Boolean Factor Analysis by Attractor Neural Network

Abstract

A common problem encountered in disciplines such as statistics, data analysis, signal processing, textual data representation, and neural network research, is finding a suitable representation of the data in the lower dimension space. One of the principles used for this reason is a factor analysis. In this paper, we show that Hebbian learning and a Hopfield-like neural network could be used for a natural procedure for Boolean factor analysis. To ensure efficient Boolean factor analysis, we propose our original modification not only of Hopfield network architecture but also its dynamics as well. In this paper, we describe neural network implementation of the Boolean factor analysis method. We show the advantages of our Hopfield-like network modification step by step on artificially generated data. At the end, we show the efficiency of the method on artificial data containing a known list of factors. Our approach has the advantage of being able to analyze very large data sets while preserving the nature of the data.

Some Remarks on Binary Data Grouping

“…We investigated capabilities and advantages of neural network based Boolean factor analysis (NBFA) [3]for searching groups of similar features. This method discovers factors which indicated the most important groups of variables presented in the data.Its advantage is the ability to find overlapped sets of features.…”

“…Four factors B 1 -B 4 were identified by NBFA algorhitm described in [3]. The variables composed of these factors are shown in Table 3.…”

Clustering variables by classical approaches and neural network Boolean factor analysis

“…On the other hand, the classical linear methods cannot take non-linearity of Boolean summation into account, and therefore they are inadequate for this task. In the present study, we use the Neural network Boolean Factor Analysis (NBFA) (see [3]), which overcomes both these difficulties.…”

“…Four factors B 1 -B 4 were identified by NBFA algorhitm described in [3]. The variables composed of these factors are shown in Table III.…”

“…It is an important task in the case of high-dimensional data for reduction of dimensionality. In this paper, we focus on the task of clustering variables; we compare three approaches -standard hierarchical clustering, standard linear factor analysis of binary variables, and Boolean factor analysis by the recurrent neural network [3]. The three approaches imply different signal space models.…”