Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - contact me Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca on Twitter Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Lumondo Photography Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Pi Art Martin Krzywinski / Genome Sciences Center / mkweb.bcgsc.ca - Hilbertonians - Creatures on the Hilbert Curve
Trance opera—Spente le Stellebe dramaticmore quotes

visualization: needed


DNA on 10th — street art, wayfinding and font


data visualization + art

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The BC Cancer Agency’s Personalized Oncogenomics Program (POG) is a clinical research initiative applying genomic sequencing to the diagnosis and treatment of patients with incurable cancers.

Art of the Personalized Oncogenomics Program

Nature uses only the longest threads to weave her patterns, so that each small piece of her fabric reveals the organization of the entire tapestry.
— Richard Feynman

Art is Science in Love
— E.F. Weisslitz

what do the circles mean?

The legend can be printed at 4" × 6". The bitmap resolution is 600 dpi.


 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Quick legend. 5 Years of Personalized Oncogenomics Project at Canada's Michael Smith Genome Sciences Centre. The poster shows 545 cancer cases. (zoom)

a case for a visual case summary

For every case, we sequence the DNA to study the genome structure and the RNA to discover which genes are expressed and to what extent. The analysis is quite complex and brings together many steps: sequence alignment, structural variation detection, expression profiling, pathway analysis and so on. Every case is "summarized" by a lengthy report, such as the one below, which can run to over 40 pages.

Personalized Oncogenomics Program at Canada's Michael Smith Genome Sciences Center / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
A report for a typical POG case is about 40–50 pages.

One of the goals of the 5-year anniversary art was to represent the cases in a way to clearly show their number, classification as well as diversity. There are many metrics that can be used and I decided to choose the case's correlation to other cancer types.

correlation to TCGA cancer database

For every POG case, the gene expression of 1,744 key genes is compared to that of 1,000's of cases in the TCGA database of cancer samples. For a given cancer type in the TCGA database (e.g. BRCA), we visualize the correlations using box plots. The box plot is ideal for showing the distribution of values in a sample.

Personalized Oncogenomics Program at Canada's Michael Smith Genome Sciences Center / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Every case is compared to a database of 1,000's of cases. Shown here are box plots for the Spearman correlation coefficient between the gene expression of the POG case and cancers of a specific type (e.g. BRCA, LUAD, etc). (zoom)

The 10 largest Spearman correlation coefficients for the case shown above are

case    corr    type     tissue
-----------------------------------------------
POG661	0.436	BRCA	 Breast
POG661	0.371	PRAD	 Urologic
POG661	0.295	OV	 Gynecologic
POG661	0.257	UCEC	 Gynecologic
POG661	0.244	LUAD	 Thoracic
POG661	0.235	CESC_CAD Gynecologic
POG661	0.225	MB_Adult Central Nervous System
POG661	0.222	KICH	 Urologic
POG661	0.219	THCA	 Endocrine
POG661	0.208	UCS	 Gynecologic

In the figure below I show how the final encoding of the correlations is done. First, the top three correlations are taken—using more generates a busy look and diminishes visual impact. The correlations are encoded as concentric rings.

Because in most cases the differences in the top 3 correlations are relatively small, differences are emphasized by non-linearly scaling the encoding (the correlations are first scaled `r^3`).

Personalized Oncogenomics Program at Canada's Michael Smith Genome Sciences Center / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Case POG661. Median gene expression correlations with different cancer types from TCGA database. (A) Top 10 correlations shown as a bar plot. Color coding is by source tissue associated with the cancer type. (B) Top 10 correlations encoded as concentric rings. The width of the ring is proportional to the correlation. (C) Top 3 correlations. (D) Top 3 correlations scaled with a power to emphasize differences. (zoom)

The type face is Proxima Nova. The colors for each tissue source are

         Gastrointestinal  234,62,144
                   Breast  237,75,51
                 Thoracic  242,130,56
              Gynecologic  253,188,61
              Soft tissue  244,217,59
                     Skin  193,216,51
                 Urologic  114,197,49
              Hematologic  29,166,68
            Head and neck  43,168,224
                Endocrine  71,82,178
   Central nervous system  127,65,146
                    Other  150,150,150
VIEW ALL

news + thoughts

Markov Chains

Tue 30-07-2019

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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

Mon 22-07-2019

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
3.6 gigapixel map of the near side of the Moon, annotated with 6,733. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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

Sat 01-06-2019
Quantile regression robustly estimates the typical and extreme values of a response.

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?"

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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

Sat 30-03-2019
Robust regression generates more reliable estimates by detecting and downweighting outliers.

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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

Fri 22-03-2019
To find which experimental factors have an effect, simultaneously examine the difference between the high and low levels of each.

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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

Tue 12-03-2019

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
116 digits in 64 languages. (details)
Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.