Toric ideals with linear components: an algebraic interpretation of clustering the cells of a contingency table

Abstract

In this paper we show that the agglomeration of rows or columns of a contingency table with a hierarchical clustering algorithm yields statistical models defined through toric ideals. In particular, starting from the classical independence model, the agglomeration process adds a linear part to the toric ideal generated by the $2\times 2$ minors.

17 pages, 1 figure

References in corpus (1)

• Markov bases for two-way subtable sum problems