Modified Mahalanobis-Taguchi System based on proper orthogonal decomposition for high-dimensional-small-sample-size data classification

Ting Mao; Lanting Yu; Yueyi Zhang; Li Zhou; Ting Mao; Lanting Yu; Yueyi Zhang; Li Zhou

doi:10.3934/mbe.2021023

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 426-444. doi: 10.3934/mbe.2021023

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Modified Mahalanobis-Taguchi System based on proper orthogonal decomposition for high-dimensional-small-sample-size data classification

1.
School of Economics and Management, China Jiliang University, Hangzhou 310000, China
2.
China National Institute of Standardization, Beijing 100000, China

Received: 09 October 2020 Accepted: 23 November 2020 Published: 07 December 2020

Mahalanobis-Taguchi System (MTS) is an effective algorithm for dimensionality reduction, feature extraction and classification of data in a multidimensional system. However, when applied to the field of high-dimensional small sample data, MTS has challenges in calculating the Mahalanobis distance due to the singularity of the covariance matrix. To this end, we construct a modified Mahalanobis-Taguchi System (MMTS) by introducing the idea of proper orthogonal decomposition (POD). The constructed MMTS expands the application scope of MTS, taking into account correlations between variables and the influence of dimensionality. It can not only retain most of the original sample information features, but also achieve a substantial reduction in dimensionality, showing excellent classification performance. The results show that, compared with expert classification, individual classifiers such as NB, RF, k-NN, SVM and superimposed classifiers such as Wrapper + RF, MRMR + SVM, Chi-square + BP, SMOTE + Wrapper + RF and SMOTE + MRMR + SVM, MMTS has a better classification performance when extracting orthogonal decomposition vectors with eigenvalues greater than 0.001.
- Mahalanobis-Taguchi System,
- proper orthogonal decomposition,
- high-dimensional-small-sample-size data,
- classification
Citation: Ting Mao, Lanting Yu, Yueyi Zhang, Li Zhou. Modified Mahalanobis-Taguchi System based on proper orthogonal decomposition for high-dimensional-small-sample-size data classification[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 426-444. doi: 10.3934/mbe.2021023

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Abstract

Mahalanobis-Taguchi System (MTS) is an effective algorithm for dimensionality reduction, feature extraction and classification of data in a multidimensional system. However, when applied to the field of high-dimensional small sample data, MTS has challenges in calculating the Mahalanobis distance due to the singularity of the covariance matrix. To this end, we construct a modified Mahalanobis-Taguchi System (MMTS) by introducing the idea of proper orthogonal decomposition (POD). The constructed MMTS expands the application scope of MTS, taking into account correlations between variables and the influence of dimensionality. It can not only retain most of the original sample information features, but also achieve a substantial reduction in dimensionality, showing excellent classification performance. The results show that, compared with expert classification, individual classifiers such as NB, RF, k-NN, SVM and superimposed classifiers such as Wrapper + RF, MRMR + SVM, Chi-square + BP, SMOTE + Wrapper + RF and SMOTE + MRMR + SVM, MMTS has a better classification performance when extracting orthogonal decomposition vectors with eigenvalues greater than 0.001.

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