Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Eigentaste: A Constant Time Collaborative Filtering Algorithm
Information Retrieval
Algorithm 844: Computing sparse reduced-rank approximations to sparse matrices
ACM Transactions on Mathematical Software (TOMS)
Subspace sampling and relative-error matrix approximation: column-row-based methods
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Subspace sampling and relative-error matrix approximation: column-based methods
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
The Boolean column and column-row matrix decompositions
Data Mining and Knowledge Discovery
Wisdom of the better few: cold start recommendation via representative based rating elicitation
Proceedings of the fifth ACM conference on Recommender systems
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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.