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To overcome the disadvantages of the least squares twin support vector hypersphere (LS-TSVH), some improvements are proposed in this paper. First, LS-TSVH ignores the local sample information; it treats each sample equally when constructing the separating hyperspheres, which causes LS-TSVH to be highly sensitive to noisy samples. To solve this problem, we introduce local density information into LS-TSVH and propose a weighted LS-TSVH (WLSTSVH) approach. Then, we use the Newton downhill algorithm to solve it efficiently. Furthermore, to overcome the limitation that LS-TSVH is suitable only for binary classification problems and cannot be used to solve multi-class classification problems, we employ the one-versus-rest method, extending WLSTSVH to achieve multi-class classification capability. Computational comparisons with other classical multi-class classification algorithms are performed on several benchmark data sets and practical problems. The results indicate that the proposed algorithm achieves better classification performance.

A Multi-Class Classification Weighted Least Squares Twin Support Vector Hypersphere Using Local Density Information