SVD, discrepancy, and regular structure of contingency tables

Factors, obtained by correspondence analysis, are used 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. This 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 Butler for estimating the discrepancy of a contingency table by the largest non-trivial singular value of the normalized table (one-cluster, rectangular case), and partly the result of Bolla 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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