Topological Data Analysis
2012 · WORLD SCIENTIFIC eBooks · 16 citations
In recent years, a new approach to data analysis has been developed, based on topological methods. The basic idea is to understand structures in a (large) set of data in a (high-dimensional) space, by associating to it a simplicial topological space and studying its topology. The starting point is a set of data with a proximity parameter (such as a distance function). The simplicial complex (Vietoris-Rips complex) is constructed by taking the set of data as the vertex set and assigning a k-dimensional face (k-simplex) to a k + 1-tuple of data {x0,..., xk} iff the distances satisfy d(xi, xj) ≤…
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