A new algorithm for seriation and its use in similarity dendrograms

A new algorithm (DSA: Direct Seriation Algorithm) for the seriation (optimal re-ordering of the objects) is described. Seriation can be applied also to make easier the interpretation of the dendrograms obtained with many clustering techniques. The algorithm directly works on the similarity dendrogram, instead of the similarity matrix, by translation or rotation of the leaves of one or more branches of the dendrogram. DSA maximises an objective function, the sum of the similarities between objects adjacent on the abscissa of the dendrogram. The algorithm has been tested on some real and simulated data, from 11 to 300 objects about. In the case of unidimensional data, where the optimal order of the objects is known (the order of the variable) the algorithm always reaches rapidly the underlying order.