Factorizing three-way binary data

Abstract

We present a problem of factor analysis of three-way binary data, i.e. data described by a 3-dimensional binary matrix I, describing a relationship between objects, attributes, and conditions. The problem consists in finding a small number of factors which explain the data. In terms of matrix decompositon, we look for a decomposition of I into three binary matrices, an object-factor matrix A, an attribute-factor matrix B, and a condition-factor matrix C, with the number of factors as small as possible. Compared to other decomposition-based methods, the difference consists in the composition operator and the constraint on A, B, and C to be binary. Due to the space limit, we present the problem statement, a non-technical description of our approach, and, as the main part, an illustrative example.