Abstract
We compare four methods for Boolean matrix factorization (BMF). The oldest of these methods is the 8M method implemented in the BMDP statistical software package developed in the 1960s. The three other methods were developed recently. All the methods compute from an input object-attribute matrix I two matrices, namely an object-factor matrix A and a factor-attribute matrix B in such a way that the Boolean matrix product of A and B is approximately equal to I. Such decompositions are utilized directly in Boolean factor analysis or indirectly as a dimensionality reduction method for Boolean data in machine learning. While some comparison of the BMF methods with matrix decomposition methods designed for real valued data exists in the literature, a mutual comparison of the various BMF methods is a severely neglected topic. In this paper, we compare the four methods on real datasets. In particular, we observe the reconstruction ability of the first few computed factors as well as the number of computed factors necessary to fully reconstruct the input matrix, i.e. the approximation to the Boolean rank of I computed by the methods. In addition, we present some general remarks on all the methods being compared.
E. Bartl and H. Rezankova acknowledge support by Grant No. 202/10/0262 of the Czech Science Foundation. R. Belohlavek and P. Osicka acknowledge support by the ESF project No. CZ.1.07/2.3.00/20.0059, the project is co-financed by the European Social Fund and the state budget of the Czech Republic.
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Notes
- 1.
We thank P. Miettinen for providing us with the datasets DBLP, DNA, and Paleo.
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Bartl, E., Belohlavek, R., Osicka, P., Řezanková, H. (2015). Dimensionality Reduction in Boolean Data: Comparison of Four BMF Methods. In: Masulli, F., Petrosino, A., Rovetta, S. (eds) Clustering High--Dimensional Data. CHDD 2012. Lecture Notes in Computer Science(), vol 7627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48577-4_8
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