%0 Generic %1 linderman2017clustering %A Linderman, George C. %A Steinerberger, Stefan %D 2017 %K cluster clustering tsne visualization %T Clustering with t-SNE, provably %U http://arxiv.org/abs/1706.02582 %X t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of the algorithm are not well understood. The purpose of this paper is to prove that t-SNE is able to recover well-separated clusters; more precisely, we prove that t-SNE in the `early exaggeration' phase, an optimization technique proposed by van der Maaten & Hinton (2008) and van der Maaten (2014), can be rigorously analyzed. As a byproduct, the proof suggests novel ways for setting the exaggeration parameter $\alpha$ and step size $h$. Numerical examples illustrate the effectiveness of these rules: in particular, the quality of embedding of topological structures (e.g. the swiss roll) improves. We also discuss a connection to spectral clustering methods.

@misc{linderman2017clustering, abstract = {t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of the algorithm are not well understood. The purpose of this paper is to prove that t-SNE is able to recover well-separated clusters; more precisely, we prove that t-SNE in the `early exaggeration' phase, an optimization technique proposed by van der Maaten & Hinton (2008) and van der Maaten (2014), can be rigorously analyzed. As a byproduct, the proof suggests novel ways for setting the exaggeration parameter $\alpha$ and step size $h$. Numerical examples illustrate the effectiveness of these rules: in particular, the quality of embedding of topological structures (e.g. the swiss roll) improves. We also discuss a connection to spectral clustering methods.}, added-at = {2021-06-15T17:19:24.000+0200}, author = {Linderman, George C. and Steinerberger, Stefan}, biburl = {https://www.bibsonomy.org/bibtex/22e5548502142ab6b868197b210bcda81/bsc}, description = {[1706.02582] Clustering with t-SNE, provably}, interhash = {ea31eaa1cdd0f42d9e00198600e93349}, intrahash = {2e5548502142ab6b868197b210bcda81}, keywords = {cluster clustering tsne visualization}, note = {cite arxiv:1706.02582}, timestamp = {2021-06-15T17:19:24.000+0200}, title = {Clustering with t-SNE, provably}, url = {http://arxiv.org/abs/1706.02582}, year = 2017 }