Linear discriminant analysis (LDA) is a fundamental method in statistical pattern recognition and classification, achieving Bayes optimality under Gaussian assumptions. However, it is well-known that classical LDA may struggle in high-dimensional settings due to instability in covariance estimation. In this work, we propose LDA with gradient optimization (LDA-GO), a new approach that directly optimizes the inverse covariance matrix via gradient descent. The algorithm parametrizes the inverse covariance matrix through Cholesky factorization, incorporates a low-rank extension to reduce computational complexity, and considers a multiple-initialization strategy, including identity initialization and warm-starting from the classical LDA estimates. The effectiveness of LDA-GO is demonstrated through extensive multivariate simulations and real-data experiments.

Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension reduction. It has been used widely in many ap- plications involving high-dimensional data, such as face recognition and image retrieval. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singu- lar. A well-known approach to deal with the singularity problem is to apply an intermediate dimension reduction stage using Principal Com- ponent Analysis (PCA) before LDA. The algorithm, called PCA LDA, is used widely in face recognition.

Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension reduction. It has been used widely in many applications involving high-dimensional data, such as face recognition and image retrieval. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singular. A well-known approach to deal with the singularity problem is to apply an intermediate dimension reduction stage using Principal Component Analysis (PCA) before LDA. The algorithm, called PCA LDA, is used widely in face recognition. However, PCA LDA has high costs in time and space, due to the need for an eigen-decomposition involving the scatter matrices. In this paper, we propose a novel LDA algorithm, namely 2DLDA, which stands for 2-Dimensional Linear Discriminant Analysis.

Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension reduction. It has been used widely in many applications involving high-dimensional data, such as face recognition and image retrieval. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singular. A well-known approach to deal with the singularity problem is to apply an intermediate dimension reduction stage using Principal Component Analysis (PCA) before LDA. The algorithm, called PCA LDA, is used widely in face recognition. However, PCA LDA has high costs in time and space, due to the need for an eigen-decomposition involving the scatter matrices. In this paper, we propose a novel LDA algorithm, namely 2DLDA, which stands for 2-Dimensional Linear Discriminant Analysis.

Linear Discriminant Analysis (LDA) is a well-known scheme for feature extraction and dimension reduction. It has been used widely in many applications involvinghigh-dimensional data, such as face recognition and image retrieval. An intrinsic limitation of classical LDA is the so-called singularity problem, that is, it fails when all scatter matrices are singular. Awell-known approach to deal with the singularity problem is to apply an intermediate dimension reduction stage using Principal Component Analysis(PCA) before LDA. The algorithm, called PCA LDA, is used widely in face recognition. However, PCA LDA has high costs in time and space, due to the need for an eigen-decomposition involving the scatter matrices. In this paper, we propose a novel LDA algorithm, namely 2DLDA, which stands for 2-Dimensional Linear Discriminant Analysis.