Development of a hybrid methodology for dimensionality reduction in Mahalanobis–Taguchi system using Mahalanobis distance and binary particle swarm optimization

Abstract

Mahalanobis–Taguchi System (MTS) is a pattern recognition method applied to classify data into categories – “healthy” and “unhealthy” or “acceptable” and “unacceptable”. MTS has found applications in a wide range of problem domains. Dimensionality reduction of the input set of attributes forms an important step in MTS. The current practice is to apply Taguchi’s design of experiments (DOE) and orthogonal array (OA) method to achieve this end. Maximization of Signal-to-Noise (S/N) ratio forms the basis for selection of the optimal combination of variables. However the DOE–OA method has been reviewed to be inadequate for the purpose. In this research study, we propose a dimensionality reduction method by addressing the problem as feature selection exercise. The optimal combination of attributes minimizes a weighted sum of total fractional misclassification and the percentage of the total number of variables employed to obtain the misclassification. Mahalanobis distances (MDs) of “healthy” and “unhealthy” conditions are used to compute the misclassification. A mathematical model formulates the feature selection approach and it is solved by binary particle swarm optimization (PSO). Data from an Indian foundry shop is adopted to test the mathematical model and the swarm heuristic. Results are compared with that of DOE–OA method of MTS.