Abstract: Support vector machine (SVM) has shown great potential in pattern recognition and regressive estimation. Due to the industrial development demands, such as the fermentation process modeling, improving the training performance on increasingly large sample sets is an important problem. However, solving a large optimization problem is computationally intensive and memory intensive. In this paper, a geometric interpretation of SVM re-gression (SVR) is derived, and μ-SVM is extended for both L1-norm and L2-norm penalty SVR. Further, Gilbert al-gorithm, a well-known geometric algorithm, is modified to solve SVR problems. Theoretical analysis indicates that the presented SVR training geometric algorithms have the same convergence and almost identical cost of computa-tion as their corresponding algorithms for SVM classification. Experimental results show that the geometric meth-ods are more efficient than conventional methods using quadratic programming and require much less memory.

Key words: support vector machine, pattern recognition, regressive estimation, geometric algorithms

摘要： Support vector machine (SVM) has shown great potential in pattern recognition and regressive estimation. Due to the industrial development demands, such as the fermentation process modeling, improving the training performance on increasingly large sample sets is an important problem. However, solving a large optimization problem is computationally intensive and memory intensive. In this paper, a geometric interpretation of SVM re-gression (SVR) is derived, and μ-SVM is extended for both L1-norm and L2-norm penalty SVR. Further, Gilbert al-gorithm, a well-known geometric algorithm, is modified to solve SVR problems. Theoretical analysis indicates that the presented SVR training geometric algorithms have the same convergence and almost identical cost of computa-tion as their corresponding algorithms for SVM classification. Experimental results show that the geometric meth-ods are more efficient than conventional methods using quadratic programming and require much less memory.

关键词: support vector machine, pattern recognition, regressive estimation, geometric algorithms