equilibrium cluster
Nearest Neighbour Equilibrium Clustering
A novel and intuitive nearest neighbours based clustering algorithm is introduced, in which a cluster is defined in terms of an equilibrium condition which balances its size and cohesiveness. The formulation of the equilibrium condition allows for a quantification of the strength of alignment of each point to a cluster, with these cluster alignment strengths leading naturally to a model selection criterion which renders the proposed approach fully automatable. The algorithm is simple to implement and computationally efficient, and produces clustering solutions of extremely high quality in comparison with relevant benchmarks from the literature. R code to implement the approach is available from https://github.com/DavidHofmeyr/ I. Introduction Clustering, or cluster analysis, is the task of partitioning a set of data into groups, or clusters, which are seen to be relatively more homogeneous than the data as a whole. Clustering is one of the fundamental data analytic tasks, and forms an integral component of exploratory data analysis. Clustering is also of arguably increasing relevance, as data are increasingly being collected/generated from automated processes, where typically very little prior knowledge is available, making exploratory methods a necessity. In the classical clustering problem there is no explicit information about how the data should be grouped, and various interpretations of how clusters of points may be defined have led to the development of a very large number of methods for identifying them. Almost universally, however, clusters are determined from the geometric properties of the data, with pairs of points which are near to one another typically being seen as likely to be in the same cluster and pairs which are distant more likely to be in different clusters.
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