Extended polynomial growth transforms for design and training of generalized support vector machines

Ahana Gangopadhyay, Oindrila Chatterjee, Shantanu Chakrabartty

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Growth transformations constitute a class of fixed-point multiplicative update algorithms that were originally proposed for optimizing polynomial and rational functions over a domain of probability measures. In this paper, we extend this framework to the domain of bounded real variables which can be applied towards optimizing the dual cost function of a generic support vector machine (SVM). The approach can, therefore, not only be used to train traditional soft-margin binary SVMs, one-class SVMs, and probabilistic SVMs but can also be used to design novel variants of SVMs with different types of convex and quasi-convex loss functions. In this paper, we propose an efficient training algorithm based on polynomial growth transforms, and compare and contrast the properties of different SVM variants using several synthetic and benchmark data sets. The preliminary experiments show that the proposed multiplicative update algorithm is more scalable and yields better convergence compared to standard quadratic and nonlinear programming solvers. While the formulation and the underlying algorithms have been validated in this paper only for SVM-based learning, the proposed approach is general and can be applied to a wide variety of optimization problems and statistical learning models.

Original languageEnglish
Pages (from-to)1961-1974
Number of pages14
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number5
StatePublished - May 2018


  • Baum-Eagon inequality
  • Binary classification
  • Fixed point optimization
  • Growth transforms
  • Loss functions
  • Maximum margin classifiers
  • One-class support vector Mach-ines (SVMs)
  • Quasi-convex loss functions
  • SVMs
  • Sparse SVMs


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