Wyniki wyszukiwania - Biblioteka Nauki

1

A complete gradient clustering algorithm formed with kernel estimators

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Kulczycki P. , Charytanowicz M.

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2010

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tom Vol. 20, no 1

123-134

EN

The aim of this paper is to provide a gradient clustering algorithm in its complete form, suitable for direct use without requiring a deeper statistical knowledge. The values of all parameters are effectively calculated using optimizing procedures. Moreover, an illustrative analysis of the meaning of particular parameters is shown, followed by the effects resulting from possible modifications with respect to their primarily assigned optimal values. The proposed algorithm does not demand strict assumptions regarding the desired number of clusters, which allows the obtained number to be better suited to a real data structure. Moreover, a feature specific to it is the possibility to influence the proportion between the number of clusters in areas where data elements are dense as opposed to their sparse regions. Finally, the algorithm-by the detection of one-element clusters-allows identifying atypical elements, which enables their elimination or possible designation to bigger clusters, thus increasing the homogeneity of the data set.

2

An algorithm for reducing the dimension and size of a sample for data exploration procedures

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Kulczycki P. , Łukasik S.

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tom Vol. 24, no. 1

133--149

EN

The paper deals with the issue of reducing the dimension and size of a data set (random sample) for exploratory data analysis procedures. The concept of the algorithm investigated here is based on linear transformation to a space of a smaller dimension, while retaining as much as possible the same distances between particular elements. Elements of the transformation matrix are computed using the metaheuristics of parallel fast simulated annealing. Moreover, elimination of or a decrease in importance is performed on those data set elements which have undergone a significant change in location in relation to the others. The presented method can have universal application in a wide range of data exploration problems, offering flexible customization, possibility of use in a dynamic data environment, and comparable or better performance with regards to the principal component analysis. Its positive features were verified in detail for the domain’s fundamental tasks of clustering, classification and detection of atypical elements (outliers).

3

An algorithm for Bayes parameter identification with quadratic asymmetrical loss function

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Kulczycki P. , Mazgaj A.

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tom Vol. 34, no 4

1127-1148

EN

The paper deals with the estimation problem of model parameter values, in tasks where overestimation implies results other than underestimation, and wliere losses arising from this can be described by a quadratic function with different coefficients characterizing positive and negative errors. In the approach presented, the Bayes decision rule was used, allowing for minimizing potential losses. Calculation algorithms were based on the theory of statistical kernel estimators, which frees the method from distribution type. The result constitutes a complete numerical procedure enabling effective calculation of the value of an identified parameter or - in the multidimensional case - the vector of parameters. The method is aimed at both of the main contemporary approaches to uncertainty modeling: probabilistic and fuzzy logic. It is universal in nature and can be applied in a wide range of tasks of engineering, economy, sociology, biomedicine and other related fields.

4

On the application of statistical kernel estimators for the demand-based design of a wireless data transmission system

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Kulczycki P. , Waglowski J.

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tom Vol. 34, no 4

1149-1167

EN

The subject of this paper is the task of designing the LMDS (Local Multipoint Distribution System) wireless broadband data transmission system. The methodology of statistical kernel estimators and fuzzy logic using operations research and mathematical programming is applied to find optimal locations for its basestations. A procedure which allows to obtain such locations on the basis of potential customer distribution and their expected demand, also in the cases of uncertain and non-stationary data, is investigated.

5

Zastosowanie miar zachowania struktury topologicznej zbioru w wielowymiarowej analizie danych w przestrzeni zredukowanej

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Łukasik S. , Kulczycki P.

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tom R. 109, z. 1-AC

5--15

PL

Przedmiotem niniejszego artykułu jest wielowymiarowa analiza danych, która realizowana jest poprzez uzupełnienie standardowych procedur ekstrakcji cech odpowiednimi miarami zachowania struktury topologicznej zbioru. Podejście to motywuje obserwacja, że nie wszystkie elementy zbioru pierwotnego w toku redukcji są właściwie zachowane w ramach reprezentacji w przestrzeni o zmniejszonej wymiarowości. W artykule przedstawiono najpierw istniejące miary zachowania topologii zbioru, a następnie omówiono możliwości ich włączenia w klasyczne procedury eksploracyjnej analizy danych. Załączono również ilustracyjne przykłady użycia omawianego podejścia w zadaniach analizy skupień i klasyfikacji.

EN

This paper deals with high-dimensional data analysis accomplished through supplementing standard feature extraction procedures with topology preservation measures. This approach is based on an observation that not all elements of an initial dataset are equally preserved in its low-dimensional embedding space representation. The contribution first overviews existing topology preservation measures, then their inclusion in the classical methods of exploratory data analysis is discussed. Finally, some illustrative examples of presented approach in the tasks of cluster analysis and classification are given.