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This paper presents a weighted support vector machine (WSVM) to improve the outlier sensitivity problem of standard support vector machine (SVM) for two-class data classification. The basic idea is to assign different weights to different data points such that the WSVM training algorithm learns the decision surface according to the relative importance of data points in the training data set. The weights used in WSVM are generated by kernel-based possibilistic c-means (KPCM) algorithm, whose partition generates relative high values for important data points but low values for outliers. Experimental results indicate that the proposed method reduces the affect of outliers and yields higher classification rate than standard SVM does when outliers exist in the training data set.