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3d: more


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


data visualization + art

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
To view the art you'll need a pair of red-blue 3D glasses.
The data will stand out—and you will too.

BD Genomics stereoscopic art exhibit — AGBT 2017

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

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Our art exhibit at AGBT 2017 asked new school questions in old school ways.

The final art pieces are the outcome of a long process of exploration, experimentation and more than a few dead-ends. Here I'll take you through the process of parsing, exploring and drawing the data and finding a story.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Early sketches, looking for a data encoding.

The first step was to identify how to present the theme of "differences" in the exhibit. We wanted to draw attention to the fact that the extent to which we can answer questions about biological states depends on how accurate and precise the measurements are. Initially, I thought that this might be a useful theme—highlighting both biological and technical variation.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Early sketches, shaping the data.

In parallel, I thought about different functional sources of variation and the kinds of questions that the data might be used to answer. I narrowed them down to differences that cause disease, differences that cause disease progression and differences that allow for a variety of normal function.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Early sketch, attempting an organic, cellular look.

We also considered the idea of showing differences due to purely experimental error, which are fluctuations due to the technology not necessarily the biology.

single-cell gene expression

For each of the difference scenarios, the input data set were single-cell gene expression counts.

cell1 sample cell_type gene1 count
cell1 sample cell_type gene2 count
...
cell2 sample cell_type gene1 count
cell2 sample cell_type gene2 count
...

Each cell was identified by its sample (e.g. blood normal vs tumor) and type (e.g. B cell, T cell, etc). Typically, we had counts for about 500 genes of 100's or 1000's of cells of a given type and sample.

dimensional reduction

The transcriptome of each cell is a point in high-dimensional space—one dimension for each gene for which we have a count. To find a projection of the data onto the page, we dimensionally reduced the data using tSNE (t-distributed stochastic neighbour embedding) into either 2 or 4 dimensions.

# 2 dimensions (x,y)
cell1 sample cell_type tsne_x tsne_y
cell2 sample cell_type tsne_x tsne_y
...

# 4 dimensions (x,y,u,v)
cell1 sample cell_type tsne_x tsne_y tsne_u tsne_v
cell2 sample cell_type tsne_x tsne_y tsne_u tsne_v
...

When the cells are drawn as points based on their tSNE coordinates, typically they will cluster both by type and disease status. They cluster by type because the gene expression profile for each cell type is different—this is what causes cells to have different function.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Transcripts of the cells in the healthy vs disease data set shown by their 2-dimensional tSNE coordinates. Each point represesents a cell. On the left cells are colored by type and on the right by normal (black) or disease (orange) state. The black dashed lines highlightes the classical monocyte cluster. (zoom)

What we're looking for here is cells that cluster by disease state within a given cell type cluster, like the classical monocytes highlighted in the figure above. What this happens, we can say that there's something fundamentally different for this cell type between the normal and diseased states. For cell types that don't have a differential expression in disease, we see more of a random mixing of the normal and disease cell populations within their clusters.

exploring encodings

I like to start by exploring ways to map the data onto the page. Typically, at this stage I try a lot of different approaches and many take the shortest route to the trash.

The focus of our story is "differences". So, I'll be looking for visuals that capture the Gestalt of a difference. Because we're aiming for an equal mix of art and data visualization, it's not critical that we can judge the differences quantitatively—ability to make qualitative assessments will suffice—but it is important that something obviously appears to be different, both within one panel and across panels.

In the search for an encoding, two basic questions have to be addressed: how cells are to be (a) placed and (b) represented on the page. For example, placement could be systematic, such as on a grid, with order based on some property such as total gene count. With this approach, we can achieve a tiling that covers the full canavs.

Or, placement could be based on properties such as tSNE coordinates. In this case, we settle in not populating the canvas evenly and hope that the cells fall into groups in a meaningful way.

Below is one attempt at a tiling encoding. The cells are represented by a grid of squares and each square shows a comparison of gene counts in disease vs normal for four genes. This layout can be adapted into triangles (3 genes) or hexagons (6 genes).

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Encoding the counts of 4 genes.
BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Comparison of 400 normal vs diseased CD4 cells. (zoom)

The genes can be chosen based on ones that are known to be of clinical significance or, as below, identified from the data set as ones that have the largest change in expression between normal and disease. Cells can be ordered based on similarity in counts between normal and disease.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Comparison of 400 normal vs diseased CD4 cells for (A) genes that had the largest increase in count in disease and (b) genes that had the largest decrease count in disease. The position of the triangle vertex along each square encodes log2 of count ratio. Cells are in decreasing ordered of similarity in counts between normal and disease. (zoom)

I then tried using the 4-dimensional `(x,y,u,v)` tSNE coordinates to represent each cell, still sticking to a tiling of cells. Cells are drawn in a row-dominant order and those with more similar tSNE coordinates are drawn closer together. For example, for the circular encoding, each concentric circle radius is `(x,x+y,x+y+u,x+y+u+v)`.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Cells are represented by a set of concentric circles sized by the cell's 4-dimensional tSNE coordinates. For each coordinate, I tried (A) randomized color palette and (B) Fixed color palette. Optionally, the cell can be sized based on its total gene count. For a given cell, the next cell in the grid is one that has the most similar tSNE coordinates. (zoom)
BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Cells are represented by a set of nested triangles sized by the cell's 4-dimensional tSNE coordinates. For each coordinate, I tried (A) randomized color palette and (B) Fixed color palette. Optionally, (C) the cell can be sized based on its total gene count. For a given cell, the next cell in the grid is one that has the most similar tSNE coordinates. (zoom)

Playing with colors and shapes makes for interesting tilings.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Cells are represented by a set of nested triangles sized by the cell's 4-dimensional tSNE coordinates. For each coordinate, I tried (A) randomized color palette and (B) Fixed color palette. Optionally, (C) the cell can be sized based on its total gene count. For a given cell, the next cell in the grid is one that has the most similar tSNE coordinates. (zoom)

As much as all these attempts have pretty shapes and colors, it's hard to point your finger at any part of these encodings and say, "Here's a difference worth investigating."

As well, by placing cells on a grid makes for a rigid represntation. We agreed that we needed something that looked a little more organic. Could the way the cells were drawn look like actual cells?

clusters, networks and tesselation

We started looking at drawing the cells based on their 2-dimensional tSNE coordinates. In this representation, cells that are closer together on the plane have more similar transcription profiles.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Transcripts of the cells in the healthy vs tumor and in tumor vs metastasis data set shown by their 2-dimensional tSNE coordinates. Each point represesents a cell, color either by cell type (top) or normal, tumor or metastasis state (bottom). (zoom)

With this approach, it was really easy to draw attention to differences—either by cell type (which we wanted to do in the normal function case) or disease status. We also felt that this would be a familiar approach and one that showed populations of cells at the resolution of single cells.

One of the data sets that we identified early was the internal validation set, which captured the variability between operators and technical replication. Below are the results of six experiments, each done by a different operator on two different days. Here, we don't expect (and we don't see) any clustering based on days or operators. In the end, we chose not make use of this data set in the final exhibit and focus instead on clinically relevant differences.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Transcripts of normal cells in a series of internal validation trials performed by different operators on different days. There's no difference in the distribution of cells relative to either operator or day. The clusters that you see are the different cell types. (zoom)

We then explored ways in which the tSNE coordinates could be used to derive different representations, such as a network or tesselation.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Transcripts of the cells in the healthy vs tumor shown by their 2-dimensional tSNE coordinates (left). Nearest normal and tumor cells of a given cell type are connected into a minimum spanning tree graph (right). (zoom)
BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Transcripts of the cells in the healthy vs tumor. Cells are originally placed by tehir 2-dimensional tSNE coordinates and then a Voronoi tesselation is applied to generate polygons that bound the cells (one polygon per cell). The cell positions are then shifted to be closer to the center of each polygon and cell size adjusted to fit within the polygon. (zoom)

By hiding the cells and filling the polygons based on cell type and mixing the neighbouring polygon colors, we get a

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
The Voronoi tesselation 'gems' shown in the figure above with polygon colors based on cell types. Adjacent polygon colors are blended together to provide smoother transition across clusters. The two figures represent two different experiments from the normal vs disease data set. (zoom)

A more organic feel can be achieved by perturbing the edges of both the cells and polygons. We were happy enough with this representation to use it on the introductory panel in the exhibit.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
An organic perturbation to the Voronoi tesselation of the normal vs disease data set. Diseased cells have their polygons and cell shapes filled. (zoom)
BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
An organic perturbation to the Voronoi tesselation of the normal vs disease data set. Diseased cells have their polygons and cell shapes filled. (zoom)

The distance between a given tumor cell and its nearest normal cell of the same type can be emphasized by encoding the distance with color, such as below.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Cells placed based on Voronoi tesselation with polygons hidden. Cell color is either grey (normal) or yellow-red (tumor), where it maps the distance to the nearest normal cell of the same type. (zoom)

At this point we decided to explore mapping this difference by the 3rd dimension, literally.

BD Genomics 3D art exhibit - AGBT 2017 / Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
Cells placed based on Voronoi tesselation with polygons hidden. Image is stereoscopic (requires red-blue 3d glasses) and depth towards the viewer encodes the distance between a tumor cell and its nearest normal neighbour of the same type. (zoom)

The stereoscopic image shown above is a quick prototype generated in Illustrator. The final images were rendered in a full 3D environment using Cinema4D.

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news + thoughts

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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

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.

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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

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).

Martin Krzywinski @MKrzywinski mkweb.bcgsc.ca
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.