Factorization Methods of Binary, Triadic, Real and Fuzzy Data

We compare two methods regarding the factorization problem of binary, triadic, real and fuzzy data, namely Hierarchical Classes Analysis and the formal concept analytical approach to Factor Analysis. Both methods search for the smallest set of hidden variables, called factors, to reduce the dimensionality of the attribute space which describes the objects without losing any information. First, we show how the notions of Hierarchical Classes Analysis translate to Formal Concept Analysis and prove that the two approaches yield the same decomposition even though the methods are different. Finally, we give the generalisation of Hierarchical Classes Analysis to the fuzzy setting. The main aim is to connect the two fields as they produce the same results and we show how the two domains can benefit from one another.