DocumentCode :
2772549
Title :
A Walk from 2-Norm SVM to 1-Norm SVM
Author :
Kujala, Jussi ; Aho, Timo ; Elomaa, Tapio
Author_Institution :
Dept. of Software Syst., Tampere Univ. of Technol., Tampere, Finland
fYear :
2009
fDate :
6-9 Dec. 2009
Firstpage :
836
Lastpage :
841
Abstract :
This paper studies how useful the standard 2-norm regularized SVM is in approximating the 1-norm SVM problem. To this end, we examine a general method that is based on iteratively re-weighting the features and solving a 2-norm optimization problem. The convergence rate of this method is unknown. Previous work indicates that it might require an excessive number of iterations. We study how well we can do with just a small number of iterations. In theory the convergence rate is fast, except for coordinates of the current solution that are close to zero. Our empirical experiments confirm this. In many problems with irrelevant features, already one iteration is often enough to produce accuracy as good as or better than that of the 1-norm SVM. Hence, it seems that in these problems we do not need to converge to the 1-norm SVM solution near zero values. The benefit of this approach is that we can build something similar to the 1-norm regularized solver based on any 2-norm regularized solver. This is quick to implement and the solution inherits the good qualities of the solver such as scalability and stability.
Keywords :
convergence; iterative methods; optimisation; stability; support vector machines; 1-norm SVM; 2-norm SVM; 2-norm optimization problem; convergence; iteration; solver; stability; Data mining; Iterative algorithms; Kernel; Optimization methods; Paper technology; Scalability; Software systems; Stability; Support vector machine classification; Support vector machines; 1-norm minimization; SVM; large-scale data; reductions;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Data Mining, 2009. ICDM '09. Ninth IEEE International Conference on
Conference_Location :
Miami, FL
ISSN :
1550-4786
Print_ISBN :
978-1-4244-5242-2
Electronic_ISBN :
1550-4786
Type :
conf
DOI :
10.1109/ICDM.2009.100
Filename :
5360320
Link To Document :
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