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Scatter matrix decomposition for jointly sparse learning *
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AI
DOI：10.1016/j.patcog.2023.109485.png)
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Abstract
En 中文
Orthogonal Linear Discriminant Analysis (OLDA) based on generalized Eigen-equation is widely used in the field of computer vision and pattern recognition. However, the performance of OLDA for feature ex-traction and classification needs to be improved as it lacks sparsity for better interpretation of the fea-tures. Moreover, computing the orthogonal sparse projections based on LDA is very difficult and is still unsolved. To solve these problems, in this paper, we propose a method called Jointly Sparse Orthogonal Linear Discriminant Analysis (JSOLDA). Different from the existing OLDA, JSOLDA is proposed from a novel viewpoint of scatter matrix decomposition. Theoretical analysis shows that OLDA can be derived by the constrained scatter matrix decomposition. In addition, by imposing L 2,1-norm on the penalty term, the proposed JSOLDA can obtain the jointly sparse orthogonal projections to perform feature extraction. We also design an iterative algorithm to obtain the optimal solution. Systematic theoretical analysis between the OLDA and JSOLDA are uncovered. Both of convergence and computational complexity are also dis-cussed. Experimental results on four data sets (i.e., COIL10 0, USPS, ICADAR20 03 and CMU PIE) indicate that JSOLDA outperforms several well-known LDA-based and L 2,1-norm based methods. (c) 2023 Elsevier Ltd. All rights reserved.
Keywords:
Feature extraction
Pattern recognition
Classification
Linear discriminant analysis
Joint sparsity