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Open access

Oleg Uzhga-Rebrov and Galina Kuleshova

Problems of Fuzzy Clustering of Microarray Data

Microarray technology has been the leading research direction in medicine, pharmacology, genome studies and other related areas over the past years. This technology enables researches to simultaneously study activity expression of tens of thousands of genes. After the experimental data have been processed, arrays of numerical values of gene expressions are obtained that are the basis for receiving relevant information and new knowledge. This paper briefly overviews the basics of microarray technology as well as task classes that could be solved using microarray data. The existing approaches to clustering gene expression sets are discussed. It is shown that the fuzzy c-means clustering method appears the most appropriate for that purpose. Due to that, the problem of choosing an optimal size of fuzziness parameter arises. Three widespread techniques for solving the problem are considered and their comparative analysis is provided.

Open access

Arnis Kirshners, Galina Kuleshova and Arkady Borisov

Demand Forecasting Based on the Set of Short Time Series

This paper addresses the task of short historical time series and discrete descriptive parameters processing aimed at making demand forecast only on the basis of new product describing parameters. Several data mining methods are used for data processing including data extraction, pre-processing, cluster analysis and classification. Data preparation for data mining processes is made with user-defined parameters entered in the forecasting system. In the selected short historical time series the membership of an object in any class, which is a basis for creating prototypes, is determined using clustering. The k-means clustering algorithm is employed for finding the optimal number of clusters in the sample. The number of clusters is determined on the basis of the mean absolute error. As a result of classification, using inductive decision trees, a correlation between the prototype produced in the course of clustering and product describing parameters is determined. For new product demand clustering, a decision tree obtained as a result of classification is used. New product describing parameters are then projected on the tree, and a tree leave indicating the number of the prototype produced by means of clustering is found. The prototype curve structure depicts possible demand for a new product for the next period.

Open access

Oleg Uzhga-Rebrov and Galina Kuleshova

Abstract

Probability boxes (p-boxes) are used as a tool for modeling uncertainty regarding probability distributions in the sets of relevant elements (random events, values of the random variable etc.). To combine information produced by two or more p-boxes, Dempster’s rule for belief combination is commonly used. However, there are plenty of other rules for belief combination developed within the theory of evidence. The purpose of this paper is to present and analyze some widespread rules of that kind as well as examine their potentialities regarding combining the information provided by probability boxes.

Open access

Oleg Uzhga-Rebrov and Galina Kuleshova

Abstract

This paper considers different techniques of operating with fuzzy probability estimates of relevant random events in decision making tasks. The recalculation of posterior probabilities of states of nature based on the information provided by indicator events is performed using a fuzzy version of Bayes’ theorem. The choice of an optimal decision is made on the basis of fuzzy expected value maximisation.

Open access

Oleg Uzhga-Rebrov and Galina Kuleshova

Abstract

Different types of uncertainty are widely spread in all areas of human activity. Probabilistic uncertainties are related to the chances of occurrence of random events. To deal with this kind of uncertainty, statistics and probability theory are successfully employed. Another kind of uncertainty, fuzzy uncertainties refer to imprecision and fuzziness of different kinds of measurements. To cope with this kind of uncertainty, the fuzzy set theory is used. This paper addresses widespread approaches to combining probabilistic and fuzzy uncertainties. The theoretical fundamentals of the approaches are considered within the context of the generalized theory of uncertainty (GTU).

Open access

Oleg Uzhga-Rebrov and Galina Kuleshova,

Abstract

Probabilistic estimates are numerical representations of chances of random event occurrence. The classical theory of probability is based on the assumption that probabilistic estimates are deterministic. If available initial data are sufficient, this kind of estimates can be really obtained. However, when such data are not available, probabilistic estimates become uncertain. This paper analyses and compares three widespread approaches to modelling uncertain estimates and provides practical recommendations on their use.

Open access

Pavels Osipovs, Andrejs Rinkevics, Galina Kuleshova and Arkady Borisov

Abstract

This paper examines the possibility of using Markov chains when constructing a profile of author’s writing style. Thus, the constructed profile can be then used to analyze other texts and calculate their level of similarity. The extraction of the unique profile of text writing style that is characteristic of a specific human can be a topical task in many spheres of human activity. As an example, the task of detecting authorship for scientific and fiction texts can be mentioned. The paper describes a basic theoretical apparatus used for profile construction, software implementation of the experimental system as well as the experiments made and provides experimental results and their analysis.