document: Interpretable nonnegative matrix decompositions 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 ) . We present two algorithms to solve these problems and provide an extensive experimental evaluation where we assess the quality of our algorithms ' results as well as the intuitiveness of nonnegative CX and CUR decompositions . We show that our algorithms return intuitive answers with smaller reconstruction errors than the previously-proposed methods for column and column-row decompositions .
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