Posterior probability support vector Machines for unbalanced data

This paper proposes a complete framework of posterior probability support vector machines (PPSVMs) for weighted training samples using modified concepts of risks, linear separability, margin, and optimal hyperplane. Within this framework, a new optimization problem for unbalanced classification prob...

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Bibliographic Details
Published in:IEEE transaction on neural networks and learning systems 2005-11, Vol.16 (6), p.1561-1573
Main Authors: QING TAO, WU, Gao-Wei, WANG, Fei-Yue, JUE WANG
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Automation
Bayesian decision theory
Bayesian methods
classification
Computer science
control theory
systems
Computer Simulation
Connectionism. Neural networks
Databases, Factual
Decision theory
Exact sciences and technology
Information Storage and Retrieval - methods
Intelligent systems
Laboratories
Machine learning algorithms
margin
maximal margin algorithms
Models, Statistical
Pattern Recognition, Automated - methods
posterior probability
Probability
Statistical learning
Studies
Support vector machine classification
Support vector machines
support vector machines (SVMs)
unbalanced data
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Summary:This paper proposes a complete framework of posterior probability support vector machines (PPSVMs) for weighted training samples using modified concepts of risks, linear separability, margin, and optimal hyperplane. Within this framework, a new optimization problem for unbalanced classification problems is formulated and a new concept of support vectors established. Furthermore, a soft PPSVM with an interpretable parameter /spl nu/ is obtained which is similar to the /spl nu/-SVM developed by Scho/spl uml/lkopf et al., and an empirical method for determining the posterior probability is proposed as a new approach to determine /spl nu/. The main advantage of an PPSVM classifier lies in that fact that it is closer to the Bayes optimal without knowing the distributions. To validate the proposed method, two synthetic classification examples are used to illustrate the logical correctness of PPSVMs and their relationship to regular SVMs and Bayesian methods. Several other classification experiments are conducted to demonstrate that the performance of PPSVMs is better than regular SVMs in some cases. Compared with fuzzy support vector machines (FSVMs), the proposed PPSVM is a natural and an analytical extension of regular SVMs based on the statistical learning theory.
ISSN:1045-9227
2162-237X
1941-0093
2162-2388
DOI:10.1109/TNN.2005.857955