An Algorithm for the Exact Computation of the Centroid of Higher Dimensional Polyhedra and its Application to Kernel Machines
Maire, Frederic D. (2003) An Algorithm for the Exact Computation of the Centroid of Higher Dimensional Polyhedra and its Application to Kernel Machines. In Third IEEE International Conference on Data Mining (ICDM'03), November 19-22, 2003, Melbourne, Florida, USA.
The Support Vector Machine (SVM) solution corresponds to the centre of the largest sphere inscribed in version space. Alternative approaches like Bayesian Point Machines (BPM) and Analytic Centre Machines have suggested that the generalization performance can be further enhanced by considering other possible centres of version space like the centroid (centre of mass) or the analytic centre. We present an algorithm to compute exactly the centroid of higher dimensional polyhedra, then derive approximation algorithms to build a new learning machine whose performance is comparable to BPM. We also show that for regular kernel matrices (Gaussian kernels for example), the SVM solution can be obtained by solving a linear system of equalities.
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|Item Type:||Conference Paper|
|Keywords:||Bayesian Point Machines, centroid of higher dimensional polyhedra|
|Subjects:||Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100) > Pattern Recognition and Data Mining (080109)|
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MARITIME ENGINEERING (091100) > Ship and Platform Structures (091105)
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
|Copyright Owner:||Copyright 2003 IEEE|
|Copyright Statement:||Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.|
|Deposited On:||04 Jan 2006|
|Last Modified:||29 Feb 2012 22:58|
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