Higher dimensional embeddings about fit-sne

[linqiaozhi]

Hi Leland, thanks for trying out FIt-SNE! While our interpolation approach can be extended to embedding in higher dimensions (at the cost of using more interpolation points), dimensions >2 have not been implemented. In other words, the no_dims parameter can only take 1 or 2.

You are absolutely right that this is not clear in the documentation, and in the next update to the python package I will change it to give an error if any number other than 1 or 2 are passed in. Thanks for finding this...it can be confusing to people.

[dkobak]

I can do it for the python wrapper that I provided. Not sure about the other python interface.

[linqiaozhi]

Thanks @dkobak, that would be great.

@lmcinnes, just for some context, there is a Python wrapper (fast_tsne.py) in this repository that @dkobak provided which uses the same binary as the R and MATLAB wrappers. The PyPI implementation you are using does not yet implement the most recent commits to this repo (including the preliminary results of our multithreading), as I plan to update the PyPI package once we finish the multithreading in a week or so.

[lmcinnes]

Thanks for clarifying. Do you have any idea how the Fourier interpolation will scale with embedding dimension? The space tree approach in Barnes-Hut scales exponentially, but I thought your approach may perhaps be slightly more efficient?

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On Sun, Sep 9, 2018 at 1:18 PM George Linderman ***@***.***> wrote: Thanks @dkobak <https://github.com/dkobak>, that would be great. @lmcinnes <https://github.com/lmcinnes>, just for some context, there is a Python wrapper (fast_tsne.py) in this repository that @dkobak <https://github.com/dkobak> provided which uses the same binary as the R and MATLAB wrappers. The PyPI implementation you are using does not yet implement the most recent commits to this repo (including the preliminary results of our multithreading), as I plan to update the PyPI package once we finish the multithreading in a week or so. — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub <#34 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ALaKBWlSrq9nSxglTNOlhoKrpRu7FvG5ks5uZU2DgaJpZM4WgFZQ> .

[linqiaozhi]

Our approach is O(N), but the constant scales exponentially in embedding dimension. For 3-dimensional, there are Fast Multipole Methods that would work well here, but for even higher dimensions a different approach entirely would probably be required.

Most applications we are aware of for t-SNE are 2-dimensional, so we did not try 3-dimensional or higher...so I'm afraid I don't have any actual benchmarks I could share.

[dkobak]

@linqiaozhi I thought, maybe it's easier to add a check to the C++ code and let it exit with an error if no_dims>2 for the FFT method. Can Barnes-Hut handle any no_dims?

[lmcinnes]

Thanks George; I agree that for most t-SNE use cases 3 dimensions at most are likely sufficient, and it sounds like you could get that far at least. I appreciate the work to get it this fast in 2 dimensions!

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On Mon, Sep 10, 2018 at 4:12 AM Dmitry Kobak ***@***.***> wrote: @linqiaozhi <https://github.com/linqiaozhi> I thought, maybe it's easier to add a check to the C++ code and let it exit with an error if no_dims>2 for the FFT method. Can Barnes-Hut handle any no_dims? — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub <#34 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/ALaKBby-Yr4kojxeUZ1BCs2c1qO94993ks5uZh7vgaJpZM4WgFZQ> .

[linqiaozhi]

@dkobak I agree, adding a check to the C++ code would be best. And yes, BH can handle any no_dims.

@lmcinnes Thanks again for letting us know about this issue!