Abstract: Linear discriminant analysis (LDA) is a well-known classification and dimensionality reduction tool commonly used in face recognition, text mining, and other fields. However, in high-dimensional environments, i.e., the number of sample features is much larger than the number of samples, the traditional linear discriminant analysis suffers from the singularity problem. To solve this problem, this paper equates LDA to a least squares problem and proposes a new method for LDA based on block coordinate descent (BCD). In addition, in order to make the solution of LDA more interpretable and sparse, we introduce the regular term of L1 paradigm in the model, which makes LDA can handle high-dimensional data. Through sparsification, the dimensionality of the data can be reduced and the computation can be reduced, and the robustness of the data can also be improved to suppress the influence of noise and outliers, and the interpretability of the data can also be enhanced by selecting important features for easy analysis and understanding.