Enhanced multi-weight vector projection support vector machine

• For get more satisfactory results, EMVSVM enlarges the rank of the between-class scatter matrix.
• EMVSVM gets multiple weight vectors for each class by defining a new criterion.
• EMVSVM shows the more promising classification accuracy than other multisurface classifiers.
• From the statistical viewpoint, the analysis of EMVSVM is done.

Recently, we have developed an effective classifier, called Multi-weight vector projection support vector machine (MVSVM). Like traditional multisurface support vector machine Generalized-Eigenvalue-based Mulitisurface Support Vector Machine (GEPSVM), MVSVM can fast complete the computation and simultaneously handle the complex Exclusive Or (XOR) problems well. In addition, MVSVM still shows the more promising results than GEPSVM for different classification tasks. Despite the effectiveness of MVSVM, there is a serious limitation, which is that the number of the projection weight vectors for each class is limited to one. Intuitively, it is not enough to use only one projection weight vector for each class to obtain better classification. In order to address this problem, we, in this paper, develop enhanced MVSVM (EMVSVM), which is based on MVSVM. For a particular class, EMVSVM maximizes the distances from its projected average vector to the projected points from different classes to find better separability, which is different from MVSVM which maximizes the separability between classes by enforcing the maximization of the distances between the average vectors of different classes. Doing so can make EMVSVM obtain more than one discriminative weight-vector projections for each class due to that the rank of the newly-formed between-class scatter matrix is enlarged. From the statistical viewpoint, we analyze the proposed approach. Experimental results on public datasets indicate the effectiveness and efficiency of EMVSVM.