I have 20 fasta files and I want to perform t-SNE analysis on these files. Is it possible?
This is the workflow that I want to follow in R:
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You may already know this, but just for the random reader: t-SNE does not work with FASTA files, but rather with number matrices. If you create a symmetric distance matrix for all your sequences, those data points can be embedded into a low-dimensional space. This is to say that your general approach will work as far as producing some kind of a result, but I don't have a good feel how biologically relevant that embedding would be on a large scale.
On a small scale, it appears to work reasonably well. Below is an embedding of 3 groups of proteins (60-70 members each) that are related within a group, but not between each other.

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Can you explain the experiment in more detail? It's unclear what you want to do.
I want to perform t-SNE analysis on multiple fasta files
"Doing a t-SNE" is not a biological question. A relevant type of question would be "I want to measure parameter X on this data" or "test hypothesis A". For example if you want to know the evolutionary relatedness of the genes you sequenced, you would usually build a phylogenetic tree from an alignment, while a t-SNE would likely be irrelevant.