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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 happening seeing that 1960. a considerable element of this paintings has seemed in lots of journals, together with quite a few utilized journals, and a unified ex­ place is missing. the aim of this monograph is to provide such an exposition by way of featuring a short survey on cluster research. the most reason of the monograph is to offer the reader a short account of the prob­ lem of cluster research and to show to him many of the points thereof. With this cause in brain a lot element has been passed over, rather in as far as particular examples are thought of. lots of the references acknowledged in the textual content comprise examples and the reader can seek advice them for additional info on particular themes. Efforts have been made to incorporate within the reference part all papers that performed a job in constructing the "theory" of cluster research. Any omission of such references was once no longer intentional and we might enjoy realizing approximately them. Many references to papers in utilized journals also are contained, although, the list-is faraway from being whole. This monograph has been vastly inspired by way of the paintings of many of us, such a lot significantly, J. A. Hartigan, D. Wishart, J. okay. Bryan, R. E. Jensen, H. D. Vinod, and M. R. Rao. a number of parts of the monograph have been prompted through examine played below the aid of NASA Manned Spacecraft heart, Earth Observations department, below agreement NAS 9-12775.

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See Wishart (396). For example, changes in scale will modify the For a discussion of this and other objections His paper also contains a discussion of the methods outlined above. Friedman and Rubin (122) discuss some invariant criteria for grouping data. 7. An Algorithm for Heirarchical Clustering The scheme in hierarchical clustering is to consider I = {I l ,I 2 , ••• ,I n } as a set of clusters {II}' {I 2 }, ••• ,{I n } and then select those two clusters, say I. , which are nearest in some 1 J sense, and "clumping" or "fusing" them into cluster set of n-l clusters becomes 01,,,, cluster.

25. 26. 27. 28. 29. 30. 3l. 32. 33. 3A. 35. 36. 37. 38. 39. 40. H. A2. 43. 44. 45. 46. 47. 48. A9. 50. ( 1, (1, (1, (1, (5, (1, ( 1, ( 1, (6, ( 1, (1, (5, (5, ( 1, (5, ( 1, ( 1, (1, ( 1, ( 1, (1, ( 1, (1, (1, (1, (2, (2, (2 , (2, (2 , (2, (3 , (3, (3, (4, (1, (1, (1, ( 1, (1, (2, (2, (2, (2, (3 , (3, (3 , (A, (A, (5, 2, 2, 2, 5, 2, 2, 2, 6, 2, 2, 5, 6, 2, 5, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 3, 3, 3, 4, 4, 5, 4, 3, 3, 5, 3, 3, 3, 6, 3, 3, 5, 6, 3, 3, 3, 6, 3) 4) 5) 6) 4) 5 6) 5) 6) 6) 4) 5) 6) 5) 6) 6) 5) 4, 6) 5, 6) 5, 6) 2) 3) 4) 5) 6) 3) 4) 5) 6) 4) 5) 6) 5) 6) 6) Stage 3 Stage 2 4) 5) 4) 4) 4) 6) 4) 4) 4) 6) 4) 4) ::~ 4) 1.

The total number of clusters available for the first stage, denoted by NS(l) is given by NS (1) max(l) E j=min(l) (j). 4) The first stage of the algorithm consists of computing the quantity T(z) for each of the NS(l) possible clusters. In general the maximum number of objects in anyone state in stage k is equal to the maximum sum of distribution form components 56 from stages 1 through k inclusive. The minimum number of states is the minimum sum of the distribution form components. 6) and min(k) if n is an even multiple of m.

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