TECHNIQUES OF APPROXIMATION FOR BUILDING TWO TREE STRUCTURES

Publisher Summary This chapter presents two new algorithms, one for building a hierarchic tree clustering and the other providing with a non-hierarchic tree representation. Both algorithms start with a distance or a dissimilarity matrix. The chapter also presents a comparison of the results with those of classical algorithms, such as average link agglomerative method and minimum spanning tree. Among clustering methods, the most popular are the sequential, agglomerative, hierarchic, non-overlapping techniques (SAHN). The chapter presents a different algorithmic approach, which is neither agglomerative nor divisive. Any scaled hierarchic tree may be associated with an ultrametric distance. The first algorithm discussed in the chapter, works up the distance matrix, modifying step by step its values to fulfill the ultrametric inequality. The second algorithm is designed to build up an additive tree metric out of the given dissimilarities. It works in an analogous way, striving to meet with the four-point condition; this condition is the characteristic property of additive trees, in which the distance between two vertices is measured as the sum of the edge lengths along the path joining them.