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Abstract: Methods for the discovery of hidden structures of high-dimensional binary data are one of the most important challenges facing the community of machine learning researchers. There are many approaches in the literature that try to solve this hitherto rather ill-defined task. In the present study, we propose a general generative model of binary data for Boolean Factor Analysis and introduce two new Expectation-Maximization Boolean Factor Analysis algorithms which maximize the likelihood of a Boolean Factor Analysis solution. To show the maturity of our solutions we propose an informational measure of Boolean Factor Analysis efficiency. Using the so-called bars problem benchmark, we compare the efficiencies of the proposed algorithms to that of Dendritic Inhibition Neural Network, Maximal Causes Analysis, and Boolean Matrix Factorization. Last mentioned methods were taken as related methods as they are supposed to be the most efficient in bars problem benchmark. Then we discuss the peculiarities of the two methods we proposed and the three related methods in performing Boolean Factor Analysis. [Copyright &y& Elsevier]

Abstract: Factor analysis is used in a number of applications. One example is image recognition, where it is often necessary to learn representations of the underlying components of images, such as objects, object-parts, or features. Another example is data compression when original data is transformed into a space of lower dimension. The goal of factor analysis is to find the underlying factors (factor loadings) and the contributions of these factors into the original observations (factor scores). Recently, we have proposed the method of Boolean factor analysis based on the ability of the Hopfield-like network to create attractors for factors . It shows that an obstacle to using this network for Boolean factor analysis is the appearance of two global spurious attractors that have no relation to internal structure of analyzed signals. To eliminate these attractors we had to modify the common architecture of Hopfield network, adding a special inhibitory neuron. The existence of two global attractors and their elimination by the special inhibitory neuron were illustrated by Frolov et al. only by some computer simulations. Since the appearance of those attractors is a novel important phenomenon, in this paper we investigate it both analytically and by additional computer simulations, to prove its validity, and explain its origin. [Copyright &y& Elsevier]