Studied are differences of two approaches targeted to reveal latent variables in binary data. These approaches assume that the observed high dimensional data are driven by a small number of hidden binary sources combined due to Boolean superposition. The first approach is the Boolean matrix factorization (BMF) and the second one is the Boolean factor analysis (BFA). The two BMF methods are used for comparison. First is the M8 method from the BMDP statistical software package and the second one is the method suggested by Belohlavek \& Vychodil. These two are compared to BFA, especially with the Expectation-maximization Boolean Factor Analysis we had developed earlier has, however, been extended with a binarization step developed here. The well-known bars problem and the mushroom dataset are used for revealing the methods' peculiarities. In particular, the reconstruction ability of the computed factors and the information gain as the measure of dimension reduction was under scrutiny. It was shown that BFA slightly loses to BMF in performance when noise-free signals are analyzed. Conversely, BMF loses considerably to BFA when input signals are noisy.
An assembly neural network based on the binary Hebbian rule is suggested for pattern recognition. The network consists of several sub-networks according to the number of classes to be recognized. Each sub-network consists of several neural columns according to the dimensionality of the signal space so that the value of each signal component is encoded by activity of adjacent neurons of the column. A new recognition algorithm is presented which realizes the nearest-neighbor method in the assembly neural network. Computer simulation of the network is performed. The model is tested on a texture segmentation task. The experiments have demonstrated that the network is able to segment reasonably real-world texture images.
This paper examines the performance of four classifiers for Brain Computer Interface (BCI) systems based on multichannel EEG recordings. The classifiers are designed to distinguish EEG patterns corresponding to performance of several mental tasks. The first one is the basic Bayesian classifier (BC) which exploits only interchannel covariance matrices corresponding to different mental tasks. The second classifier is also based on Bayesian approach but it takes into account EEG frequency structure by exploiting interchannel covariance matrices estimated separately for several frequency bands (Multiband Bayesian Classifier, MBBC). The third one is based on the method of Multiclass Common Spatial Patterns (MSCP) exploiting only interchannel covariance matrices as BC. The fourth one is based on the Common Tensor Discriminant Analysis (CTDA), which is a generalization of MCSP, taking EEG frequency structure into account. The MBBC and CTDA classifiers are shown to perform significantly better than the two other methods. Computational complexity of the four methods is estimated. It is shown that for all classifiers the increase in the classifying quality is always accompanied by a significant increase of computational complexity.