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A Study on Sigmoid Kernels for SVM and the Training of non-PSD Kernels by SMO-type Methods
 

Summary: A Study on Sigmoid Kernels for SVM and the Training of
non-PSD Kernels by SMO-type Methods
Hsuan-Tien Lin and Chih-Jen Lin
Department of Computer Science and
Information Engineering
National Taiwan University
Taipei 106, Taiwan
cjlin@csie.ntu.edu.tw
Abstract
The sigmoid kernel was quite popular for support vector machines due to its origin
from neural networks. Although it is known that the kernel matrix may not be positive
semi-definite (PSD), other properties are not fully studied. In this paper, we discuss
such non-PSD kernels through the viewpoint of separability. Results help to validate
the possible use of non-PSD kernels. One example shows that the sigmoid kernel matrix
is conditionally positive definite (CPD) in certain parameters and thus are valid kernels
there. However, we also explain that the sigmoid kernel is not better than the RBF kernel
in general. Experiments are given to illustrate our analysis. Finally, we discuss how
to solve the non-convex dual problems by SMO-type decomposition methods. Suitable
modifications for any symmetric non-PSD kernel matrices are proposed with convergence
proofs.

  

Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology

 

Collections: Computer Technologies and Information Sciences