Support vector machine (SVM) has a good effect in the supervised classification of hyperspectral images. In view of the shortcomings of the existing parallel structure SVM, this article proposes a non-parallel SVM model. Based on the traditional parallel boundary structure vector machine, this model adds an additional empirical risk minimization term to the original optimization problem by adding the least square term of the sample and obtains two non-parallel hyperplanes, respectively, forming a new non-parallel SVM algorithm to minimize the additional empirical risk of non-parallel SVM (Additional Empirical Risk Minimization Non-parallel Support Vector Machine, AERM-NPSVM). On the basis of AERM-NPSVM, the bias constraint is added to it, and AERM-NPSVM (BC-AERM-NPSVM) is further obtained. The experimental results show that, compared with the traditional parallel SVM model and the classical non-parallel SVM model, Twin Support Vector Machine (TWSVM), the new model, has a better effect in hyperspectral image classification and better generalization performance.

Hyperspectral image classification technology is important for the application of hyperspectral technology. Support vector machines (SVMs) work well in supervised classifications of hyperspectral images; however, they still have some shortcomings, and their use of a parallel decision plane makes it difficult to conform to real hyperspectral data distribution. The improved nonparallel support vector machine based on SVMs, i.e., the bias constraint additional empirical risk minimization nonparallel support vector machine (BC-AERM-NSVM), has improved classification accuracy compared its predecessor. However, BC-AERM-NSVMs have a more complicated solution problem than SVMs, and if the dataset is too large, the training speed is significantly reduced. To solve this problem, this paper proposes a least squares algorithm, i.e., the least square bias constraint additional empirical risk minimization nonparallel support vector machine (LS-BC-AERM-NSVM). The dual problem of the LS-BC-AERM-NSVM is an unconstrained convex quadratic programming problem, so its solution speed is greatly improved. Experiments on hyperspectral image data demonstrate that the LS-BC-AERM-NSVM displays a vast improvement in terms of solution speed compared with the BC-AERM-NSVM and achieves good classification accuracy.