Hierarchical divisive clustering

Thielemans, A., Derde, M. P., Rousseeuw, P., Kaufman, L., Massart, D, L. CLUE, a program for hierarchical divisive clustering , Elsevier, Amsterdam 1985... 

The hierarchical methods so far discussed are called agglomerative. Good results can also be obtained with hierarchical divisive methods, i.e., methods that first divide the set of all objects in two so that two clusters result. Then each cluster is again divided in two, etc., until all objects are separated. These methods also lead to a hierarchy. They present certain computational advantages [21,22]. 

E. Marengo and R. Todeschini, Linear discriminant hierarchical clustering a modeling and cross-validable divisive clustering method. Chemom. Intell. Lab. Syst., 19 (1993) 43-51. 

Little has been reported on the use of hierarchical divisive methods for processing chemical data sets (other than the inclusion of the minimum-diameter method in some of the comparative studies mentioned above). Recursive partitioning, which is a supervised classification technique very closely related to monothetic divisive clustering, has, however, been used at the GlaxoSmithKline and Organon companies. 

Hierarchical Monothetic Divisive Clustering Algorithms for Structure-Property Correlation. 

Divisive hierarchical simultaneous clustering procedures build a fuzzy hierarchy of objects and a fuzzy hierarchy of characteristics. Each node of the corresponding tree is labeled by a pair (C, D), where C is a fuzzy class of objects and D is a fuzzy class of characteristics. At the first level a binary fuzzy partition of data set X and the corresponding binary partition of characteristics set Y are computed. The classes that emerge are subdivided until no pair of real clusters can be obtained. 

A hybrid method, bisecting K-means, combines the divisive hierarchical and K-means methods to produce a controlled number of hierarchical document clusters. It has been shown to perform as good as or better than hierarchical methods while retaining the performance of the K-means approach [32]. The process of this method involves bisecting a selected cluster of documents (biggest or poorest quality) into two smaller clusters but optimizing the centroids to obtain new clusters with the best possible quality. An example of an implementation of this type of method is the Oracle Text hierarchical K-means algorithm. 

In order to develop the classifications presented in this section, we will apply the fuzzy divisive hierarchical clustering (FDHiC) procedure described in the theoretical section to different characteristic sets considered here. The hierarchical procedure obtained in this way is called fuzzy hierarchical characteristics clustering (FHiChC). 

There are two main types of clustering techniques hierarchical and nonhierarchical. Hierarchical cluster analysis may follow either an agglomerative or a divisive scheme agglomerative techniques start with as many clusters as objects and, by means of repeated similarity-based fusion steps, they reach a final situation with a unique cluster containing all of the objects. Divisive methods follow exactly the opposite procedure they start from an all-inclusive cluster and then perform a number of consecutive partitions until there is a bijective correspondence between clusters and objects (see Fig. 2.12). In both cases, the number of clusters is defined by the similarity level selected. 

Guenoche A, Hansen P, Jaumard B, Efficient algorithms for divisive hierarchical clustering with diameter criterion, J. Classif, 8 5-30, 1991. 

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