A Study on SMO Algorithm for Solving ϵ-SVR with Non-PSD Kernels
| Autor: | Xiaojian Zhou, Yi-Zhong Ma |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Statistics and Probability
Mathematical optimization Artificial neural network Process (computing) Sigmoid function Positive-definite matrix Support vector machine symbols.namesake Modeling and Simulation Lagrange multiplier Kernel (statistics) symbols Sequential minimal optimization Algorithm Mathematics |
| Zdroj: | Communications in Statistics - Simulation and Computation. 42:2175-2196 |
| ISSN: | 1532-4141 0361-0918 |
| DOI: | 10.1080/03610918.2012.695843 |
| Popis: | Sequential minimal optimization (SMO) algorithm is effective in solving large-scale support vector machine (SVM). The existing algorithms all assume that the kernels are positive definite (PD) or positive semi-definite (PSD) and should meet the Mercer condition. Some kernels, however, such as sigmoid kernel, which originates from neural network and then is extensively used in SVM, are conditionally PD in certain circumstances; in addition, practically, it is often difficult to prove whether a kernel is PD or PSD or not except some well-known kernels. So, the applications of the existing algorithm of SMO are limited. Considering the deficiency of the traditional ones, this algorithm of solving ϵ-SVR with nonpositive semi-definite (non-PSD) kernels is proposed. Different from the existing algorithms which must consider four Lagrange multipliers, the algorithm proposed in this article just need to consider two Lagrange multipliers in the process of implementation. The proposed algorithm simplified the implem... |
| Databáze: | OpenAIRE |
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