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Vol. 39, No. 2, 2025

Improvement and application of Mahalanobis-Taguchi system based on metric learning

Title

Improvement and application of Mahalanobis-Taguchi system based on metric learning

Author

CHANG Zhipeng; GU Yuping; CHEN Wenhe

Abstract

The Mahalanobis-Taguchi system (MTS) is a simple principle-based pattern recognition method proposed in the early 1990s by Dr. Taguchi, a famous Japanese quality engineer, which is easy to operate in practice. The MTS was introduced into China in 2000, and it is widely used in product quality inspection and improvement, mechanical fault, and medical diagnoses and multi-attribute decision-making. The method is integrated by Mahalanobis distance and Taguchi method. As a pattern recognition method, the unique advantage of MTS is that it uses Mahalanobis distance to construct a measurement scale with a reference base for recognition and does not need complicated statistical theory. However, with the expansion of the application field of MTS, its limitations are gradually manifested; therefore, some scholars have suggested improvements to the MTS, which mainly focus on two aspects: One is the improvement of Mahalanobis distance. When a variable has multicollinearity, the covariance matrix in the Mahalanobis distance is invertible. Taguchi proposes to calculate the Mahalanobis distance using Schmidt orthogonalization, which does not depend on the covariance matrix and is, therefore, not affected by the multicollinearity. Some other scholars propose other methods, such as pseudo-inverse, ridge estimation, and regularization, to calculate Mahalanobis distance to solve the multicollinearity problem. With the rapid development of the Internet and big data technology, the types of data to be processed are increasingly complex, such that the MTS often needs to process data with dynamic, high-dimensional, high-noise, and nonlinear characteristics. To solve this problem, some scholars attempted to construct the interval Mahalanobis distance, steady Mahalanobis distance, sparse principal component Mahalanobis distance, kernel principal component Mahalanobis distance, kernel interval Mahalanobis distance, and other variations, all of which have achieved good results. The other aspect is the improvement of the Taguchi method. To improve the robustness of the Mahalanobis distance, the Taguchi method is used to screen features. It uses signal to noise ratio (SNR) as the evaluation function of feature subsets, and two-level orthogonal experiment to optimize feature subsets. However, the recognition performance of the feature subsets screened by Taguchi method is typically not ideal. Therefore, some scholars construct binary multi-objective integer programming models, rather than the Taguchi method, to screen features, but it is difficult to solve the model. While the above improvements play an important role in improving the performance of MTS, there are still some shortcomings. For example, these improvements of the Mahalanobis distance all regard its distance as a “constant.” Therefore, these improvements cannot adaptively provide the Mahalanobis distance, which best reflects the internal relationship between data from the perspective of learning so that subsequent recognition tasks can better understand the data and improve the recognition performance of MTS. Furthermore, some improvements use optimization models instead of the Taguchi method to screen features. However, while those improvements can improve the recognition performance of MTS, it is difficult to solve the optimization models. Further, the improvements require high levels of statistical knowledge from users, which makes the MTS lose its advantages of simple principle and easy operation. This paper proposes to introduce metric learning theory to improve the MTS in three aspects: 1) Mahalanobis distance is defined as a metric function whose inputs are homogeneous and non-homogeneous paired-samples and the optimization variable is a metric matrix. Then, KISSME metric learning algorithm is used to estimate the metric matrix, which can make homogeneous samples more compact and non-homogeneous samples more separated to improve the recognition performance of MTS. 2) A new feature subset of evaluation function is proposed to replace the SNR, and the two-level orthogonal test is redesigned accordingly. 3) The calculation process of the Taguchi method is improved by “vectorization,” which makes it easy to speedily realize feature screening by computer programming. To compare the performance difference between the conventional and improved MTS, six University of California, Irvine (UCI), data sets are selected; 20% of the samples in each data set are selected as training samples and the rest as test samples. By comparing the results of the six data sets, it could be observed that the improved MTS is superior to a conventional MTS in terms of accuracy, specificity, and g-means score, which also indicates that the improved MTS has stronger recognition ability. Furthermore, the improved MTS has higher dimensionality reduction efficiency than a conventional MTS with most data sets. According to the AUC value, the comprehensive performance of the improved MTS is better than that of a conventional MTS in all six data sets, and its number of adopted features is less. In conclusion, the recognition performance, dimension reduction ability, and unbalanced data processing ability of the improved MTS are greatly improved. The feasibility of the improved MTS is verified by an example of poverty-returning recognition.However, it can also be observed that the metric learning theory is rich and has spawned many learning algorithms. This study only uses the relatively simple and direct KISSME learning algorithm. Additional studies need to select more metric learning algorithms for comparison and verification to find a better metric learning algorithm under the double constraints of computational complexity and improved recognition performance.

Keywords

Mahalanobis-Taguchi system; Metric learning; KISSME; Poverty-returning recognition

Issue

Vol. 39, No. 2, 2025

References