Classification and Seriation by Iterative Reordering of a Data Matrix

A heuristic algorithm is presented which searches for the reordering of rows and columns of a symmetric similarity matrix in order to fulfill, at least approximatively, the Robinson condition. The algorithm uses pairwise interchanges in constructive and iterative strategies. — A rectangular m×n matrix of two different sets of parameters can be treated by first converting or preprocessing the data into two square similarity matrices, each for rows and columns, before applying the above mentioned technique. The resulting orderings for rows and columns in the m×n matrix yields a pattern whose underlying structure can be interpreted by inspection. — Agglomerative hierarchical classification can be obtained after the rearrangement using only neighbouring objects (rows, columns). — A computer program has been implemented with a fast reordering algorithm and a graphical dendrogram presentation.1