PCA provides principal directions, what does tSNE provide?

Question

One of my main frustrations with the current state of single cell transcriptome analysis is representations of cells within $tSNE$ plots.

These $tSNE$ plots provide amazing separation of the data and are championed as better than $PCA$ for revolutionary displays. But $PCA$ provides an easy understanding of what is separating the data.

So, by using $PCA$ for my dimensional reduction technique I also obtain the principal directions of the data. From a $n x m$ matrix where $n = cells$ and $m=genes$, the principal components show the $cells$ separation. This analysis also provides the principal directions for the understanding of the structure of the $cells$ separation due to the $genes$. This is nice because I can search and localize genes providing this separation in different quadrants of the graph.

What i'm struggling to understand with the $tSNE$ is how can I achieve something synonymous to the principal directions in these plots. I want to know what genes are guiding each cluster of cells in these $tSNE$ plots with the ultimate goal of providing context to these beautiful $tSNE$ graphs.

Answer 1

I can't comment since I don't have enough reputation, but I will try to give a small answer.

Essentially, the reduced dimensions of t-SNE are not intended to carry meaning (although they might be correlated to something meaningful by chance). t-SNE is mostly used as a visualization technique, and its use as a dimensionality reduction technique is muddled.

In addition, since t-SNE is non-convex and depends on initialization, your final dimensions might have different "meaning" every time you re-run it. It is entirely dependent on the run and your full dataset (part of the reason why sklearn's tSNE does not provide a transform function, only fit_transform).

The original t-SNE paper discusses this and how t-SNE dimensionality reduction is not clear for reduced components of dimensionality d>3.

In addition, distances in the reduced space do not mean much as t-SNE is trying to minimize KL-divergence.

See this question and this one too