Choose this method to set the distance between clusters to the average distance between pairs of observations .This method tends to join clusters with small variances and is biased toward producing clusters with the same variance. ^{ 1 } Choose this method to set the distance between clusters to the squared Euclidean Distance between the means of each cluster. ^{ 2 }
1 A new dissimilarity measure, d* , is computed based on density estimates and adjacencies.You must specify the specific type of density linkage to be performed, in the Additional PROC CLUSTER Options field. Options include k th-nearest neighbor, uniform kernel, and hybrid.You must specify one of the following options:
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• HYBRID to specify the Wong hybrid clustering method. Choose this option to use the flexible- beta method developed by Lance and Williams (1967) ^{ 3 } .The BETA= n option is recommended ( n = the beta parameter, usually between 0 and -1, -0.25 is specified by default). Choose this option to use the combinatorial method developed independently by Sokal and Michener (1958) 1 and McQuitty (1966) ^{ 4 } . Choose this option to use the median method developed by Gower (1967) ^{ 5 } . This method is a modification of density linkage that ensures that all points are assigned to modal clusters before the modal clusters are permitted to join. The CLUSTER procedure supports the same three varieties of two-stage density linkage as of ordinary density linkage: k th-nearest neighbor, uniform kernel, and hybrid.You must specify one of the following options:
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• HYBRID to specify the Wong hybrid clustering method. Choose this method to set the distance between clusters to the ANOVA sum of squares between the two clusters summed over all the variables . At each generation, two clusters from the previous generation are merged to reduce the within-cluster sum of squares over all partitions. The sums of squares are easier to interpret when they are divided by the total sum of squares to give the proportions of variance (squared semipartial correlations).This method joins clusters to maximize the likelihood at each level of the hierarchy under the assumptions of multivariate normal mixtures, spherical covariance matrices, and equal sampling probabilities.
Sokal, R.R., and C.D. Michener. (1958) A statistical method for evaluating systematic relationships. University of Kansas Science Bulletin 38: 1409-1438.
Milligan, G.W. (1980) An examination of the effect of six types of error perturbation on fifteen clustering algorithms. Psychometrika 45: 325-342.
Lance, G. N. and Williams, W. T. (1967) A general theory of classificatory sorting strategies. I. hierarchical systems. Computer Journal 9: 373–380.
McQuitty, L. L. (1966) Similarity analysis by reciprocal pairs for discrete and continuous data. Educational and Psychological Measurement 26: 825–831
Refer to the SAS PROC CLUSTER documentation for more information.