AKth Nearest Neighbour Clustering Procedure
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1983 · Volume 45 · Issue 3
DOI: 10.1111/j.2517-6161.1983.tb01262.x
Abstract
Due to the lack of development in the probabilistic and statistical aspects of clustering research, clustering procedures are often regarded as heuristics generating artificial clusters from a given set of sample data. In this paper, a clustering procedure that is useful for drawing statistical inference about the underlying population from a random sample is developed. It is based on the uniformly consistentkth nearest neighbour density estimate, and is applicable to both case-by-variable data matrices and case-by-case dissimilarity matrices. The proposed clustering procedure is shown to be asymptotically consistent for high-density clusters in several dimensions, and its small-sample behaviour is illustrated by an empirical example.
Keywords
clustering procedure, high-density clusters, kth nearest neighbour density estimation, set-consistency
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