Learning Simple Relations: Theory and Applications

In addition to classic clustering algorithms, many different approaches to clustering are emerging for objects of special nature. In this article we deal with the grouping of rows and columns of a matrix with non-negative entries. Two rows (or columns) are considered similar if corresponding cross-distributions are close. This grouping is a dual clustering of two sets of elements, row and column indices. The introduced approach is based on the minimization of reduction of mutual information contained in a matrix that represents the relationship between two sets of elements. Our clustering approach contains many parallels with K-Means clustering due to certain common algebraic properties. The obtained results have many applications, including grouping of Web visit data.