On Finding Joint Subspace Boolean Matrix Factorizations

Finding latent factors of the data using matrix factorizations is a tried-and-tested approach in data mining. But finding shared factors over multiple matrices is more novel problem. Specifically, given two matrices, we want to find a set of factors shared by these two matrices and sets of factors specific for the matrices. Not only does such decomposition reveal what is common between the two matrices, it also eliminates the need of explaining that common part twice, thus concentrating the non-shared factors to uniquely specific parts of the data. This paper studies a problem called Joint Subspace Boolean Matrix Factorization asking exactly that: a set of shared factors and sets of specific factors. Furthermore, the matrix factorization is based on the Boolean arithmetic. This restricts the presented approach suitable to only binary matrices. The benefits, however, include much sparser factor matrices and greater interpretability of the results. The paper presents three algori...

• Type: Journal
• Year: 2012
• Where: SDM
• Authors: Pauli Miettinen
• Keywords: Data Mining, Factor Matrices, Matrix Factorization, Matrix Factorizations, SDM 2012