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Dimension reduction in representation of the data

25 February 2009
A.G.Ramm
ArXiv (abs)PDFHTML
Abstract

Suppose the data consist of a set SSS of points xjx_jxj​, 1≤j≤J1\leq j \leq J1≤j≤J, distributed in a bounded domain D⊂RND\subset R^ND⊂RN, where NNN is a large number. An algorithm is given for finding the sets LkL_kLk​ of dimension k≪Nk\ll Nk≪N, k=1,2,...Kk=1,2,...Kk=1,2,...K, in a neighborhood of which maximal amount of points xj∈Sx_j\in Sxj​∈S lie. The algorithm is different from PCA (principal component analysis)

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