On the SVMpath initialization

This paper presents a novel algorithm for the initial configuration to the model selection problem in the two-class support vector machine (SVM) classification when fitting the entire path of SVM solutions for every value of the regularization parameter. Instead of using quadratic programming for initialization in the conventional two-class SVM regularization path fitting methods, we propose a piecewise linear method which reduces the computational cost significantly. Furthermore, an efficient treatment is provided to deal with the singular case where the data set contains linearly dependent points, duplicate points or nearly duplicate points. The performance of the proposed algorithm in terms of computational complexity and the ability to handle singular cases are backed by strict mathematical analysis and proof, and verified by the experimental results.

► We propose a piecewise linear method for solving the SVMpath initialization.
► We provide two path finding algorithms based on different initializations.
► The new path finding algorithms reduce computational cost up to one order.
► We include a random ridge term to solve instability issue in path finding process.