Dimensionality Reduction in Boolean Data: Comparison of Four BMF Methods

Autoři: Hana Řezanková
Rok vydání: 2015
Typ publikace: Konferenční příspěvek (mezinárodní konf.)
Periodikum: Clustering High-Dimensional Data
Projekty: Rozklady matic s binárními a ordinálními daty: teorie, algoritmy, složitost
Bibliografická citace: BARTL, E., BĚLOHLÁVEK, R., OSICKA, P., ŘEZANKOVÁ, Hana. Dimensionality Reduction in Boolean Data: Comparison of Four BMF Methods. In: MASULLI, F., PETROSINO, A., ROVETTA, S., eds. Clustering High-Dimensional Data. Berlin: Springer, 2015, S. 118-133. Lecture Notes in Computer Science, 7627. ISBN 978-3-662-48576-7. ISSN 0302-9743
Dostupné z: doi:10.1007/978-3-662-48577-4_8
DOI: 10.1007/978-3-662-48577-4_8
ID: 454876

Abstrakt

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.