SVD, discrepancy, and regular structure of contingency tables

Bolla, Marianna (2014) SVD, discrepancy, and regular structure of contingency tables. DISCRETE APPLIED MATHEMATICS, 176. pp. 3-11. ISSN 0166-218X

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Abstract

We will use the factors obtained by correspondence analysis to find biclustering of a contingency table such that the row–column cluster pairs are regular, i.e., they have small discrepancy. In our main theorem, the constant of the so-called volume-regularity is related to the SVD of the normalized contingency table. Our result is applicable to two-way cuts when both the rows and columns are divided into the same number of clusters, thus extending partly the result of [7] estimating the discrepancy of a contingency table by the second largest singular value of the normalized table (one-cluster, rectangular case), and partly the result of [5] for estimating the constant of volume-regularity by the structural eigenvalues and the distances of the corresponding eigen-subspaces of the normalized modularity matrix of an edge-weighted graph (several clusters, symmetric case).

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