BSVM: A Banded Support Vector Machine
We describe a novel binary classication technique called Banded SVM (B-SVM). In the standard
C-SVM formulation of Cortes and Vapnik (1995), the decision rule is encouraged to lie in the interval
[1, ∞]. The new B-SVM objective function contains penalty terms that encourage the decision rule
to lie in a user specied range [ρ1, ρ2]. In addition to the standard set of support vectors (SVs)
near the class boundaries, B-SVM results in a second set of SVs in the interior of each class.
- Scalar linear projections of multivariate random vectors with finite co-variance have a finite variance.
- Chebyshev's inequality implies that most of the values of the above scalar linear projection are concentrated around its mean.
- If we consider the SVM decision rule as a measure of membership in class +1 and class -1 then the decision rule values should also be concentrated in each class.
- The standard C-SVM objective function does not enforce this band formation in each class.
- B-SVM includes a novel penalty term in the objective function that encourages class specific band formation and this leads to a novel Lagrangian dual optimization problem of which the C-SVM dual is a special case.
- Gautam V. Pendse. BSVM: A Banded Support Vector Machine. [pdf ], arXiv:1107.2347v1, 2011. (this work)
- B. E. Boser, I. M. Guyon and V. Vapnik. A training algorithm for optimal margin classiers. Proceedings of the 5th Annual ACM Workshop on Computational
Learning Theory, 144-152, 1992. [pdf ]
- C. Cortes and V. Vapnik. Support vector networks. Machine Learning, 20:273-297, 1995. [pdf ]
Download Webpage and Data
Toy data used for comparing C-SVM and B-SVM along with this webpage can be downloaded here: bsvm_webpage_data.zip
. This data is freely available under the terms of the license
described below. This zip file includes the following directories:
This directory contains a standalone version of this webpage bsvm.html
for offline browsing.
This directory contains a MATLAB .mat file: demo_data.mat
which contains the data used to generate Figure 2 and Figure 3. A README.m
file contains a brief description of the data.
BSVM toy data and webpage
by Gautam V. Pendse
is licensed under a Creative Commons Attribution 3.0 Unported License
Copyright © 2011, Gautam V. Pendse