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1
Content available Ensembling a linear regression model with an error mitigation component
Nowosielski A., Kowalski P. A., Kulczycki P.
Journal of Automation Mobile Robotics and Intelligent Systems
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2018
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Vol. 12, No. 1
40--43
EN
This paper presents a proposal of a model error mitigation technique based on the error distribution analysis of the original model and creatng the additional model that tempers the error impact in particular domain areas identified as the most sensitive. both models are then combined into single ensemble model. The idea is demonstrated on the trivial two-dimensional linear regression model.
2
Content available An algorithm for reducing the dimension and size of a sample for data exploration procedures
Kulczycki P., Łukasik S.
International Journal of Applied Mathematics and Computer Science
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2014
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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
Content available remote Zastosowanie miar zachowania struktury topologicznej zbioru w wielowymiarowej analizie danych w przestrzeni zredukowanej
Łukasik Sz., Kulczycki P.
Czasopismo Techniczne. Automatyka
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2012
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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.
4
Content available Bayes classification of imprecise information of interval type
Kulczycki P., Kowalski P. A.
Control and Cybernetics
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2011
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Vol. 40, no 1
101-123
EN
The subject of the investigation presented here is Bayes classification of imprecise multidimensional information of interval type by means of patterns defined through precise data, e.g. deterministic or sharp. For this purpose the statistical kernel estimators methodology was applied, which makes the resulting algorithm independent of the pattern shape. In addition, elements of pattern sets which have insignificant or negative influence on the correctness of classification are eliminated. The concept for realizing the procedure is based on the sensitivity method, used in the domain of artificial neural networks. As a result of this procedure the number of correct classifications and - above all - calculation speed increased significantly. A further growth in quality of classification was achieved with an algorithm for the correction of classifier parameter values. The results of numerical verification, carried out on pseudorandom and benchmark data, as well as a comparative analysis with other methods of similar conditioning, have validated the concept presented here and its positive features.
5
Content available remote A complete gradient clustering algorithm formed with kernel estimators
Kulczycki P., Charytanowicz M.
International Journal of Applied Mathematics and Computer Science
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2010
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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.
6
Content available remote Applicational possibilities of nonparametric estimation of distribution density for control engineering
Kulczycki P.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2008
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Vol. 56, nr 4
347-359
EN
Together with the dynamic development of modern computer systems, the possibilities of applying refined methods of nonparametric estimation to control engineering tasks have grown just as fast. This broad and complex theme is presented in this paper for the case of estimation of density of a random variable distribution. Nonparametric methods allow here the useful characterization of probability distributions without arbitrary assumptions regarding their membership to a fixed class. Following an illustratory description of the fundamental procedures used to this end, results will be generalized and synthetically presented of research on the application of kernel estimators, dominant here, in problems of Bayes parameter estimation with asymmetrical polynomial loss function, as well as for fault detection in dynamical systems as objects of automatic control, in the scope of detection, diagnosis and prognosis of malfunctions. To this aim the basics of data analysis and exploration tasks – recognition of outliers, clustering and classification – solved using uniform mathematical apparatus based on the kernel estimators methodology were also investigated.
7
Content available remote On the application of statistical kernel estimators for the demand-based design of a wireless data transmission system
Kulczycki P., Waglowski J.
Control and Cybernetics
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2005
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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.
8
Content available remote An algorithm for Bayes parameter identification with quadratic asymmetrical loss function
Kulczycki P., Mazgaj A.
Control and Cybernetics
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2005
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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.
9
Content available remote Hard and soft sub-time-optimal controllers for a mechanical system with uncertain mass
Kulczycki P., Wisniewski R., Kowalski P., Krawiec K.
Control and Cybernetics
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2004
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Vol. 33, no 4
573-587
EN
An essential limitation in using the classical optimal control has been its limited robustness to modeling inadequacies and perturbations. This paper presents the concepts of two practical control structures based on the time-optimal approach, a hard and soft one. The hard structure is defined by the parameters selected in accordance with the rules of the statistical decision theory: however, the soft structure allows additionally for elimination of rapid changes in control values. The object is a basic mechanical system, with uncertain (also non-stationary) mass treated as a stochastic process. The methodology proposed here is of a universal nature and may easily be applied with respect to other elements of uncertainty of time-optimal controlled mechanical systems.
10
Content available remote Euler-Poincare reduction of externally forced rigid body motion
Wiśniewski R., Kulczycki P.
Control and Cybernetics
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2004
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Vol. 33, no 2
297-310
EN
If a mechanical system experiences symmetry, the Lagrangian becomes invariant under a certain group action. This property leads to substantial simplification of the description of movement. The standpoint in this article is a mechanical system affected by an external force of a control action. Assuming that the system possesses symmetry and the configuration manifold corresponds to a Lie group, the Euler-Poincare reduction breaks up the motion into separate equations of dynamics and kinematics. This becomes of particular interest for modeling, estimation and control of mechanical systems. A control system generates an external force, which may break the symmetry in the dynamics. This paper shows how to model and to control a mechanical system on the reduced phase space, such that complete state space asymptotic stabilization can be achieved. The paper comprises a specialization of the well-known Euler-Poincare reduction to a rigid body motion with forcing. An example of satellite attitude control illustrates usefulness of the Euler-Poincare reduction in control engineering. This work demonstrates how the energy shaping method applies for Euler-Poincare equations.
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