Information Criterion for Selection of Ubiquitous Factors

Factor analysis is a statistical procedure to describe observed data in terms of unobserved variables called factors. Naturally, it is necessary to determine the number of factors to represent the system. There are several existent criteria to deal with the tradeoff between reduction of approximation error and avoidance of overparameterization. However, given the factors there is a lack of an approach to verify if they are really equally inherent to the entire data. In this paper, the term ubiquitous factors is coined to describe such equally omnipresent factors. An information criterion is proposed to fill the existent blank. Additionally, we show the possibility to use the criterion to compare ubiquity of factors from two different techniques: principal component analysis and non-negative matrix factorization. Finally, the proposed criterion is extended to identify factors more suitable to describe only a partition of the data.