SPADE updates

[maxentile]

So a couple things that came up in our meetings were:

• That time-course data would be very useful
• What new algorithms may have corrected the problems in SPADE?

I just found a paper with time-course mass cytometry data, a clearer analysis task, and a bit of discussion / an attempt to correct some problems in SPADE:

• A Continuous Molecular Roadmap to iPSC Reprogramming through Progression Analysis of Single-Cell Mass Cytometry (Zunder et al., 2015, Cell Stem Cell)
• Highlighted in: Charting a Map through the Cellular Reprogramming Landscape

Their analysis of SPADE / suggested alternative: "The MST used by SPADE is susceptible to overfitting the data and is not robust to local variation... to robustly identify high-dimensional relationships between cell types, the MST was replaced with a more highly connected graph structure... This new graph structure is then employed to produce a force-directed layout of a weighted graph containing multidimensional agglomeratively clustered points (FLOW-MAP) plot. The FLOW-MAP layout of cell clusters is more reproducible than a MST-derived layout, because the underlying graph structure is highly connected and therefore less susceptible to local edge and cluster variability"

Cartoon of FLOW-MAP vs. SPADE

Example output of FLOW-MAP:

Initial comments:

• Unlike SPADE, I think the end-goal of FLOW-MAP is just the 2D visualization (with some ill-posed robustness goals), not a 'lineage tree': I'm not sure I see why such a complicated procedure (involving clustering, graph construction, and then 2D layout) is necessary-- thoughts?
• Force-directed graph layouts can be misleading: the visualization certainly makes it look like there are dense clusters separated by large, sparse transition regions, but I don't know whether that's a qualitatively accurate picture of this data: a linear projection might be 'safer' in that it can't artificially exaggerate or distort this kind of structure.
• There is probably room for improvement in how we use the time component of the data-- here's what they did: "SPADE and the FLOW-MAP algorithm draw connections between populations that are similar in n-dimensional space, but cannot utilize the temporal information present in time course data sets. To exploit this temporal information, the FLOW-MAP algorithm was extended to include multiple graph drawing steps, where cell clusters are added to the graph sequentially for each time point"

Some questions:

• Are there any significant barriers to using a linear dimensionality reduction method like PCA?
• How can we better exploit the temporal component of the data?
• Do the 3 reprogramming methods considered have essentially the same end-points?

[maxentile]

So, I just did something simple that works pretty well and gave results that should probably be biologically interpretable-- also might be a good baseline for better approaches we might come up with:

• Strategy: think of this as a regression problem: given molecular measurements for a cell, try to predict which day it was measured. If you do well at this task, then you have probably learned a good 'progression' function. You also have a more straightforward objective to optimize than in the unsupervised case.
• Tactic: Partial Least Squares regression.
• Results: Just looking at the Nanog-GFP data first, PLS regression gets ~50% accuracy for a 1-component model, ~65% accuracy for a 2-component model, ~80% accuracy for a 5-component model, no significant improvement for 6- up to 40-component models. (Training and test accuracies are about equal for all models examined.)

Projection onto PLS components yields a very different qualitative picture of the data than the stringy connected clusters in "FLOW-MAP" :

We can also just look at the first component a bit more clearly by plotting density, rather than individual cells:

Next up:

• Replace the 2D scatter plot with 2D density contours?
• How to compare with SPADE / FLOW-MAP?
• How to compare the different reprogramming methods?
• Interpret coefficients of model?
• Nonlinear methods?

[maxentile]

As an alternative to plopping all timepoints onto the same axes, I also created animated GIFs where each frame is a timepoint: http://imgur.com/a/b4qjl (scatterplot colored by local point-density)

[maxentile]

Oh, just noticed another issue: the number of cells observed each day varies widely within each reprogramming trajectory (~5-10x):

We'll probably need to compensate for this somehow.

[maxentile]

Here's another way to plot how the distribution of cells along some progression axis changes over time: encode probability density as color intensity, and then have time on the x axis and progression on the y axis (each timestep is a column)

[maxentile]

Another way: represent each timestep by its vector of probability density, and then compute a distance matrix between all timesteps:

[maxentile]

We can also use distributions along a discrete progression function* instead of continuous distributions over a linear progression function:

(*here defined by doing k-means on the full-dataset, then for each day counting how many cells belong to each cluster)

[maxentile]

So here's the thing I said I'd make where we use 2D contours instead of a scatterplot