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

Ting Mao1, Lanting Yu1, Yueyi Zhang1

  • 1School of Economics and Management, China Jiliang University, Hangzhou 310000, China.

Mathematical Biosciences and Engineering : MBE
|February 2, 2021
PubMed
Summary

A modified Mahalanobis-Taguchi System (MMTS) effectively reduces dimensionality and enhances classification for high-dimensional data. This novel approach, using proper orthogonal decomposition (POD), overcomes limitations of the original Mahalanobis-Taguchi System (MTS).

Keywords:
high-dimensional-small-sample-size dataMahalanobis-Taguchi Systemclassificationproper orthogonal decomposition

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Area of Science:

  • Data Science
  • Machine Learning
  • Statistical Analysis

Background:

  • The Mahalanobis-Taguchi System (MTS) is recognized for dimensionality reduction, feature extraction, and classification in multidimensional systems.
  • Standard MTS faces challenges with high-dimensional, small-sample data due to covariance matrix singularity, hindering Mahalanobis distance calculation.

Purpose of the Study:

  • To develop a Modified Mahalanobis-Taguchi System (MMTS) to address the limitations of MTS in high-dimensional small-sample data scenarios.
  • To improve the applicability of MTS by incorporating proper orthogonal decomposition (POD) for enhanced dimensionality reduction and classification.

Main Methods:

  • Introduced proper orthogonal decomposition (POD) into the Mahalanobis-Taguchi System (MTS) framework, creating the Modified Mahalanobis-Taguchi System (MMTS).
  • MMTS retains essential sample information while significantly reducing dimensionality by considering variable correlations and dimensional influence.
  • Evaluated MMTS classification performance by extracting orthogonal decomposition vectors with eigenvalues greater than 0.001.

Main Results:

  • MMTS demonstrated superior classification performance compared to expert classification and various individual and ensemble classifiers (NB, RF, k-NN, SVM, Wrapper + RF, MRMR + SVM, Chi-square + BP, SMOTE + Wrapper + RF, SMOTE + MRMR + SVM).
  • The method effectively handles high-dimensional small-sample data, preserving key features while achieving substantial dimensionality reduction.

Conclusions:

  • The Modified Mahalanobis-Taguchi System (MMTS) offers a robust solution for classification tasks involving high-dimensional small-sample data.
  • MMTS expands the utility of the Mahalanobis-Taguchi System (MTS) by effectively managing data complexity and improving classification accuracy.