Hi, Brian Ripley already replied "don't use average linkage"... You may think about k-medoid (pam) in package cluster instead. However, often average linkage is not such a bad choice, and if you really want to use it for your data, you may try the following: Among the hierarchical methods, single linkage has the smallest problem with equal distances, because possible agglomerations based on equal distances between clusters are all carried out regardless of the order. If at some step the smallest between cluster-distance is d(a,b)=d(a,c)<d(b,c), it may happen that a and b are merged first, or a and c are merged first, but before merging anything else with distance larger than d(a,b), a, b *and* c are merged. Thus, you have order dependence only between the steps where you merge clusters with the same distance, but not afterwards.
If your problem occurs only at a low level of agglomeration (and you don't have situations where d(a,b) and d(a,c) are small and d(b,c) is very large; I do not know if the triangle inequality holds for your data), you may do some first steps with Single Linkage and then continue with average linkage (I haven't thought about if this can be done in R without extra effort). But if you have already observed that the averarge linkage outcome depends critically (from the viewpoint of interpretation) on the order of points, then it seems that you are in an unstable situation, if you are able to define a unique clustering or not. Christian On Wed, 3 Dec 2003, Bruno Giordano wrote: > Hi, > I'm clustering objects defined by categorical variables with a hierarchical > algorithm - average linkage. > My distance matrix (general dissimilarity coefficient) includes several > distances with exactly the same values. > As I see, a standard agglomerative procedure ignores this problems, simply > selecting, above equal distances, the one that comes first. > For this reason the analysis in output depends strongly on the orderings of > the objects within the raw data matrix. > Is there a standard procedure to deal with this? > Thanks > Bruno > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help > *********************************************************************** Christian Hennig Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg [EMAIL PROTECTED], http://www.math.uni-hamburg.de/home/hennig/ ####################################################################### ich empfehle www.boag-online.de ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
