SVD, discrepancy, and regular structure of contingency tables

Marianna Bolla

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arXiv · 1301.5259

SVD, discrepancy, and regular structure of contingency tables

Marianna Bolla

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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 Butler estimating the discrepancy of a contingency table by the second largest singular value of the normalized table (one-cluster, rectangular case), and partly a former result of the author 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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Marianna Bolla. 2013-01-22. SVD, discrepancy, and regular structure of contingency tables. https://arxiv.org/abs/1301.5259

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