Аннотация:A matrix decomposition expresses a matrix as a product of at least two factor matrices. Equivalently, it expresses each column of the input matrix as a linear combination of the columns in the first factor matrix. The interpretability of the decompositions is a key issue in many data-analysis tasks. We propose two new matrix-decomposition problems: the nonnegative CX and nonnegative CUR problems, that give naturally interpretable factors. They extend the recently-proposed column and column-row based decompositions, and are aimed to be used with nonnegative matrices. Our decompositions represent the input matrix as a nonnegative linear combination of a subset of its columns (or columns and rows).
