On Parsimonious Explanations for 2-D Tree- and Linearly-Ordered Data

This paper studies the “explanation problem” for tree- and linearly-ordered array data, a problem motivated by database applications and recently solved for the one-dimensional treeordered case. In this paper, one is given a matrix A = (aij) whose rows and columns have semantics: special subsets of the rows and special subsets of the columns are meaningful, others are not. A submatrix in A is said to be meaningful if and only if it is the cross product of a meaningful row subset and a meaningful column subset, in which case we call it an “allowed rectangle.” The goal is to “explain” A as a sparse sum of weighted allowed rectangles. Specifically, we wish to find as few weighted allowed rectangles as possible such that, for all i, j, aij equals the sum of the weights of all rectangles which include cell (i, j). In this paper we consider the natural cases in which the matrix dimensions are tree-ordered or linearly-ordered. In the tree-ordered case, we are given a rooted tre...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Howard J. Karloff, Flip Korn, Konstantin Makarychev, Yuval Rabani
• Keywords: Columns, CORR 2011, Education, Explanation Problem, Meaningful