Sparse Linear Discriminant Analysis With Constant Between-Class Distance for Feature Selection - Shuangle Guo; Yongxia Li; Jianguang Zhang; Yue Liu; Tian Tian; Mengchen Guo (IEEE Access)
Feature selection is an important preprocessing step in machine learning to remove irrelevant and redundant features. Due to its ability to effectively maintain the discriminability of extracted features, Trace Ratio Linear Discriminant Analysis (TR-LDA) has become the foundation for many feature selection algorithms. As is known, TR-LDA is a challenging problem to solve because of its trace-ratio form, and it also faces the scale invariance problem. These two drawbacks of TR-LDA significantly reduce the performance of feature selection algorithms based on it. To overcome these drawbacks, this paper proposes the sparse LDA with constant between-class distance (SLDA-CBD) model to select relavant features. This model first transforms TR-LDA into a non-trace ratio problem with a constant between-class distance constraint, and then imposes row constraints on the projection matrix to implement feature selection. Since the SLDA-CBD model is rooted in TR-LDA, it ensures the discriminative performance of the selected features. The constant between-class distance constraint successfully avoids the scale invariance problem. Additionally, due to the non-trace ratio form of the SLDA-CBD model, it is easily solvable. The experimental results show that the proposed method has better performance compared to the baseline and six state-of-the-art relative methods, with improvements of over 1% on image datasets and over 2% on video datasets in most cases, while also demonstrating high stability, proving its effectiveness and advantage in practical applications.