A new approach to the maximum-flow problem
Journal of the ACM (JACM)
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ACM Transactions on Information Systems (TOIS)
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Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
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Journal of the ACM (JACM)
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A randomized polynomial-time simplex algorithm for linear programming
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Nonorthogonal decomposition of binary matrices for bounded-error data compression and analysis
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Automatic SIMD vectorization of fast fourier transforms for the larrabee and AVX instruction sets
Proceedings of the international conference on Supercomputing
A hierarchical model for ordinal matrix factorization
Statistics and Computing
Domination analysis of algorithms for bipartite boolean quadratic programs
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
An optimization framework for role mining
Journal of Computer Security
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Mining discrete patterns in binary data is important for subsampling, compression, and clustering. We consider rank-one binary matrix approximations that identify the dominant patterns of the data, while preserving its discrete property. A best approximation on such data has a minimum set of inconsistent entries, i.e., mismatches between the given binary data and the approximate matrix. Due to the hardness of the problem, previous accounts of such problems employ heuristics and the resulting approximation may be far away from the optimal one. In this paper, we show that the rank-one binary matrix approximation can be reformulated as a 0-1 integer linear program (ILP). However, the ILP formulation is computationally expensive even for small-size matrices. We propose a linear program (LP) relaxation, which is shown to achieve a guaranteed approximation error bound. We further extend the proposed formulations using the regularization technique, which is commonly employed to address overfitting. The LP formulation is restricted to medium-size matrices, due to the large number of variables involved for large matrices. Interestingly, we show that the proposed approximate formulation can be transformed into an instance of the minimum s-t cut problem, which can be solved efficiently by finding maximum flows. Our empirical study shows the efficiency of the proposed algorithm based on the maximum flow. Results also confirm the established theoretical bounds.