Maximal Margin Support Vector Machine for Feature Representation and Classification

High-dimensional small sample size data, which may lead to singularity in computation, are becoming increasingly common in the field of pattern recognition. Moreover, it is still an open problem how to extract the most suitable low-dimensional features for the support vector machine (SVM) and simultaneously avoid singularity so as to enhance the SVM's performance. To address these problems, this article designs a novel framework that integrates the discriminative feature extraction and sparse feature selection into the support vector framework to make full use of the classifiers' characteristics to find the optimal/maximal classification margin. As such, the extracted low-dimensional features from high-dimensional data are more suitable for SVM to obtain good performance. Thus, a novel algorithm, called the maximal margin SVM (MSVM), is proposed to achieve this goal. An alternatively iterative learning strategy is adopted in MSVM to learn the optimal discriminative sparse subspace and the corresponding support vectors. The mechanism and the essence of the designed MSVM are revealed. The computational complexity and convergence are also analyzed and validated. Experimental results on some well-known databases (including breastmnist, pneumoniamnist, colon-cancer, etc.) show the great potential of MSVM against classical discriminant analysis methods and SVM-related methods, and the codes can be available on https://www.scholat.com/laizhihui.