Factorization with Hierarchical Classes Analysis and with Formal Concept Analysis

We present a comparison between Hierarchical Classes Analysis and the formal concept analytical approach to Factor Analysis regarding the factorization problem of binary matrices. Both methods decompose a binary matrix into the Boolean matrix product of two binary matrices such that the number of factors is as small as possible. We show that the two approaches yield the same decomposition even though the methods are different. The main aim of this paper is to connect the two fields as they produce the same results and we show how the two domains can benefit from one another.