John C. Gower

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We assemble here properties of certain dissimilarity coefficients and are specially concerned with their metric and Euclidean status. No attempt is made to be exhaustive as far as coefficients are concerned, but certain mathematical results that we have found useful are presented and should help establish similar properties for other coefficients. The(More)
A set of n base points Pi (i = 1,2, ... ,n), with known co-ordinates relative to orthogonal axes, and a further point Pn +l , with known distance from each of the base set, are given. The co-ordinates of Pn +l relative to the axes of the base set are found. The formula is particularly simple when the base set is referred to its principal axes, when the(More)
Consider N entities to be classified (e.g., geographical areas), a matrix of dissimilarity between pairs of entities, a graph H with vertices associated with these entities such that the edges join the vertices corresponding to contiguous entities. The split of a cluster is the smallest dissimilarity between an entity of this cluster and an entity outside(More)
Triadic distances t defined as functions of the Euclidean (dyadic) distances a1, a2, a3 between three points are studied. Special attention is paid to the contours of all points giving the same value of t when a3 is kept constant . These isocontours allow some general comments to be made about the suitability, or not, for practical investigations of certain(More)
This paper is about Guttman's method for assigning optimal numerical scores to categorical variables, and related methods, which underlie Healy's TW1 and TW2 bone-age standards. In giving the methodological underpinning, Healy and Goldstein noted that the scores they obtained could depend critically on how essential constraints were specified, thus(More)