Bias correction for linear discriminant analysis
Zollanvari A. Abibullaev B.
November 2021Elsevier B.V.
Pattern Recognition Letters
2021#15141 - 47 pp.
Linear discriminant analysis (LDA) is perhaps one of the most fundamental statistical pattern recognition techniques. In this work, we explicitly present, for the first time, an asymptotically exact estimator of the LDA optimal intercept in terms of achieving the lowest overall risk in the classification of two multivariate Gaussian distributions with a common covariance matrix and arbitrary misclassification costs. The proposed estimator of the optimal bias term is developed based on the theory of random matrices of increasing dimension in which the observation dimension and the sample size tend to infinity while keeping their magnitudes comparable. The simple form of this estimator provides us with some analytical insights into the working mechanism of the bias correction in LDA. We then complement these analytical insights with numerical experiments. In particular, empirical results using real data show that insofar as the overall risk is concerned, the proposed bias-corrected form of LDA can outperform the conventional LDA classifier in a wide range of misclassification costs. At the same time, the superiority of the proposed form over LDA tends to be more evident as dimensionality or the ratio between class-specific costs increase.
Bias-correction , Discriminant analysis
Text of the article Перейти на текст статьи
Department of Electrical and Computer Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Robotics and Mechatronics, School of Engineering and Digital Sciences, Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Electrical and Computer Engineering
Department of Robotics and Mechatronics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026