| Citation: | WANG Keyao, WANG Huiwen, ZHAO Qing, et al. A modified Mahalanobis distance discriminant method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(5): 824-830. doi: 10.13700/j.bh.1001-5965.2020.0652(in Chinese)
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Mahalanobis distance discriminant method is an effective multivariate statistical analysis method based on the Mahalanobis distance. An important feature of the Mahalanobis distance is its introduction of the inverse of covariance matrix, which avoids the disturbance to the distance measurement from the scales of the attribute variables and the correlations among these variables. However, when there is multicollinearity among the attribute variables, the singularity of the covariance matrix will affect the stability of the inverse matrix estimation, and will greatly damage the effect of the Mahalanobis distance discriminant method. We propose a modified Mahalanobis distance discriminant method, which adopts the general cross-validation (GCV) to choose the dimensions of these variables with the best prediction effect, so that the inverse of the covariance matrix can be well estimated when these attribute variables are highly correlated. The modified Mahalanobis distance discriminant method can provide a reliable estimation of the covariance matrix, resist the disturbances outside the sample set, improve the discriminant accuracy of the model, and enhance the generalization ability of the model. Simulations are conducted to verify the improvement of the discriminant performance of the modified Mahalanobis distance discriminant method compared with the classical one.
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