We propose a new nonparametric classification framework for numerical patterns, which can also be exploitable for exploratory data analysis. The key idea is approximating each class region by a family of convex geometric sets which can cover samples of the target class without containing any samples of other classes. According to this framework, we consider a combinatorial classifier based on a family of spheres, each of which is the minimum covering sphere for a subset of positive samples and does not contain any negative samples. We also present a polynomial-time exact algorithm and an incremental randomized algorithm to compute it. In addition, we discuss the soft-classification version and evaluate these algorithms by some numerical experiments. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Takigawa, I., Kudo, M., & Nakamura, A. (2005). The convex subclass method: Combinatorial classifier based on a family of convex sets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3587 LNAI, pp. 90–99). Springer Verlag. https://doi.org/10.1007/11510888_10
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