Art is science in love.
— E.F. Weisslitz
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.
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.
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.
We also considered the idea of showing differences due to purely experimental error, which are fluctuations due to the technology not necessarily the biology.
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.
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.
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.
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).
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.
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)`.
Playing with colors and shapes makes for interesting tilings.
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?
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.
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.
We then explored ways in which the tSNE coordinates could be used to derive different representations, such as a network or tesselation.
By hiding the cells and filling the polygons based on cell type and mixing the neighbouring polygon colors, we get a
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.
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.
At this point we decided to explore mapping this difference by the 3rd dimension, literally.
The stereoscopic image shown above is a quick prototype generated in Illustrator. The final images were rendered in a full 3D environment using Cinema4D.
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.
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.
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).
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 (PCA) simplifies the complexity in high-dimensional data by reducing its number of dimensions.
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.
Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. Nature Methods 14:545–546.
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.
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.
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