Dušan Húsek

Boolean Factor Analysis by Attractor Neural Network

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

Informational capacity and recall quality in sparsely encoded Hopfield-like neural network: analytical approaches and computer simulation

A sparsely encoded Hopfield-like attractor neural network is investigated analytically and by computer simulation. Informational capacity and recall quality are evaluated. Three analytical approaches are used: replica method (RM); method of statistical neurodynamics (SN); and single-step approximation (SS). Computer simulation confirmed the good accuracy of RM and SN for all levels of network activity. SS is accurate only for large sparseness. It is shown that informational capacity monotonically increases when sparseness increases, while recall quality changes nonmonotonically: initially it decreases and then increases. Computer simulation revealed the main features of network behaviour near the saturation which are not predicted by the used analytical approaches. Copyright 1997 Elsevier Science Ltd.

Evaluation of Categorical Data Clustering

Methods of cluster analysis are well known techniques of multivariate analysis used for many years. Their main applications concern clustering objects characterized by quantitative variables. For this case various coefficients for clustering evaluation and determination of cluster numbers have been proposed. However, in some areas, i.e., for segmentation of Internet users, the variables are often nominal or ordinal as their origin in questionnaire responses. That is why we are dealing with the evaluation criteria for the case of categorical variables here. The criteria based on variability measures are proposed. Instead of variance as a measure for quantitative variables, three measures for nominal variables are considered: the variability measure based on a modal frequency, Gini’s coefficient of mutability, and the entropy. The proposed evaluation criteria are applied to a real-dataset.

Comparison of neural network Boolean factor analysis method with some other dimension reduction methods on bars problem

In this paper, we compare performance of novel neural network based algorithmfor Boolean factor analysiswith several dimension reduction techniques as a tool for feature extraction. Compared are namely singular value decomposition, semi-discrete decomposition and non-negative matrix factorization algorithms, including some cluster analysis methods as well. Even if the mainly mentioned methods are linear, it is interesting to compare them with neural network based Boolean factor analysis, because they arewell elaborated. Second reason for this is to show basic differences between Boolean and linear case. So called bars problem is used as the benchmark. Set of artificial signals generated as a Boolean sum of given number of bars is analyzed by thesemethods. Resulting images show that Boolean factor analysis is upmost suitable method for this kind of data.

Bars problem solving - new neural network method and comparison

Bars problem is widely used as a benchmark for the class of feature extraction tasks. In this model, artificial data set is generated as a Boolean sum of a given number of bars. We show that the most suitable technique for feature set extraction in this case is neural network based Boolean factor analysis. Results are confronted with several dimension reduction techniques. These are singular value decomposition, semi-discrete decomposition and non-negative matrix factorization. Even if these methods are linear, it is interesting to compare them with neural network attempt, because they are well elaborated and are often used for a similar tasks. We show that frequently used cluster analysis methods can bring interesting results, at least for first insight to the data structure.

SOURCES OF EEG ACTIVITY MOST RELEVANT TO PERFORMANCE OF BRAIN-COMPUTER INTERFACE BASED ON MOTOR IMAGERY

The paper examines sources of brain activity, contributing to EEG pat- terns which correspond to motor imagery during training to control brain-computer interface. To identify individual source contribution into electroencephalogram recorded during the training Independent Component Analysis was used. Then those independent components for which the BCI system classification accuracy was at maximum were treated as relevant to performing the motor imagery tasks, since they demonstrated well exposed event related de-synchronization and event related synchronization of the sensorimotor -rhythm during imagining of contra- and ipsilateral hand movements. To reveal neurophysiological nature of these com- ponents we have solved the inverse EEG problem to locate the sources of brain activity causing these components to appear in EEG. The sources were located in hand representation areas of the primary sensorimotor cortex. Their positions practically coincide with the regions of brain activity during the motor imagination obtained in fMRI study. Individual geometry of brain and its covers provided by anatomical MR images was taken into account when localizing the sources.

On the Implementation of Boolean Matrix Factorization

Matrix factorization or factor analysis is an important task helpful in the analysis of high dimensional real world data. There are several well known methods and algorithms for factorization of real data but many application areas including information retrieval, pattern recognition and data mining require processing of binary rather than real data. Unfortunately, the methods used for real matrix factorization fail in the latter case. In this paper we introduce the background of the task as well as genetic algorithm based solver and present results obtained from computer experiments.

New Neural Network Based Approach Helps to Discover Hidden Russian Parliament Voting Patterns

The sparse encoded Hopfield like neural network is modified to provide the Boolean factor analysis. New, more efficient method of sequential factor extraction, based on the characteristics behavior of the Lyapunov function is introduced. Efficiency of this attempt is shown not only on simulated data but on real data from Russian parliament but as well.

Two Expectation-Maximization algorithms for Boolean Factor Analysis

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.

Localization of brain electrical activity sources and hemodynamic activity foci during motor imagery

The sources of brain activity that make the maximum contribution to EEG patterns corresponding to motor imagery have been studied. The accuracy of their classification determines the efficiency of brain-computer interface (BCI) for controlling external technical devices directly by brain signals, without the involvement of muscle activity. Brain activity sources are identified by independent component analysis. The independent components providing the maximum BCI classification accuracy are considered relevant for the motor imagery task. The two most relevant sources exhibit clearly marked event-related desynchronization and synchronization of the μ-rhythm during the imagery of contra- and ipsilateral hand movements. These sources were localized by solving the inverse EEG problem with due consideration for individual geometry of the brain and its covers, as determined by magnetic resonance imaging. Each of the sources was shown to be localized in the 3a area of the primary somatosensory cortex corresponding to proprioceptive sensitivity of the contralateral hand. Their positions were close to the foci of BOLD activity obtained by fMRI.