Question: Is it possible to interpret similarities between gene expression in clusters based on distance from one cluster center to another cluster center in the 2D t-SNE space? If not, is there another way to use the 10x single-cell data to say that two clusters are more similar to each other than they are to the rest of the clusters?
Answer: We recommend against using the distances between the clusters in t-SNE space to interpret how similar any two particular clusters are. The distances between points/cells are relative - because the algorithm is non-linear and adapts to underlying data, the distances on the x and y-axis have no direct interpretation. As described in this t-SNE primer, "The algorithm is non-linear and adapts to the underlying data, performing different transformations on different regions."
If you want to evaluate differences between any two clusters, you could run a differential expression analysis between the clusters to identify the differentially expressed genes. You can do this in Loupe Cell Browser. Here is some more information on how to compute differential expression between cell clusters.
Prior to t-SNE, the normalized gene-barcode matrix is reduced from having dimensions (number of genes x number of barcodes) to (top 10 principal components x number of barcodes) via principal components analysis. In turn, the top 10 PCs are used as inputs to both t-SNE and the various clustering approaches (graph-based or k-means). The t-SNE visualization and clustering/cluster assignment are independent steps/approaches. Thus you may see some cells assigned to a cluster that overlap or co-localize with cells in another cluster in the t-SNE space.
For more information on t-SNE, please refer to this publication:
Maaten, L.V.D. and Hinton, G., 2008. Visualizing data using t-SNE. Journal of Machine Learning Research, Vol 9(Nov), pp. 2579—2605.