The Boolean column and column-row matrix decompositions
Data Mining and Knowledge Discovery
Mining non-redundant high order correlations in binary data
Proceedings of the VLDB Endowment
A generative pattern model for mining binary datasets
Proceedings of the 2010 ACM Symposium on Applied Computing
Model order selection for boolean matrix factorization
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Comparing apples and oranges: measuring differences between data mining results
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
Maximum entropy models and subjective interestingness: an application to tiles in binary databases
Data Mining and Knowledge Discovery
A hierarchical model for ordinal matrix factorization
Statistics and Computing
Discrete Eckart-Young Theorem for Integer Matrices
SIAM Journal on Matrix Analysis and Applications
Fast and reliable anomaly detection in categorical data
Proceedings of the 21st ACM international conference on Information and knowledge management
Discovering descriptive tile trees: by mining optimal geometric subtiles
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Discovering relations using matrix factorization methods
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
An optimization framework for role mining
Journal of Computer Security
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Matrix decomposition methods represent a data matrix as a product of two factor matrices: one containing basis vectors that represent meaningful concepts in the data, and another describing how the observed data can be expressed as combinations of the basis vectors. Decomposition methods have been studied extensively, but many methods return real-valued matrices. Interpreting real-valued factor matrices is hard if the original data is Boolean. In this paper, we describe a matrix decomposition formulation for Boolean data, the Discrete Basis Problem. The problem seeks for a Boolean decomposition of a binary matrix, thus allowing the user to easily interpret the basis vectors. We also describe a variation of the problem, the Discrete Basis Partitioning Problem. We show that both problems are NP-hard. For the Discrete Basis Problem, we give a simple greedy algorithm for solving it; for the Discrete Basis Partitioning Problem we show how it can be solved using existing methods. We present experimental results for the greedy algorithm and compare it against other, well known methods. Our algorithm gives intuitive basis vectors, but its reconstruction error is usually larger than with the real-valued methods. We discuss about the reasons for this behavior.