The nearest polyhedral convex conic regions for high-dimensional classification

Authors: HAKAN ÇEVİKALP, EMRE ÇİMEN, GÜRKAN ÖZTÜRK

Abstract: In the nearest-convex-model type classifiers, each class in the training set is approximated with a convexclass model, and a test sample is assigned to a class based on the shortest distance from the test sample to these classmodels. In this paper, we propose new methods for approximating the distances from test samples to the convex regionsspanned by training samples of classes. To this end, we approximate each class region with a polyhedral convex conicregion by utilizing polyhedral conic functions (PCFs) and its extension, extended PCFs. Then, we derive the necessary formulations for computing the distances from test samples to these new models. We tested the proposed methodson different high-dimensional classification tasks including face, digit, and generic object classification as well as onsome lower-dimensional classification problems. The experimental results on different datasets show that the proposedclassifiers achieve either the best or comparable results on high-dimensional classification problems compared to othernearest-convex-model classifiers, which shows the superiority of the proposed methods.

Keywords: Classification, polyhedral conic region, a?ine hull, convex hull, convex cone, face recognition

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