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.
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Takigawa, I., Kudo, M., Nakamura, A. (2005). The Convex Subclass Method: Combinatorial Classifier Based on a Family of Convex Sets. In: Perner, P., Imiya, A. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2005. Lecture Notes in Computer Science(), vol 3587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11510888_10
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DOI: https://doi.org/10.1007/11510888_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26923-6
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