The convex subclass method: combinatorial classifier based on a family of convex sets

Authors:
Ichigaku Takigawa;Mineichi Kudo;Atsuyoshi Nakamura
Affiliations:
Bioinformatics Center, Institute for Chemical Research, Kyoto University, Kyoto, Japan;Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan;Graduate School of Information Science and Technology, Hokkaido University, Sapporo, Japan
Venue:
MLDM'05 Proceedings of the 4th international conference on Machine Learning and Data Mining in Pattern Recognition
Year:
2005

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Abstract

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.