Distributed Sparse Manifold-Constrained Optimization Algorithm in Linear Discriminant Analysis

Abstract

In the field of video image processing, high definition is one of the main directions for future development. Faced with the curse of dimensionality caused by the increasingly large amount of ultra-high-definition video data, effective dimensionality reduction techniques have become increasingly important. Linear discriminant analysis (LDA) is a supervised learning dimensionality reduction technique that has been widely used in data preprocessing for dimensionality reduction and video image processing tasks. However, traditional LDA methods are not suitable for the dimensionality reduction and processing of small high-dimensional samples. In order to improve the accuracy and robustness of linear discriminant analysis, this paper proposes a new distributed sparse manifold constraint (DSC) optimization LDA method, called DSCLDA, which introduces $L_{2,0}$-norm regularization for local sparse feature representation and manifold regularization for global feature constraints. By iterating the hard threshold operator and transforming the original problem into an approximate non-convex sparse optimization problem, the manifold proximal gradient (ManPG) method is used as a distributed iterative solution. Each step of the algorithm has an explicit solution. Simulation experiments have verified the correctness and effectiveness of this method. Compared with several advanced sparse linear discriminant analysis methods, this method effectively improves the average classification accuracy by at least $0.90\%$.