New decision function for support vector data description

In conventional support vector data description (SVDD), for each class we look for the smallest sphere that encloses its data. in the decision phase a sample is classified into class i only when the value of the i^th decision function is positive. following this architecture, an unclassifiable region (s) can be appeared if the values of more than one decision function are positives. To overcome this problem, we propose a new simple and powerful decision function, which is used only in the overlappeds regions, this membership function can be calculated in the feature space and can be represented by kernels functions. This method gives good performance on reducing the effects of overlap and significantly improves the classification. We demonstrate the performance of our decision function using six benchmark datasets.