NDLI: Fusing sequential minimal optimization and Newton’s method for support vector training

Content Provider	Springer Nature Link
Author	Abe, Shigeo
Copyright Year	2014
Abstract	Sequential minimal optimization (SMO) is widely used for training support vector machines (SVMs) because of fast training. But the training slows down when a large margin parameter value is used. Training by Newton’s method (NM) accelerates training in such a situation but it slows down for a small margin parameter value. To solve this problem, in this paper we fuse SMO with NM and call it SMO-NM. Because slow training is caused by repetitive corrections of the same variables, we modify the working set selection when they are detected. We call the variables that are selected by SMO, SMO variables. At the current step, if a variable selected as an SMO variable was selected in a previous step, we consider that a loop is detected. And in addition to the SMO variables, we add, to the working set, the unbounded variables that were selected as SMO variables and correct the variables by NM. If no loop is detected, the training procedure is the same as that of SMO. As a variant of this working set strategy, we further add violating variables to the working set. We clarify that if the classification problem is not linearly separable in the feature space, the solutions of L1/L2 SVMs (with the linear sum/square sum of slack variables) are unbounded as the margin parameter value approaches infinity but that, if the mapped training data are not linearly independent in the feature space, the solution of the least squares SVM is unbounded as the margin parameter approaches infinity. We also clarify the condition, in which the increment of the objective function value by SMO-NM is larger than that by SMO. We evaluate SMO-NM for several benchmark data sets and confirm the effectiveness over SMO especially for a large margin parameter value.
Starting Page	345
Ending Page	364
Page Count	20
File Format	PDF
ISSN	18688071
Journal	International Journal of Machine Learning and Cybernetics
Volume Number	7
Issue Number	3
e-ISSN	1868808X
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-05-22
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Least squares support vector machines Newton’s method Sequential minimal optimization Support vector machines Working set selection Computational Intelligence Artificial Intelligence (incl. Robotics) Control, Robotics, Mechatronics Statistical Physics, Dynamical Systems and Complexity Systems Biology Pattern Recognition
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Vision and Pattern Recognition Software

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