TY - GEN
T1 - Nyström approximate model selection for LSSVM
AU - Ding, Lizhong
AU - Liao, Shizhong
PY - 2012
Y1 - 2012
N2 - Model selection is critical to least squares support vector machine (LSSVM). A major problem of existing model selection approaches is that a standard LSSVM needs to be solved with O(n 3) complexity for each iteration, where n is the number of training examples. In this paper, we propose an approximate approach to model selection of LSSVM. We use Nyström method to approximate a given kernel matrix by a low rank representation of it. With such approximation, we first design an efficient LSSVM algorithm and theoretically analyze the effect of kernel matrix approximation on the decision function of LSSVM. Based on the matrix approximation error bound of Nyström method, we derive a model approximation error bound, which is a theoretical guarantee of approximate model selection. We finally present an approximate model selection scheme, whose complexity is lower than the previous approaches. Experimental results on benchmark datasets demonstrate the effectiveness of approximate model selection.
AB - Model selection is critical to least squares support vector machine (LSSVM). A major problem of existing model selection approaches is that a standard LSSVM needs to be solved with O(n 3) complexity for each iteration, where n is the number of training examples. In this paper, we propose an approximate approach to model selection of LSSVM. We use Nyström method to approximate a given kernel matrix by a low rank representation of it. With such approximation, we first design an efficient LSSVM algorithm and theoretically analyze the effect of kernel matrix approximation on the decision function of LSSVM. Based on the matrix approximation error bound of Nyström method, we derive a model approximation error bound, which is a theoretical guarantee of approximate model selection. We finally present an approximate model selection scheme, whose complexity is lower than the previous approaches. Experimental results on benchmark datasets demonstrate the effectiveness of approximate model selection.
KW - Nyström method
KW - least squares support vector machine
KW - matrix approximation
KW - model selection
UR - http://www.scopus.com/inward/record.url?scp=84861434759&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-30217-6_24
DO - 10.1007/978-3-642-30217-6_24
M3 - Conference contribution
AN - SCOPUS:84861434759
SN - 9783642302169
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 282
EP - 293
BT - Advances in Knowledge Discovery and Data Mining - 16th Pacific-Asia Conference, PAKDD 2012, Proceedings
T2 - 16th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining, PAKDD 2012
Y2 - 29 May 2012 through 1 June 2012
ER -