Optimal Factorization of Three-Way Binary Data

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 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. The scenario is similar to that of decomposition-based methods of analysis of three-way data but the difference consists in the composition operator and the constraint on A, B, and C to be binary. We present a theoretical analysis of the decompositions and show that optimal factors for such decompositions are provided by triadic concepts developed in formal concept analysis. Moreover, we present an illustrative example and propose a greedy approximation algorithm for computing the decompositions.

• Type: Conference
• Year: 2010
• Where: GRC
• Authors: Radim Belohlávek, Vilém Vychodil
• Keywords: 3-dimensional Binary Matrix, Applied Computing, Attribute-factor Matrix B, GRC 2010, Three-way Binary Data