Clustering in N dimensions by use of a system of forces

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Abstract
This paper describes a model and associated computer program for carrying out clustering of elements in a space of a predetermined number of dimensions. In addition to clustering of elements, the model may be used for multi‐dimensional scale analysis and for construction of sociograms. The model takes as input data a set of ‘affinities’ between elements, the inverse of which may be considered as psychological or sociological distances. It then moves elements in a Euclidean n‐space toward the point at which the geometric distance is equal to the given psychological or social ‘distance,’ as if a set of attractive and repulsive forces was acting upon each element from other elements. The second major portion of the paper consists of ten examples, which are analyzed by means of the accompanying computer program.