A Robust Regularization Path Algorithm for $\nu $ -Support Vector Classification

The v-support vector classification has the advantage of using a regularization parameter v to control the number of support vectors and margin errors. Recently, a regularization path algorithm for v-support vector classification (v-SvcPath) suffers exceptions and singularities in some special cases. In this brief, we first present a new equivalent dual formulation for v-SVC and, then, propose a robust v-SvcPath, based on lower upper decomposition with partial pivoting. Theoretical analysis and experimental results verify that our proposed robust regularization path algorithm can avoid the exceptions completely, handle the singularities in the key matrix, and fit the entire solution path in a finite number of steps. Experimental results also show that our proposed algorithm fits the entire solution path with fewer steps and less running time than original one does.