Journal ArticleDOI
A Dynamic Programming Algorithm for Cluster Analysis
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A dynamic programming approach is presented that reduces the amount of redundant transitional calculations implicit in a total enumeration approach to partitioning N entities into M disjoint and nonempty subsets clusters.Abstract:
This paper considers the problem of partitioning N entities into M disjoint and nonempty subsets clusters. Except when both N and N-M are very small, a search for the optimal solution by total enumeration of all clustering alternatives is quite impractical. The paper presents a dynamic programming approach that reduces the amount of redundant transitional calculations implicit in a total enumeration approach. A comparison of the number of calculations required under each approach is presented in Appendix A. Unlike most clustering approaches used in practice, the dynamic programming algorithm will always converge on the best clustering solution. The efficiency of the dynamic programming approach depends upon the rapid-access computer memory available. A numerical example is given in Appendix B.read more
Citations
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An optimal graph theoretic approach to data clustering: theory and its application to image segmentation
Z. Wu,Richard M. Leahy +1 more
TL;DR: A novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated, resulting in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices.
Journal ArticleDOI
K‐means clustering: A half‐century synthesis
TL;DR: This paper synthesizes the results, methodology, and research conducted concerning the K-means clustering method over the last fifty years, leading to a unifying treatment of K-Means and some of its extensions.
Journal ArticleDOI
Cluster analysis and mathematical programming
Pierre Hansen,Brigitte Jaumard +1 more
TL;DR: In this article, a survey of clustering from a mathematical programming viewpoint is presented, focusing on solution methods, i.e., dynamic programming, graph theoretical algorithms, branch-and-bound, cutting planes, column generation and heuristics.
Journal ArticleDOI
Numerical taxonomy with fuzzy sets
TL;DR: A solution obtained without prior knowledge of labelled pattern structure is offered in support of contention that the fuzzy clustering technique proposed affords a comparatively reliable criterion for a posteriori evaluation of cluster validity.
References
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Book
Nonparametric statistics for the behavioral sciences
TL;DR: This is the revision of the classic text in the field, adding two new chapters and thoroughly updating all others as discussed by the authors, and the original structure is retained, and the book continues to serve as a combined text/reference.
Journal ArticleDOI
Hierarchical Grouping to Optimize an Objective Function
TL;DR: In this paper, a procedure for forming hierarchical groups of mutually exclusive subsets, each of which has members that are maximally similar with respect to specified characteristics, is suggested for use in large-scale (n > 100) studies when a precise optimal solution for a specified number of groups is not practical.