Enhancement of Mahalanobis–Taguchi System via Rough Sets based Feature Selection

Abstract

The current research presents a methodology for classification based on Mahalanobis Distance (MD) and Association Mining using Rough Sets Theory (RST). MD has been used in Mahalanobis Taguchi System (MTS) to develop classification scheme for systems having dichotomous states or categories. In MTS, selection of important features or variables to improve classification accuracy is done using Signal-to-Noise (S/N) ratios and Orthogonal Arrays (OAs). OAs has been reviewed for limitations in handling large number of variables. Secondly, penalty for over-fitting or regularization is not included in the feature selection process for the MTS classifier. Besides, there is scope to enhance the utility of MTS to a classification-cum-causality analysis method by adding comprehensive information about the underlying process which generated the data. This paper proposes to select variables based on maximization of degree-of-dependency between Subset of System Variables (SSVs) and system classes or categories (R). Degree-of-dependency, which reflects goodness-of-model and hence goodness of the SSV, is measured by conditional probability of system states on subset of variables. Moreover, a suitable regularization factor equivalent to L0 norm is introduced in an optimization problem which jointly maximizes goodness-of-model and effect of regularization. Dependency between SSVs and R is modeled via the equivalent sets of Rough Set Theory. Two new variants of MTS classifier are developed and their performance in terms of accuracy of classification is evaluated on test datasets from five case studies. The proposed variants of MTS are observed to be performing better than existing MTS methods and other classification techniques found in literature.