Abstract
Decomposition methods are well-known techniques for solving quadratic programming (QP) problems arising in support vector machines (SVMs). In each iteration of a decomposition method, a small number of variables are selected and a QP problem with only the selected variables is solved. Since large matrix computations are not required, decomposition methods are applicable to large QP problems. In this paper, we will make a rigorous analysis of the global convergence of general decomposition methods for SVMs. We first introduce a relaxed version of the optimality condition for the QP problems and then prove that a decomposition method reaches a solution satisfying this relaxed optimality condition within a finite number of iterations under a very mild condition on how to select variables.
| Original language | English |
|---|---|
| Pages (from-to) | 1362-1369 |
| Number of pages | 8 |
| Journal | IEEE Transactions on Neural Networks |
| Volume | 17 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - Nov 2006 |
| Externally published | Yes |
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Keywords
- Decomposition method
- Global convergence
- Quadratic programming (QP)
- Support vector machines (SVMs)
- Termination
ASJC Scopus subject areas
- Control and Systems Engineering
- Theoretical Computer Science
- Electrical and Electronic Engineering
- Artificial Intelligence
- Computational Theory and Mathematics
- Hardware and Architecture
Cite this
Global convergence of decomposition learning methods for support vector machines. / Takahashi, Norikazu; Nishi, Tetsuo.
In: IEEE Transactions on Neural Networks, Vol. 17, No. 6, 11.2006, p. 1362-1369.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Global convergence of decomposition learning methods for support vector machines
AU - Takahashi, Norikazu
AU - Nishi, Tetsuo
PY - 2006/11
Y1 - 2006/11
N2 - Decomposition methods are well-known techniques for solving quadratic programming (QP) problems arising in support vector machines (SVMs). In each iteration of a decomposition method, a small number of variables are selected and a QP problem with only the selected variables is solved. Since large matrix computations are not required, decomposition methods are applicable to large QP problems. In this paper, we will make a rigorous analysis of the global convergence of general decomposition methods for SVMs. We first introduce a relaxed version of the optimality condition for the QP problems and then prove that a decomposition method reaches a solution satisfying this relaxed optimality condition within a finite number of iterations under a very mild condition on how to select variables.
AB - Decomposition methods are well-known techniques for solving quadratic programming (QP) problems arising in support vector machines (SVMs). In each iteration of a decomposition method, a small number of variables are selected and a QP problem with only the selected variables is solved. Since large matrix computations are not required, decomposition methods are applicable to large QP problems. In this paper, we will make a rigorous analysis of the global convergence of general decomposition methods for SVMs. We first introduce a relaxed version of the optimality condition for the QP problems and then prove that a decomposition method reaches a solution satisfying this relaxed optimality condition within a finite number of iterations under a very mild condition on how to select variables.
KW - Decomposition method
KW - Global convergence
KW - Quadratic programming (QP)
KW - Support vector machines (SVMs)
KW - Termination
UR - http://www.scopus.com/inward/record.url?scp=34248677013&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34248677013&partnerID=8YFLogxK
U2 - 10.1109/TNN.2006.880584
DO - 10.1109/TNN.2006.880584
M3 - Article
C2 - 17131653
AN - SCOPUS:34248677013
VL - 17
SP - 1362
EP - 1369
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
SN - 2162-237X
IS - 6
ER -