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I have a classification problem, to have a first look at my data I do a PCA followed by TSNE and UMAP.

My clusters are nicely separated by TSNE and UMAP but not by PCA.

Does it have implication for the classification methods I'm going to use ?

Does it mean my groups are not linearly differentiable ?

Thank you

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This means that your data is non-linear.

PCA is a dimensionality reduction (or data visualization) tool that assumes a linearity in the data. On the other hand, t-SNE and UMAP are non-linear visualization tools. They allow to visualize data in a lower dimensional space withouth losing so much information and without assuming any linearity. Thus, this basically means that your data is non-linear. Don't be afraid, because most of the data is non-linear, just take it into account.

P.D: I always use UMAP over t-SNE. In my experience, it offers better results and it's less stochastic in some way. Furthermore, in UMAP you can prudently trust in clusters size and clusters distances, but in t-SNE you cannot trust in these measures.

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  • $\begingroup$ Thank you for your answer, If data are more nicely separated with UMAP than t-SNE, do you have an interpretation ? $\endgroup$
    – dantferno
    Dec 26 '20 at 15:14
  • $\begingroup$ @dantferno That sounds like a good new question to post on here! $\endgroup$
    – Dave
    Dec 26 '20 at 15:19
  • $\begingroup$ Hi @dantferno, from my point of view it's usual that UMAP works better than t-SNE just because of their mathematical roots. If you're interested in that you can go to the papers and check it, but to sum up: UMAP is a enhanced version of t-SNE. I always use UMAP over t-SNE, I didn't find yet a single case in which t-SNE works better than UMAP. It doesn't mean anything about your data or its structure, it's just because of the mathematical operations of the algorithms. $\endgroup$
    – Ale
    Dec 26 '20 at 18:09

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