BICA: a Boolean Independent Component Analysis Approach

We analyze the potentialities of an approach to represent general data records through Boolean vectors in the philosophy of ICA. We envisage these vectors at an intermediate step of a clustering procedure aimed at taking decisions from data. With a “divide et conquer” strategy we first look for a suitable representation of the data and then assign them to clusters. We assume a Boolean coding to be a proper representation of the input of the discrete function computing assignments. We demand the following of this coding: to preserve most information so as to prove appropriate independently of the particular clustering task; to be concise, in order to get understandable assignment rules; and to be sufficiently random, to prime statistical classification methods. In the paper we toss these properties in terms of entropic features and connectionist procedures, whose validation is checked on a series of benchmarks.