Provable dimension detection using principal component analysis

Abstract

We present simple algorithms for detecting the dimension k of a smooth manifold M ⊂ Rd from a set P of point samples, provided that P satisfies a standard sampling condition as in previous results. The best running time so far is O(d2O(k7 log k)) worst-case by Giesen and Wagner after the adaptive neighborhood graph is constructed in O(d|P|2) worst-case time… (More)
DOI: 10.1145/1064092.1064125

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