SVD, discrepancy, and regular structure of contingency tables
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).
Cite
@article{arxiv.1301.5259,
title = {SVD, discrepancy, and regular structure of contingency tables},
author = {Marianna Bolla},
journal= {arXiv preprint arXiv:1301.5259},
year = {2013}
}