2024-03-28T17:48:19Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/479792022-11-17T02:08:08Zhdl_2115_20053hdl_2115_145Construction of convex hull classifiers in high dimensionsTakahashi, TetsujiKudo, MineichiNakamura, AtsuyoshiPattern recognitionConvex hullClassifier selection007We propose an algorithm to approximate each class region by a small number of approximated convex hulls and to use these for classification. The classifier is one of non-kernel maximum margin classifiers. It keeps the maximum margin in the original feature space, unlike support vector machines with a kernel. The construction of an exact convex hull requires an exponential time in dimension, so we find an approximate convex hull (a polyhedron) instead, which is constructed in linear time in dimension. We also propose a model selection procedure to control the number of faces of convex hulls for avoiding over-fitting, in which a fast procedure is adopted to calculate an upper-bound of the leave-one-out error. In comparison with support vector machines, the proposed approach is shown to be comparable in performance but more natural in the extension to multi-class problems.Elsevier B.V.Journal Articleapplication/pdfhttp://hdl.handle.net/2115/47979https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/47979/1/PRL32-16_2224-2230.pdf0167-8655Pattern Recognition Letters3216222422302011-12-01enginfo:doi/10.1016/j.patrec.2011.06.020author