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Classical unidimensional scaling provides a difficult combinatorial task. A procedure formulated as a nonlinear programming (NLP) model is proposed to solve this problem. The new method can be implemented with standard mathematical programming software. Unlike the traditional procedures that...
A natural extension of classical metric multidimensional scaling is proposed. The result is a new formulation of nonmetric multidimensional scaling in which the strain criterion is minimized subject to order constraints on the disparity variables. Innovative features of the new formulation...
Clustering with a criterion which minimizes the sum of squared distances to cluster centroids is usually done in a heuristic way. An exact polynomial algorithm, with a complexity in O(N
p+1 logN), is proposed for minimum sum of squares hierarchical divisive clustering of points in a...
The set of k points that optimally represent a distribution in terms of mean squared error have been called principal points (Flury 1990). Principal points are a special case of self-consistent points. Any given set of k distinct points in R
induce a partition of R
into Voronoi regions...
A new set of derived variables is proposed for exhibiting grouped multivariate data in a small number of dimensions, in such a way as to highlight `extremeness' of one or more groups relative to the rest of the data. Such display can provide a useful exploratory tool in multivariate ranking and...
This paper studies the random indexed dendograms produced by agglomerative hierarchical algorithms under the non-classifiability hypothesis of independent identically distributed (i.i.d.) dissimilarities. New tests for classifiability are deduced. The corresponding test statistics are random...
I consider a new problem of classification into n(n ≥ 2) disjoint classes based on features of unclassified data. It is assumed that the data are grouped into m(M ≥ n) disjoint sets and within each set the distribution of features is a mixture of distributions corresponding to particular...
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