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I have some vectors $x_0, x_1, x_2, ... x_n$ for a fixed $n$ (the vector dimension is about 2-20). I know there are $m$ clusters for these $n$ vectors (where $1\leq m \leq n$).

For every input vector $x_i$ I should get a probability for each cluster (e.g. generated by $\mathrm{softmax}$). This algorithm should contain as few parameters as possible.

I tried to implement a differentiable k-means, but the result was not that great, especially it seems to be hard to select good initial cluster centers. Maybe there already exists such an algorithm or it is easy to port one?

Thank you

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Yes.

Please find it in the paper "Deep adaptive image clustering" at http://openaccess.thecvf.com/content_ICCV_2017/papers/Chang_Deep_Adaptive_Image_ICCV_2017_paper.pdf.

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  • $\begingroup$ It seems that many parts of the algorithm are differentiable, but not the complete (it has some discrete steps; e.g. see image on page 3): this would imply for me that the input of the neural network is a set of objects and the output the clustering. Nevertheless, the paper seems to be very interesting, I will go deeper into it. Thanks for the link:)! $\endgroup$ – Kevin Meier Oct 19 '18 at 8:51
  • $\begingroup$ And "Deep Continuous Clustering" at arxiv.org/abs/1803.01449. $\endgroup$ – Jianlong CHANG Oct 30 '18 at 8:03

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