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WEI-CHIH CHEN AND JYH-HORNG JENG*
Department of Information Engineering
I-Shou University
Kaohsiung, 804 Taiwan
It is known that a weighted order statistic filter (WOSF) generates a linearly separable
Boolean function and 2 different WOSF may generate the same Boolean function.
Therefore a natural question ¡§how to characterize WOSF which correspond the same
Boolean function¡¨ arises. In this paper, we propose a different representation of WOSF
induced from SVM. Also, we construct equivalent classes for WOSF based on the maximal
margin classification of SVM. Two types of equivalent classes are proposed. The
first one is called BF equivalent class. The parameters representing the hyperplane are
adopted as the representative of the class, which is unique. The second class is the global
equivalent class which is derived by additional sign change and permutation on the
components of the BF class representatives. Therefore we can efficiently characterize all
of the WOSF through only few representatives of equivalent classes and save computation
cost when searching for various WOSF. Finally, we provide 3 formulas to directly
generate the corresponding outputs of each WOSF.
Received January 19, 2009; revised February 23, 2009; accepted March 30, 2009.
Communicated by H. Y. Mark Liao.
* Corresponding author.