Probabilistic latent semantic indexing
Proceedings of the 22nd annual international ACM SIGIR conference on Research and development in information retrieval
The Journal of Machine Learning Research
Algorithm 844: Computing sparse reduced-rank approximations to sparse matrices
ACM Transactions on Mathematical Software (TOMS)
Approximation algorithms for the Label-CoverMAX and Red-Blue Set Cover problems
Journal of Discrete Algorithms
Less is More: Sparse Graph Mining with Compact Matrix Decomposition
Statistical Analysis and Data Mining
Interpretable nonnegative matrix decompositions
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
On the Positive--Negative Partial Set Cover problem
Information Processing Letters
Binary Matrix Factorization with Applications
ICDM '07 Proceedings of the 2007 Seventh IEEE International Conference on Data Mining
IEEE Transactions on Knowledge and Data Engineering
Optimal Boolean Matrix Decomposition: Application to Role Engineering
ICDE '08 Proceedings of the 2008 IEEE 24th International Conference on Data Engineering
The Boolean Column and Column-Row Matrix Decompositions
ECML PKDD '08 Proceedings of the 2008 European Conference on Machine Learning and Knowledge Discovery in Databases - Part I
Multi-label classification using boolean matrix decomposition
Proceedings of the 27th Annual ACM Symposium on Applied Computing
An optimization framework for role mining
Journal of Computer Security
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Matrix decompositions are used for many data mining purposes. One of these purposes is to find a concise but interpretable representation of a given data matrix. Different decomposition formulations have been proposed for this task, many of which assume a certain property of the input data (e.g., nonnegativity) and aim at preserving that property in the decomposition. In this paper we propose new decomposition formulations for binary matrices, namely the Boolean CX and CUR decompositions. They are natural combinations of two previously presented decomposition formulations. We consider also two subproblems of these decompositions and present a rigorous theoretical study of the subproblems. We give algorithms for the decompositions and for the subproblems, and study their performance via extensive experimental evaluation. We show that even simple algorithms can give accurate and intuitive decompositions of real data, thus demonstrating the power and usefulness of the proposed decompositions.