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If one wishes to use K-means on species abundance data, one has to compute a distance matrix using an appropriate, asymmetrical measure (see Chapter 2). if the computation is run from the raw data table, then the double zeros are counted as resemblances among objects, which is inappropriate. 3 below before running K-means on the matrix of objects by (transformed) species. This overview does by far not show all the clustering methods available. But it shows that numerous approaches exist, that these methods address different questions, focus on different aspects of the data and therefore do not necessarily yield the same results.

UPGMC joins the objects or groups that have the highest similarity (or the smallest distance), by Daniel Borcard Université de Montréal Université Laval Multivariate analysis - February 2006 10 replacing all the objects of the group produced by the centroid of the group. This centroid is considered as a single object at the next clustering step. A simple manner to achieve this is to replace, in the similarity matrix, the two rows and columns corresponding to the two objects about to join by a single series obtained by computing the averages of the similarities of the two objects with all the others.

Daniel Borcard Université de Montréal Université Laval Multivariate analysis - February 2006 12 The sum of squared distances is the same quantity as tho one called "error" in ANOVA. At each clustering step, Ward's method finds the pair of objects or clusters whose fusion increases as little as possible the sum, over all objects, of the squared distances between objects and cluster centroids. The within-cluster sum of squared errors can be computed either from the raw data, or as the mean of the squared distances among cluster members.

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