UMAP and "equal" objects

Question

[German.M.Demidov]

I want to plot a very large dataset. UMAP works quite good with this type of data (not single-cell expression but similar). However I have couple of clusters of absolutely equal objects, distance between all these objects is 0 (within each cluster) and UMAP somehow draws these huge clusters as "outlier" dots - even though these objects are not so dissimilar to the other objects.

I can replace these objects with only 1 representative, but are there alternative way to vizualize clusters using UMAP so it is not plotted as a dot very far from other dots?

Answer 1

[Jean-Karim Heriche]

You probably need to play with the parameters. Check these papers to get an idea of where you could focus your efforts:

• A Unifying Perspective on Neighbor Embeddings along the Attraction-Repulsion Spectrum
• Initialization is critical for preserving global data structure in both t-SNE and UMAP

Answer 2

[Mensur Dlakic]

It depends on your definition of a large dataset. I have used openTSNE with 20-30 CPUs on a 100000 x 136 dataset, and it does the embedding in ~25 minutes. Even though this implementation of t-SNE is not as fast as UMAP, it is fast enough that it should not be a problem to use t-SNE even on datasets with million data points, as long as their second dimension is not in thousands.

I am curious as to how do you define the distance between your vectors to be 0. UMAP is not supposed to separate at all data points that are (near-)identical, no matter what parameters are used.

[German.M.Demidov]

Thanks! The problem of nearly identical samples is not that they are not separated, but they are placed far far far away from the general distribution - even though they are not very far conceptually! I am fine with them being place as 1 dot, but within the general distribution of data, they are not actual outliers, but since UMAP looks for local similarities - it prefers to "push" these huge clusters of identical objects as far as possible...

[Jean-Karim Heriche]

Just for information, openTSNE is from (some of) the same people as the papers I linked to above.

Answer 3

[James]

You might try to use the linear-correlation distance instead of the Euclidean distance: the correlation distance normalizes all vectors to unit vectors.