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Clarify homology description

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Rick Winfrey 2017-01-06 14:28:16 -08:00
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@ -40,7 +40,7 @@ Homologies:
Given a data set, a homology is a cycle or loop of points in that data set that are significant given a significance function (e.g. distance function).
These data points, or topological invariants, we can use filtration to further refine the cycles or loops to find the most significant cycles. These are the strongest, or longest living, cycles.
With these data points, or topological invariants, we can use filtration to further refine the cycles or loops to find the most significant cycles. These are the strongest, or longest living, cycles. This helps us see what points in the n-dimensional data set are most important in relation to one another (rather than in relation to an assumption that is reified through a probabilistic test or approach).
How does one measure how "good" a persistent homology is? One can use a stability distance function to measure the stability of the distance function used to identify cycles.