Divisive clustering

As indicated, agglomerative methods start with single objects or pairs of objects step by step clusters are formed which are finally united in one cluster. Divisive methods, on the other hand, start from the one cluster of all objects and divide it step by step. One drawback of the commonly used agglomerative methods is that clusters formed may not be broken up in a subsequent step. With certain algorithms this sometimes leads to so-called inversions in the dendrogram, i.e. crossing lines in the diagram. 

SuNNER, J. Beech, I. B. Hiraoka, K. On the distributions of ion/neutral molecule clusters in electrospray and laser spray—A cluster division model for the electrospray process. J. Am. Soc. Mass Spectrom. 2006, 17, 151-162. 

Extrahypothalamic OX-B-like immunoreactivity, reminiscent to that of CRF, has been described in clustered GABAergic neuronal populations, in the lateral division of central nucleus ofthe amygdala, the bednucleus of the stria terminalis, and in the hippocampus. Moreover, ectopic expression of preproorexin mRNA in the gut, ependymal cells, neuroblastomas, and of orexin receptors in adrenal gland, cancer and hematopietic stem cells suggests yet unexplored roles of orexins as paracrine factors controlling blood-brain barrier, and tumor or stem cell function. 

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. 

The nucleus contains bundles of a fibrous material known as chromatin, which is made up of mixed proteins and deoxyribonucleic acid (DNA), the substance that carries the genetic information of the living organism of which the cell is a component. All cells replicate by division. When a cell replicates, DNA in the chromatin of the nucleus passes the genetic information from one generation to the next one. As the cell divides, the chromatin clusters into rodlike structures known as chromo-... 

L/evelopment of sophisticated surface analytical techniques over the past two decades has revived interest in the study of phenomena that occur at the electrode-solution interface. As a consequence of this renewed activity, electrochemical surface science is experiencing a rapid growth in empirical information. The symposium on which this book was based brought together established and up-and-coming researchers from the three interrelated disciplines of electrochemistry, surface science, and metal-cluster chemistry to help provide a better focus on the current status and future directions of research in electrochemistry. The symposium was part of the continuing series on Photochemical and Electrochemical Surface Science sponsored by the Division of Colloid and Surface Chemistry of the American Chemical Society. 

Divisive methods In the first level of the hierarchy, all n objects are in one single cluster. In the next level, this cluster is split into two smaller clusters. The next level again splits one of the clusters into two smaller clusters, and so on, until finally each object forms a separate cluster. 

Splitting a cluster is computationally more demanding than merging two clusters, because not only the cluster to be split has to be found, but also the objects that will form two new clusters have to be identified. Therefore, divisive methods are not very commonly used. 

After about 5 days and several cycles of cell division, the totipotent cells form a hollow sphere of cells called a blastocyst. The blastocyst has an outer layer of cells surrounding clusters of cells. Those cells on the outside continue... 

Central Nervous System (CNS). The human nervous system is an integrated communication network that sends and receives information throughout the body. This network is divided into two main divisions central nervous system (CNS) and peripheral nervous system (PNS). The CNS is the command center of this network and is made up of the brain and spinal cord. The PNS is the interface of the nervous system with the rest of the body and the external environment. It is comprised of nerve fibers and small clusters of nerve cells known as ganglia. 

Cultivated marine bacteria are scattered throughout the phylogenetic tree of the domain Bacteria. However, at lower phylogenetic levels, clusters of marine bacteria have been found which are distinct from those of terrestrial origin. One example is the so-called a3-subgroup of the a-Proteobacteria subclass of the division Proteobacteria, the Roseobacter clade [20]. A marine group of Actinobacteria [21] has been described, which has, to date, however not been cultivated. 

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. 

FIGURE 2.12 Scheme of agglomerative and divisive clustering approaches illustrated with five objects described by two variables. 

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

Figure 4. Dendrogram showing sub-division of main chemical group according to cluster analysis (Euclidean distance Ward s method).

---