Inductive clustering and twofold approximations in nearest neighbor clustering

Authors:
Sadaaki Miyamoto;Satoshi Takumi
Affiliations:
Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan
Venue:
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
Year:
2012

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Abstract

The aim of this paper is to study the concept of inductive clustering and two approximations in nearest neighbor clustering induced thereby. The concept of inductive clustering means that natural classification rules are derived as the results of clustering, a typical example of which is the Voronoi regions in K-means clustering. When the rule of nearest prototype allocation in K-means is replaced by nearest neighbor classification, we have inductive clustering related to the single linkage in agglomerative hierarchical clustering. The latter method naturally derives two approximations that can be compared to lower and upper approximations for rough sets. We thus have a method of inductive clustering with twofold approximations related to nearest neighbor classification. Illustrative examples show implications and significances of this concept.