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I have a data set which, no matter how I tune t-SNE, won't end in clearly separate clusters or even patterns and structures. Ultimately, it results in arbitrary distributed data points all over the plot with some more data points of the one class there and some of another one somewhere else.

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Is it up to t-SNE, me and/or the data?

I'm using

Rtsne(df_tsne
                      , perplexity = 25
                      , max_iter = 1000000
                      , eta = 10
                      , check_duplicates = FALSE)
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No, T-SNE does not have to result in clear clusters. It is a low dimension visualization of high dimension data. So, if you data points are well clustered in low dimension, it means that they can be classified in lower dimension. The idea behind T-SNE is to calculate probability of data points. Points far from each other have low probability. I would suggest to have a look at this link once, https://towardsdatascience.com/t-distributed-stochastic-neighbor-embedding-t-sne-bb60ff109561

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