I was wondering can homology give us any tool for understanding the intrinsic dimension of high-dimensional (scattered) data? If yes, available software for that kind of analysis is also appreciated.
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Persistent homology? Use the persistent homology packages for R. – Chickenmancer Aug 18 '17 at 23:03
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@Chickenmancer I am new on that topic and got interested in discussing with a helpful mathematician guy and forgot to ask about intrinsic dimension. I have read some introductory material, and mostly they have tried to explain how to find holes and clusters, ... Any recommendation for dimensionality analysis is appreciated. – mko Aug 19 '17 at 15:24
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You may want to try this paper. https://arxiv.org/pdf/1501.00179.pdf – Chickenmancer Aug 19 '17 at 19:36