Mahalanobis-Taguchi System for Symbolic Interval Data Based on Kernel Mahalanobis Distance

Abstract

Mahalanobis-Taguchi System (MTS), as a pattern recognition method by constructing a continuous measurement scale, has a very good performance on classification and feature selection for real-valued data. However, the record of symbolic interval data has become a common practice with the recent advances in database technologies. Kernel methods not only are powerful statistical nonlinear learning methods, but also can be defined over objects as diverse as graphs, sets, strings, and text documents. In this paper, we derive kernel Mahalanobis distance (KMD) to extend MTS to symbolic interval data. To evaluate the proposed method, four experiments with synthetic symbolic interval data sets and seven experiments with real symbolic interval data sets are performed and we have compared our method with MTS based on interval Mahalanobis distance (IMD). The experimental results show our method has a better classification performance than MTS based on IMD on Accuracy, Specificity, Sensitivity, and G-means. However, MTS based on IMD has a stronger dimension reduction rate than our method.

Keywords

• Kernel Mahalanobis distance
• symbolic interval data
• Mahalanobis-Taguchi system