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.
Highlights
Mahalanobis-Taguchi System (MTS) was developed by Taguchi and Jugulum [1] and it is a pattern recognition method in multidimensional systems without any assumption of statistical distribution [2], [3]
Our purpose is to get a comparison between MTS based on kernel interval Mahalanobis distance (KIMD), and MTS based on interval Mahalanobis distance (IMD) for symbolic interval data
In order to evaluate the classification performance and the dimension reduction rate provided by MTS based on IMD and MTS based on KIMD, the Accuracy, Specificity, Sensitivity, G-means, and DRR are used as comparison indexes
Summary
MTS was developed by Taguchi and Jugulum [1] and it is a pattern recognition method in multidimensional systems without any assumption of statistical distribution [2], [3]. Regarding a group of symbolic interval data X = [x1, x2, · · · , xN ]T, we define it as normal samples and the IMD of the jth normal sample can be calculated by 1 p (xL − xL )TS−L 1(xL − xL) + (xU − xU )TS−U1(xU − xU )
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