Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann manifold Pham, Duc-Son and Venkatesh, Svetha 2011, Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann manifold, in AI 2011 : Advances in Artificial Intelligence : 24th Australasian Joint Conference, Perth, Australia, December 5-8, 2011 : proceedings, Springer-Verlag, Berlin, Germany, pp. 241-250, doi: 10.1007/978-3-642-25832-9_25. Attached Files Name Description MIMEType Size Downloads Title Supervised subspace learning with multi-class Lagrangian SVM on the Grassmann manifold Author(s) Pham, Duc-Son Venkatesh, Svetha orcid.org/0000-0001-8675-6631 Conference name Advances in Artifical Intelligence. Conference (24th : 2011 : Perth, Western Australia) Conference location Perth, Western Australia Conference dates 5-8 Dec. 2011 Title of proceedings AI 2011 : Advances in Artificial Intelligence : 24th Australasian Joint Conference, Perth, Australia, December 5-8, 2011 : proceedings Editor(s) Wang, Dianhui Reynolds, Mark Publication date 2011 Series Lecture notes in artificial intelligence ; 7106 Conference series Advances in Artifical Intelligence Conference Start page 241 End page 250 Total pages 10 Publisher Springer-Verlag Place of publication Berlin, Germany Keyword(s) classification errors classifier design data sets dimensionality reduction empirical risks Grassmann manifold hypothesis space iterative algorithm Lagrangian limited training data linear projections multi-class numerical studies optimal subspace robust performance subspace learning SVM classifiers weak connection Summary Learning robust subspaces to maximize class discrimination is challenging, and most current works consider a weak connection between dimensionality reduction and classifier design. We propose an alternate framework wherein these two steps are combined in a joint formulation to exploit the direct connection between dimensionality reduction and classification. Specifically, we learn an optimal subspace on the Grassmann manifold jointly minimizing the classification error of an SVM classifier. We minimize the regularized empirical risk over both the hypothesis space of functions that underlies this new generalized multi-class Lagrangian SVM and the Grassmann manifold such that a linear projection is to be found. We propose an iterative algorithm to meet the dual goal of optimizing both the classifier and projection. Extensive numerical studies on challenging datasets show robust performance of the proposed scheme over other alternatives in contexts wherein limited training data is used, verifying the advantage of the joint formulation. ISBN 9783642258312 364225831X ISSN 0302-9743 Language eng DOI 10.1007/978-3-642-25832-9_25 Field of Research 089999 Information and Computing Sciences not elsewhere classified Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences HERDC Research category E1.1 Full written paper - refereed Copyright notice ©2011, Springer-Verlag Berlin Heidelberg Persistent URL http://hdl.handle.net/10536/DRO/DU:30044657 Document type: Conference Paper Collection: School of Information Technology Related Links Link Description Connect to published version (restricted access) Go to link with your DU access privileges     Unless expressly stated otherwise, the copyright for items in DRO is owned by the author, with all rights reserved. Versions Version Filter Type Fri, 20 Apr 2012, 13:23:41 EST Mon, 23 Apr 2012, 16:42:14 EST Mon, 23 Apr 2012, 16:44:58 EST Thu, 20 Nov 2014, 10:54:14 EST Tue, 03 Mar 2015, 11:53:23 EST Tue, 03 Mar 2015, 11:56:09 EST Sat, 21 Oct 2017, 02:03:28 EST Filtered Full Citation counts:   Cited 1 times in TR Web of Science Cited 2 times in Scopus Search Google Scholar Access Statistics: 355 Abstract Views, 4 File Downloads  -  Detailed Statistics Created: Fri, 20 Apr 2012, 13:23:40 EST

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