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.

EGOTHOR is a search engine that indexes the Web and allows us to search the Web documents. Its hit list contains URL and title of the hits, and also some snippet which tries to shortly show a match. The snippet can be almost always assembled by an algorithm that has a full knowledge of the original document (mostly HTML page). It implies that the search engine is required to store the full text of the documents as a part of the index. Such a requirement leads us to pick up an appropriate compression algorithm which would reduce the space demand. One of the solutions could be some use of common compression methods, for instance gzip or bzip2, but it might be preferable to develop a new method which would take advantage of the document structure, or rather, the textual character of the documents. There already exist special compression text algorithms and methods for a compression of XML documents. The aim of this paper is an integration of the two approaches to achieve an optimal level of the compression ratio.

Complexity of data with respect to a particular class of neural networks is studied. Data complexity is measured by the magnitude of a certain norm of either the regression function induced by a probability measure describing the data or a function interpolating a sample ofinput/output pairs of training data chosen with respect to this probability. The norm is tailored to a type of computational units in the network class. It is shown that for data for which this norm is small, convergence of infima of error functionals over networks with increasing number of hidden units to the global minima is relatively fast. Thus for such data, networks with a reasonable model complexity can achieve good performance during learning. For perceptron networks, the relationship between data complexity, data dimensionality and smoothness is investigated.

We design a formal model of an amorphous computer suit- able for theoretical investigation of its computational properties. The model consists of a ¯nite set of nodes created by RAMs with restricted memory, which are dispersed uniformly in a given area. Within a limited radius the nodes can communicate with their neighbors via a single- channel radio. The assumptions on low-level communication abilities are among the weakest possible: the nodes work asynchronously, there is no broadcasting collision detection mechanism and no network addresses. For the underlying network we design a randomized communication pro- tocol and analyze its e±ciency. The subsequent experiments and combi- natorial analysis of random networks show that the expectations under which our protocol was designed are met by the vast majority of the instances of our amorphous computer model.

In multimedia systems we usually need to retrieve database (DB) objects based on their similarity to a query object, while the similarity assessment is provided by a measure which defines a (dis)similarity score for every pair of DB objects. In most existing applications, the similarity measure is required to be a metric, where the triangle inequality is utilized to speed up the search for relevant objects by use of metric access methods (MAMs), for example, the M-tree. A recent research has shown, however, that nonmetric measures are more appropriate for similarity modeling due to their robustness and ease to model a made-to-measure similarity. Unfortunately, due to the lack of triangle inequality, the nonmetric measures cannot be directly utilized by MAMs. From another point of view, some sophisticated similarity measures could be available in a black-box nonanalytic form (e.g., as an algorithm or even a hardware device), where no information about their topological properties is provided, so we have to consider them as nonmetric measures as well. From yet another point of view, the concept of similarity measuring itself is inherently imprecise and we often prefer fast but approximate retrieval over an exact but slower one. To date, the mentioned aspects of similarity retrieval have been solved separately, that is, exact versus approximate search or metric versus nonmetric search. In this article we introduce a similarity retrieval framework which incorporates both of the aspects into a single unified model. Based on the framework, we show that for any dissimilarity measure (either a metric or nonmetric) we are able to change the “amount” of triangle inequality, and so obtain an approximate or full metric which can be used for MAM-based retrieval. Due to the varying “amount” of triangle inequality, the measure is modified in a way suitable for either an exact but slower or an approximate but faster retrieval. Additionally, we introduce the TriGen algorithm aimed at constructing the desired modification of any black-box distance automatically, using just a small fraction of the database.