Robust Pattern Classification

Abstract

In developing a classification system, we assume that the training data do not include outliers. But outliers may occur in many occasions and the detection of outliers is difficult especially for multi-dimensional data. If outliers are included, they affect classifiers’ performance. For example, in generating the fuzzy min-max classifier (cf. Section 9.1), additional hyperboxes may be generated by outliers. Or in generating the fuzzy classifier with ellipsoidal regions by postclustering, the center and covariance matrices may be affected by outliers and thus this may further cause mal-tuning of the membership functions. Outliers may be excluded by preprocessing, but in this chapter we consider excluding outliers while generating fuzzy rules. We focus our discussions on a robust training method for a fuzzy classifier with ellipsoidal regions. First, we define a fuzzy rule for each class. Next, we determine the weight for each training datum by the two-stage method in order to suppress the effect of outliers. Then, using these weights, we calculate the center and covariance matrix of the ellipsoidal region for each class and tune the fuzzy rules. After tuning, to further improve generalization ability, we introduce interclass tuning parameters to tune fuzzy rules between two classes using the training data in the class boundary. We demonstrate the effectiveness of the above method using four benchmark data sets.