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Just a few days ago the following paper was published on the ArXiv, it specifically tackles the problem of noise. I haven't had time to read it thoroughly, but
by ot 14y ago
Just a few days ago the following paper was published on the ArXiv, it specifically tackles the problem of noise. I haven't had time to read it thoroughly, but it also contains a nice introduction to persistent homology for statisticians, who are usually not familiar with the concepts of algebraic topology.
http://arxiv.org/pdf/1303.7117v1.pdf http://arxiv.org/pdf/1303.7117v1.pdf
- Sniffnoy 14y agoA note -- when linking to arXiv, please link to the abstract, not directly to the PDF.
- nkurz 14y agoA good idea. This helps so that when the paper is updated one finds the most current version. http://arxiv.org/abs/1303.7117 http://arxiv.org/abs/1303.7117
- carterschonwald 14y agoBeen working through the exposition in that paper the past few days, very very accessible writing. Very concrete intelligible examples. You can even ignore the few pieces or category theory and still take away a lot of understanding
- Topolomancer 14y agoVery good find, thanks for that. I recall that Peter Bubenik is working on a similar approach. His recent paper about "Persistence landscape" is also quite accessible, in my opinion: http://arxiv.org/abs/1207.6437 http://arxiv.org/abs/1207.6437
- tlarkworthy 14y agoYeah that looks like a step in the right direction, but the use of purely synthetic examples leaves me a little sceptical it will work in practice. I don't have time to try every papers algorithms out. If they don;t put in real examples I think perhaps they tried it on real data but it still did not work. Persistent Homology is in its infancy, its developed by pure mathematicians who are a bit innocent to the horrors of real data (or willfully ignore pragmatic trivialities in preference to interesting theoretical results).