Divisive methods

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]. 

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. 

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. 

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. 

There has been little development of polythetic divisive methods since the publication of the minimum-diameter method in 1991. Garcia et al. " developed a path-based approach with similarities to single-link. The method... 

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. 

US Environmental Protection Agency (1989) Office of Water Regulations and Standards, Industrial Technology Division. Method 1613 Tetra-through octa-chlorinated dioxins and furans by isotope dilution HRGC/HRMS... 

The spatial solution is the same as with the resistive charge division method and is given by expression The resolution is solely a function of the capacitance of the read-out elements, and so there is no fundamental improvement to be expeced as compared to the resistive charge division. However, the elegant read-out method has the advantage that the read-out plane can be produced with high mechanical accmacy, and that a minimum nimiber of components are necessary. 

Sato, Tanaka, and Yao also reported a parallel implementation of the AMBER MD module.The target machine, the APIOOO distributed-memory parallel computer developed at Fujitsu, consisted of up to 1024 processor elements connected with three different networks. To obtain a higher degree of parallelism and better load balance between processors, a particle division method was developed to randomly allocate particles to processors. Experiments showed that a problem with 41,095 atoms can be processed 226 times faster with a 512-processor APIOOO than by a single processor. 

Considerably higher selectivity can be achieved by the subtraction—division method, in which subtraction (separation) of a particular group of components from the test sample takes place in the first stage and GC analysis of the isolated (concentrated) components in the second stage. Thermal or chemical methods can be used for isolation. Thus, the use of triethanolamine, which selectively retains carbon dioxide and hydrogen sulphide, for determining impurities of these gases in ethylene and propylene has been described... 

Division method Distribution range of spontaneous combustion dangerous area (m) Width of spontaneous combustion dangerous area (m)... 

I have thus returned to the early point in my joint researches with Otto Scherbaum at which we switched (Zeuthen and Scherbaum, 1954) from repetitive, or one shock per division, methods to development of the multi-shock procedure for cell synchronization. The present time may be suitable for this because of the wealth of information now available for the multi-shock-induced synchronous Tetrahymena systems, and because of the existence of easy methods for automating temperature programs and for tracing periodic division activities in small parallel populations (technical descriptions in Plesner et al., 1964). 

Class and division method Mainly followed in North America and... 

Zone division method Mainly followed by Europe and other parts of the world. However, with introduction of lEC standards this is somewhat similar to the second type and is mainly followed globally even the NEC has included zone divisions. 

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