Algorithm 479: A minimal spanning tree clustering method
Communications of the ACM
On O(N^4) Algorithm to Contstruct all Vornoi Diagrams for K Nearest Neighbor Searching
Proceedings of the 10th Colloquium on Automata, Languages and Programming
A 3-space partition and its applications
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
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This paper deals with the relationship between cluster analysis and computational geometry describing clustering strategies using a Voronoi diagram approach in general and a line separation approach to improve the efficiency in a special case. We state the following theorems :The set of all centralized 2-clusterings (S1,S2) of a planar point set S with |S1|=a and |S2|=b is exactly the set of all pairs of labels of opposite Voronoi polygons va(S1,S) and vb(S2,S) of Va(S) and Vb(S) respectively.An optimal centralized 2-clustering [centralized divisive hierarchical 2- clustering] can be constructed in &Ogr;(n n1/2 log2n + UF(n) n n1/2 + PF(n)) [&Ogr;(n n1/2 log3n + UF(n) n n1/2 + PF(n)) respectively] steps with PF(n) and UF(n) being the time complexity to compute and update a given clustering measure f.