Trance opera—Spente le Stellebe dramaticmore quotes

# filling space: fun

EMBO Practical Course: Bioinformatics and Genome Analysis, 5–17 June 2017.

# visualization + design

Like paths? Got your lines twisted in a bunch?
Take a look at my 2014 Pi Day art that folds Pi.

# Hilbert Curve Art, Hilbertonians and Monkeys

I collaborated with Scientific American to create a data graphic for the September 2014 issue. The graphic compared the genomes of the Denisovan, bonobo, chimp and gorilla, showing how our own genomes are almost identical to the Denisovan and closer to that of the bonobo and chimp than the gorilla.

Here you'll find Hilbert curve art, a introduction to Hilbertonians, the creatures that live on the curve, an explanation of the Scientific American graphic and downloadable SVG/EPS Hilbert curve files.

Vector art files of Hilbert curves of order 1 to 10. Each curve is a path in its own layer.

The figure below shows what the files contain, except the figure has different stroke and transparency settings for each order. In the downloadable files, each order's thickness and color is the same.

### circular

The mapping of the Hilbert curve onto a circle was done using this transformation

$[x',y'] = [x\sqrt{1-y^2/2},y\sqrt{1-x^2/2}]$

which maps the region $-1 <= x <1, -1 <= y < 1$ onto the circle at $(x,y,r)=(0,0,1)$. I've used this before to transform folded paths of the digits of $\pi$. This transformation is described in detail here.

Download Hilbert curve mapped onto a circle in PDF EPS AI format.

Download order 1–10 Hilbert curve in a circle. (zoom, PDF, EPS, AI)
VIEW ALL

# Machine learning: a primer

Tue 05-12-2017
Machine learning extracts patterns from data without explicit instructions.

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.",

# Snowflake simulation

Tue 14-11-2017
Symmetric, beautiful and unique.

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)

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

# Genes that make us sick

Thu 02-11-2017
Where disease hides in the genome.

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

Mon 16-10-2017
Many heads are better than one.

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.

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

# Classification and regression trees

Mon 16-10-2017
Decision trees are a powerful but simple prediction method.

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.

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.

# Personal Oncogenomics Program 5 Year Anniversary Art

Wed 26-07-2017

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.