TY - JOUR
T1 - A Robust Regularization Path Algorithm for ν-Support Vector Classification
AU - Gu, Bin
AU - Sheng, Victor S.
N1 - Funding Information:
This work was supported in part by the National Natural Science Foundation of China under Grant 61232016, Grant 61202137, and Grant 61573191, in part by the U.S. National Science Foundation under Grant IIS-1115417, and in part by the Priority Academic Program Development, Jiangsu Higher Education Institutions.
Publisher Copyright:
© 2012 IEEE.
PY - 2017/5
Y1 - 2017/5
N2 - The μ-support vector classification has the advantage of using a regularization parameter μto control the number of support vectors and margin errors. Recently, a regularization path algorithm for μ-support vector classification (μ-SvcPath) suffers exceptions and singularities in some special cases. In this brief, we first present a new equivalent dual formulation for μ-SVC and, then, propose a robust μ-SvcPath, based on lower upper decomposition with partial pivoting. Theoretical analysis and experimental results verify that our proposed robust regularization path algorithm can avoid the exceptions completely, handle the singularities in the key matrix, and fit the entire solution path in a finite number of steps. Experimental results also show that our proposed algorithm fits the entire solution path with fewer steps and less running time than original one does.
AB - The μ-support vector classification has the advantage of using a regularization parameter μto control the number of support vectors and margin errors. Recently, a regularization path algorithm for μ-support vector classification (μ-SvcPath) suffers exceptions and singularities in some special cases. In this brief, we first present a new equivalent dual formulation for μ-SVC and, then, propose a robust μ-SvcPath, based on lower upper decomposition with partial pivoting. Theoretical analysis and experimental results verify that our proposed robust regularization path algorithm can avoid the exceptions completely, handle the singularities in the key matrix, and fit the entire solution path in a finite number of steps. Experimental results also show that our proposed algorithm fits the entire solution path with fewer steps and less running time than original one does.
KW - Finite convergence
KW - Lower upper decomposition
KW - Solution path
KW - μ-support vector classification (v-SVC)
UR - http://www.scopus.com/inward/record.url?scp=84959421728&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2016.2527796
DO - 10.1109/TNNLS.2016.2527796
M3 - Article
C2 - 26929067
AN - SCOPUS:84959421728
SN - 2162-237X
VL - 28
SP - 1241
EP - 1248
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 5
M1 - 7419254
ER -