A Voronoi diagram based adaptive k-means-type clustering algorithm for multidimensional weighted data
This paper describes a solution to the following problem: Given a set of weighted data points, find the cluster center points, which minimize the least squared errors. The k-means-type methods produce good results, but usually the quality of the representation depends on an initial cluster configuration. Also this does not allow a variable number of clusters for a given error tolerance.
The proposed method removes these disadvantages by an adaptive sequential insertion of new clusters in those areas, where the largest errors occur. This can be done more efficiently by using multidimensional Voronoi diagrams and local procedures. The data points can be weighted and arbitrarily distributed in the Euclidean space. The weight of each point may be chosen by the user depending on the importance or correctness of that point. At the same time the method produces a hierarchical multidimensional triangulation of the data at different levels of accuracy.
KeywordsClustering algorithm Delaunay triangulation hierarchical representation k-means algorithm Voronoi diagram
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