Piotr Kulczycki

Complete Gradient Clustering Algorithm for Features Analysis of X-Ray Images

Methods based on kernel density estimation have been successfully applied for various data mining tasks. Their natural interpretation together with suitable properties make them an attractive tool among others in clustering problems. In this paper, the Complete Gradient Clustering Algorithm has been used to investigate a real data set of grains. The wheat varieties, Kama, Rosa and Canadian, characterized by measurements of main grain geometric features obtained by X-ray technique, have been analyzed. The proposed algorithm is expected to be an effective tool for recognizing wheat varieties. A comparison between the clustering results obtained from this method and the classical k-means clustering algorithm shows positive practical features of the Complete Gradient Clustering Algorithm.

Fuzzy controller for mechanical systems

In many applications of motion control, the occurrence of nonlinear friction constitutes a fundamental obstacle in the design of satisfactory controlling systems. Since it is seldom possible to obtain a relatively accurate model of resistance to motion, a solution more and more often applied in practice is to introduce approaches that incorporate the inevitable imprecisions of the model in the form of uncertainties. This paper deals with the time-optimal (minimum-time) control for mechanical systems with a discontinuous and uncertain model of resistance to motion, A fuzzy approach is used in the design of suboptimal feedback controllers, convenient in practice thanks to their many advantages, especially in respect to robustness.

Kernel Estimators in Industrial Applications

The specification, based on experimental data, of functions which characterize an object under investigation, constitutes one of the main tasks in modern science and technological problems. A typical example here is the estimation of density function of random variable distribution from any given sample. The classical procedures rely here on arbitrary assumption of the form of this function, and then in specification of its parameters. These are called parametric methods. A valuable advantage is their theoretical and calculational simplicity, as well as their being commonly known and present in subject literature. Nowadays – along with the dynamic development of computer systems – nonparametric methods, whose main feature constitutes a lack of arbitrary assumptions of the form of a density function, are used more and more often. In a probabilistic approach, kernel estimators are becoming the principal method in this subject. Although their concept is relatively simple and interpretation transparent, the applications are impossible without a high class of computer which, even until recently, significantly hindered theoretical, and especially practical research.

A complete gradient clustering algorithm formed with kernel estimators

A complete gradient clustering algorithm formed with kernel estimators 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 oneelement clusters—allows identifying atypical elements, which enables their elimination or possible designation to bigger clusters, thus increasing the homogeneity of the data set.

Neural network for estimating conditional distributions

Neural networks for estimating conditional distributions and their associated quantiles are investigated in this paper. A basic network structure is developed on the basis of kernel estimation theory, and consistency is proved from a mild set of assumptions. A number of applications within statistics, decision theory, and signal processing are suggested, and a numerical example illustrating the capabilities of the elaborated network is given.

An Algorithm for Bayes Parameter Identification

This paper deals with the task of parameter identification using the Bayes estimation method, which makes it possible to take into account the differing consequences of positive and negative estimation errors. The calculation procedures are based on the kernel estimators technique. The final result constitutes a complete algorithm usable for obtaining the value of the Bayes estimator on the basis of an experimentally obtained random sample. An elaborated method is provided for numerical computations.

Rotational motion control of a spacecraft

This note describes a systematic procedure for the control synthesis of a rigid spacecraft using the energy shaping method. The geometric concept of a mechanical system in a coordinate-independent form is used to derive a control algorithm for the Euler-Poincare equations. The main result of this note is a specialization of the method on the unit quaternion group. This note is concluded with the examples of the potential functions and implementation for the three-axis attitude control problem.

Fuzzy controller for a system with uncertain load

In many applications of motion control, problems associated with imprecisely measured or changing load (a mass or a moment of inertia) can be a serious obstacle in the formation of satisfactory controlling systems. This barrier compels the designer to include various kinds of uncertainties in engineering solutions. The present paper deals with the time-optimal control for mechanical systems with uncertain load. A fuzzy approach is used in the design of suboptimal feedback controllers, robust with respect to the load. The methodology proposed in this work may be easily adapted to other modeling uncertainties of mechanical systems, e.g. parameters of drive or motion resistance.

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

Abstract 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).

The Complete Gradient Clustering Algorithm: properties in practical applications

The aim of this paper is to present a Complete Gradient Clustering Algorithm, its applicational aspects and properties, as well as to illustrate them with specific practical problems from the subject of bioinformatics (the categorization of grains for seed production), management (the design of a marketing support strategy for a mobile phone operator) and engineering (the synthesis of a fuzzy controller). The main property of the Complete Gradient Clustering Algorithm is that it does not require strict assumptions regarding the desired number of clusters, which allows to better suit its obtained number to a real data structure. In the basic version it is possible to provide a complete set of procedures for defining the values of all functions and parameters relying on the optimization criterions. It is also possible to point out parameters, the potential change which implies influence on the size of the number of clusters (while still not giving an exact number) and the proportion between their numbers in dense and sparse areas of data elements. Moreover, the Complete Gradient Clustering Algorithm can be used to identify and possibly eliminate atypical elements (outliers). These properties proved to be very useful in the presented applications and may also be functional in many other practical problems.