Can persistent homology detect "flares"
how does it do so, if it can.
I know persistent homology can certainly find "loopy" structure, like noisy circles, but I'm not sure about "flares".
2026-03-25 06:10:23.1774419023
detecting flares with persistent homology
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Gunnar Carlsson likes to talk about using Borel-Moore homology to count the number of flares. See for example slides 108-110 at http://math.stanford.edu/~gunnar/math149intro.pdf.
Roughly speaking, in Borel-Moore homology you identify the "ends" of a space, and then consider the relative homology of the space modulo its "ends". So for a contractible space, the number of flares will be one more than the rank of the 1-dimensional Borel-Moore homology group. In a data analysis context, one could hope to identify the "ends" by using a measure of eccentricity.