Cluster Analysis: A Survey by Dr. Patrick L. Odell, Dr. Benjamin S. Duran (auth.)

By Dr. Patrick L. Odell, Dr. Benjamin S. Duran (auth.)

A great quantity of labor has been performed over the past thirty years in cluster research, with an important quantity taking place considering 1960. a considerable component of this paintings has seemed in lots of journals, together with a variety of utilized journals, and a unified ex­ place is missing. the aim of this monograph is to provide such an exposition via providing a quick survey on cluster research. the most purpose of the monograph is to offer the reader a brief account of the prob­ lem of cluster research and to show to him a number of the points thereof. With this reason in brain a lot aspect has been passed over, relatively in as far as designated examples are thought of. lots of the references said in the textual content comprise examples and the reader can seek advice them for more information on particular issues. Efforts have been made to incorporate within the reference part all papers that performed a task in constructing the "theory" of cluster research. Any omission of such references was once now not intentional and we might have fun with realizing approximately them. Many references to papers in utilized journals also are contained, notwithstanding, the list-is faraway from being entire. This monograph has been enormously inspired by means of the paintings of many folks, such a lot particularly, J. A. Hartigan, D. Wishart, J. ok. Bryan, R. E. Jensen, H. D. Vinod, and M. R. Rao. numerous parts of the monograph have been stimulated via examine played lower than the help of NASA Manned Spacecraft middle, Earth Observations department, less than agreement NAS 9-12775.

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Alternatively, the numerator can be taken to be the total number of feasible arcs. In either case the dynamic pro- gramming procedure is quite efficient. However, the dynamic program- ming procedure requires more computer memory and consequently slowaccess storage could make it less useful than complete enumeration. In any event for large nand m one might be better off using some other teChnique such as ISODATA [18] or hierarchial procedures. In order to illustrate Jensen's formulation consider the example = 6 and m = 3.

Hierarchical tech- However, these techniques operate on subclasses of clustering alternatives and there is no guarantee that the solution is the optimal one or even close to the optimal one. In clustering by complete enumeration it is possible to store the data matrix X and operate directly on it without having to resort to auxilary storage. However, the amount of computation necessary warrants the task virtually hopeless in spite of the high speed computers presently available. ) Attempts to develop dynamic programming techniques to solve the cluster problem will probably require rapid access storage.

The function W will be computed for each of the fifty clusters in stage 1. At the second stage we will have 2 clusters corresponding to the first two components of the distribution forms, that is, we will have clusters of size {4} and ill, {3} and {2}, or {2} and {2}. stage 2 will be 5 or 4. (:) Thus the total number of objects at The number of ways of obtaining 5 objects is (~)= 90. The number of ways of obtaining 4 49 objects is (:) + (:) (:) (~) = 150. The total number of ways of ob- taining objects in stage 2 is therefore 240.

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