A simplification on SMO algorithm and its application in solving ε-SVR with non-positive Kernels

Sequential Minimal Optimization (SMO) algorithm is very effective when solving large-scale support vector machine (SVM). The existing algorithms need to judge which quadrant the 4 Lagrange multipliers lie in, complicating its implementation. In addition, the existing algorithms all assume that the kernel functions are positive definite or positive semidefinite, limiting their applications. Having considered these deficiencies of the traditional ones, a simplified SMO algorithm based on SVR is proposed, and further applied in solving ε-SVR with non-positive Kernels. Compared with the existing algorithms, the simplified one is much easier to be implemented without sacrificing space and time efficiency, and can achieve an ideal regression accuracy under the premise of ensuring convergence. Therefore, it has a certain theoretical and practical significance.