### Influence of probability estimation parameters
on stability of accuracy in prototype rules
using heterogeneous distance functions.

Tadeusz Wieczorek^{1}, Marcin Blachnik^{1}, and
Wlodzislaw Duch^{2,3},

^{1}Division of Computer Studies,
Department of Electrotechnology,
The Silesian University of Technology, Katowice, Poland;

^{2}School of Computer Engineering,
Nanyang Technological University, Singapore,

^{3}Department of Informatics,
Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland.

Abstract.

Many different approaches to the problem of classification have been collected. An interesting way to understand data leads to prototype rules (P-rules). In this approach the aim is to find optimal position of prototypes to which we compare unknown vectors. One of important problems in applications P-rules for real datasets are distance functions operating on different type of attributes like discrete, linear, symbolic, nominal. Solution for such
problems are heterogeneous distance functions. This type of functions are usually based on probability distance measure like Value Difference Matrix (VDM), adopted for continues attributes by estimation of probability density function for continues values. The process of estimation requires selection of several parameters, which have important influence on overall classification accuracy.
Accuracy and this impact is investigated in the paper. Various heterogeneous distance function based on VDM measure are presented, among them some new heterogeneous distance functions based on different type of probability estimation. Practical experiments using the described methods and discussion of obtained results are presented.

Reference: Wieczorek T, Blachnik M, Duch W. (2005), Influence of probability estimation parameters on stability of accuracy in prototype rules using heterogeneous distance functions.
In: Proceedings of the Artificial Intelligence Studies, Vol.2 (25), 2005, pp. 71-78.
Presented at the VII International Conference on Artificial Intelligence AI-20'2005, 22-23.09, Siedlce, Poland.

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