads: 00 01 02 03 04

World's Most Popular Questions
Today's Zeitgeist

What are the world's top questions?

Using Google's autocomplete feature, I have tabulated the world's most popular questions. By combining a interrogative term, such as what, who or why, with a term from a related set, such as do I, can I, and can't I, it is possible to sample the space of questions and obtain the most popular for a given start word combination.

I have tabulated the most popular questions by category.

Science

What kind of questions about science are people asking? From the Career & Education section,

• Can biology lead to new theorems?
• Can physics explain miracles?
• Can math be fun?
• Can science and religion coexist?
• Can history repeat itself?
• Can psychology be morally neutral?

Curios

What are the strangest questions? I'll let you explore, but these have me wondering:

• Has the world gone mad or is it me?
• Why can't I hold all these limes?
• What happens if I make a formal commitment to Satan?
• Why can't I sell my kidney?
• Who is the most powerful Jedi?
• Can Jesus microwave a burrito?
• Where is the hardest part of your head?

Circos Table Browser

Circos can be used to visualize tabular data, such as spreadsheets.

1,000s of tables have already been visualized. Has yours?

648 Ratios

Hive plots are excellent at visualizing ratios. They're not just an anti-hairball network visualization agent.

Below are visualized 3 x 8 x 27 = 648 (axes, ribbons, plots) ratios visualized.

The image above compares the relative ratios of region annotations in human, mouse and dog genomes.

Cáceres Creativa - Model and Strategy for Urban Innovation

Cáceres is a small city of 100,000 inhabitants in western Spain, where the city government is promoting Cáceres Creativa, a project to build citizens collaboratively sustainable future for the city based on activating the creative capacity of the population.

The project has been published as a book (excerpt), which provides a basis for working with city residents and businesses in this collaborative design.

Circos proved useful in showing the complex relationships that are established in such an environment is a city which combines flows of energy and resources, physical items and intellectual concepts. The online Circos tableviewer was used to generate the images.

Storage Cluster

Taking photos of inanimate objects is rewarding. Your subject doesn't complain, nor move, and a coffee break fits naturally into the workflow at any time. In this case, the inanimate object is over 3 Pb (3,000 Tb) of storage composed of a variety of Netapp appliances.

Using three gelled Hensel Integras (500 Ws monoheads — here I'm using only the modelling light for illumination along with red, blue and green filters) (lighting details), I spent some time getting to know the components up close.

See more photos.

All photos by Martin Krzywinski (Lumondo Photography).

Genesis 1.0

Our new compute cluster has been released to the user community.

This cluster consists of 420 compute nodes each with 12 cores and 48GB RAM, totaling 5,040 cores and 20TB RAM. Each node has 160GB local /tmp space and all nodes are tied together over an Inifiniband 40Gbs network.

The nodes all have access to a dedicated storage system over the Infiniband Network running GPFS with a total 700TB of usable scratch space. The filesystem is served by 8 IBM x3850 servers. All nodes are running CentOS5.4 and are using open source Grid Engine 6.2u5 as their scheduler.

Lighting details and more photos.

All photos by Martin Krzywinski (Lumondo Photography).

1 First the server room was expanded 2 It was empty and without racks, and the lights were dim. Sysadmins scurried about and unpacked equipment 3 The circuit was closed and there were electrons 4 IT staff were pleased and accounts were handed out to users 5 Who had work they called "important" 6 But which the IT staff merely called "jobs".

Photo

Periodically, I take my camera, point it at things. Here, I'll share a favourite from my creations.

This image — I will keep the subject a mystery — gives me the same feeling as some of the Hubble images. For this shot, I didn't need to reach orbit.

Other images in this series are available on flickr.

I also like geometry and lines. This shot is a tense composition of the Hancock Building at Copley Square in Boston.

and an assortment of baggage carts at St Pancreas station (London) which catches the eye.

I like to collect time in a photo, be it uniformly as in this diptych of street and traffic lights from a moving car

or blended, as in this skyline of Vancouver showing the flow of time from 5.30pm to 9.30pm.

WIZARD — Longest English Reverse Complement

DNA is composed of two strands, which are complementary. Given a sequence, its reverse complement is created by swapping A/T and G/C and writing the remapped sequence backwards (e.g. ATGC is first remapped to TACG and then reversed to GCAT).

Consider the corresponding concept applied to English words (or any language, for that matter). First, construct the complementarity map, which assigns to the nth letter of the alphabet the N-n letter, given an alphabet of N letters.

abcdefghijklmnopqrstuvwxyz
||||||||||||||||||||||||||
zyxwvutsrqponmlkjihgfedcba

For example, a becomes z, b becomes y, and so on. To create a reverse complement of a word, apply this mapping and then reverse the new word (e.g. 'dog' is remapped to 'wlt' and then reversed to obtain 'tlw').

So far, that's not very exciting.

But consider the question: What is the longest English word that is a palindrome under this set of rules (reverse complementarity). In other words, it's the same forward and backward after complementing the letters. Clearly "dog" is not such a palindrome since its reverse complement is "tlw".

The answer? wizard and hovels.

wizard
||||||
draziw -> 'wizard' backwards

It's an amazingly fitting answer, since a wizard is someone with special powers.

A few interesting 4-letter words that are their own reverse complement palindromes are bevy, grit, trig and wold. Common surnames that match are Ghrist, Elizarov and Prawdzik. Female first name Zola and male first name Iver are also reverse complement palindromes, as are trolig (Norwegian for 'likely', as well as an IKEA curtain product) and aviverez (2nd person plural future of 'aviver', French for 'brighten').

I've scanend a very large word list (4,138,000 unique English and foreign words) and identified 108 reverse complement palindromes. If you find a new entry longer than 6 letters, let me know.

Typefaces that are worth it

Finding just the right font is hard work. There are so many to choose from. Or are there?

If the type face is not on this list, don't use it (except Bodoni &mdash I hate Bodoni &mdash don't use it). If you need a shorter list, consult the quintissential 15 serif and 15 sans-serif fonts.

You'll notice a rotating image of type faces at the top of this page. Here's the full list.

I love Gotham and have used it in visualization projects. It's more rational than Helvetica and still enjoys a freshness that has evapourated from Helvetica after near-ubiquitous use. Don't get me wrong, there is still not enough Helvetica in the world, but more Gotham would be nice.

Paper

Anyone who has met me, quickly learns that I have a personal and antagonistic relationship with Comic Sans, the type face that shouldn't have been.

In a recent article in the journal Cognition, Fortune favours the bold (and the italicized): Effects of disfluence on educational outcomes, Diemand-Yauman et al. suggest that rendering educational materials in a hard-to-read font, and thereby recruiting the effects of the disfluency ("the subjective experience of difficulty associated with cognitive operations"), improves retention of material.

Regardless whether the effect is real, there must be better ways to improve education than through bad design.

Kittens

Surely you like kittens. So don't hurt your audience.

Side Interest Spawns Brazilian Fashion Line

In a cosmically improbable confluence of multidisciplinary pursuits, my work on keyboard layouts, which as one of its fruits has produced the TNWMLC keyboard layout — the most difficult for English typing — has been incorporated into the eponymously named Brazilian fashion line by Julia Valle.

Spatter of Network Communities

Looking into network data sets for the linear layout project, I found pretty hairballs which make a juicy spatter pattern.