Ayasdi: Why TDA and Clustering Are Not The Same Thing

Cluster analysis is a highly developed field within statistics. It takes as input a set X equipped with a distance function, and potentially some other information, and from that produces a partition of the set, i.e. a decomposition of the set into a collection of groups so that (a) the sets in the collection do not overlap and (b) every point in X is contained in some set in the collection. It is extremely useful because it provides a taxonomy of the points in a data set, since it frequently

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