Relaxing support vectors for classification

Onur Şeref (), Wanpracha Chaovalitwongse () and J. Brooks ()

Annals of Operations Research, 2014, vol. 216, issue 1, 229-255

Abstract: We introduce a novel modification to standard support vector machine (SVM) formulations based on a limited amount of penalty-free slack to reduce the influence of misclassified samples or outliers. We show that free slack relaxes support vectors and pushes them towards their respective classes, hence we use the name relaxed support vector machines (RSVM) for our method. We present theoretical properties of the RSVM formulation and develop its dual formulation for nonlinear classification via kernels. We show the connection between the dual RSVM and the dual of the standard SVM formulations. We provide error bounds for RSVM and show it to be stable, universally consistent and tighter than error bounds for standard SVM. We also introduce a linear programming version of RSVM, which we call RSVMLP. We apply RSVM and RSVMLP to synthetic data and benchmark binary classification problems, and compare our results with standard SVM classification results. We show that relaxed influential support vectors may lead to better classification results. We develop a two-phase method called RSVM 2 for multiple instance classification (MIC) problems, where RSVM formulations are used as classifiers. We extend the two-phase method to the linear programming case and develop RSVMLP 2 . We demonstrate the classification characteristics of RSVM 2 and RSVMLP 2 , and report our classification results compared to results obtained by other SVM-based MIC methods on public benchmark datasets. We show that both RSVM 2 and RSVMLP 2 are faster and produce more accurate classification results. Copyright Springer Science+Business Media, LLC 2014

Keywords: Classification; Support vector machines; Error bounds; Multiple instance classification (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-012-1193-3 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:216:y:2014:i:1:p:229-255:10.1007/s10479-012-1193-3

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-012-1193-3

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().