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A Proposition for Fixing the Dimensionality of a Laplacian Low-rank Approximation of any Binary Data-matrix

Authors:
Alain Lelu
Martine Cadot

Keywords: dimensionality reduction; intrinsic dimension; randomization test; low-rank approximation; graph Laplacian; bipartite graph; Correspondence Analysis; Cattell’s scree; binary matrix

Abstract:
Laplacian low-rank approximations are much appreciated in the context of graph spectral methods and Correspondence Analysis. We address here the problem of determining the dimensionality K* of the relevant eigenspace of a general binary datatable by a statistically well-founded method. We propose 1) a general framework for graph adjacency matrices and any rectangular binary matrix, 2) a randomization test for fixing K*. We illustrate with both artificial and real data.

Pages: 70 to 73

Copyright: Copyright (c) IARIA, 2013

Publication date: February 24, 2013

Published in: conference

ISSN: 2308-4375

ISBN: 978-1-61208-254-7

Location: Nice, France

Dates: from February 24, 2013 to March 1, 2013