Multi-class Support Vector Machine classifiers using intrinsic and penalty graphs

• We propose a general class of multiclass SVM classifiers.
• We use generic intrinsic and penalty graphs for multiclass SVM regularization.
• A new direct solution of the regularized multiclass SVM problem is proposed.

In this paper, a new multi-class classification framework incorporating geometric data relationships described in both intrinsic and penalty graphs in multi-class Support Vector Machine is proposed. Direct solutions are derived for the proposed optimization problem in both the input and arbitrary-dimensional Hilbert spaces for linear and non-linear multi-class classification, respectively. In addition, it is shown that the proposed approach constitutes a general framework for SVM-based multi-class classification exploiting geometric data relationships, which includes several SVM-based classification schemes as special cases. The power of the proposed approach is demonstrated in the problem of human action recognition in unconstrained environments, as well as in facial image and standard classification problems. Experiments indicate that by exploiting geometric data relationships described in both intrinsic and penalty graphs the SVM classification performance can be enhanced.