Stage Clustering

Multi-stage clustering is a variation of the traditional clustering algorithm. Multiple stages make the clustering both easier to implement and more powerful, in that it can consider operators in groups rather than individually. 

There are several advantages of multi-stage clustering  

Two Clustering Stages, with the Clusters Cut horn the First Stage Used as the Basis for the Second Stage 

Multi-stage clustering allows operators to be considered as groups. This is particularly appropriate for architectural partitioning where large groups of operators are considered. 

Different Groupings Result from Clustering with 1 and 2 Stages 

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A two-stage clustering process serves to illustrate the use of the adaptive distance ... 

To choose architectural partitions, APARTY uses a unique multistage clustering technique. Multi-stage clustering, which is described in Section 4.3, is based on an established clustering algorithm that has... 

Comparison. This cluster stage is very similar to the clustering done by McFarland and Rajan, however multi-stage clustering allows groups of operators to be considered, making this more appropriate for the architectural partitioning application. 

Figure 2 Scatter plot of clustering results Figure 3 Definition of Damage Stages...

There appear to be two stages in the collapse of emulsions flocculation, in which some clustering of emulsion droplets takes place, and coalescence, in which the number of distinct droplets decreases (see Refs. 31-33). Coalescence rates very likely depend primarily on the film-film surface chemical repulsion and on the degree of irreversibility of film desorption, as discussed. However, if emulsions are centrifuged, a compressed polyhedral structure similar to that of foams results [32-34]—see Section XIV-8—and coalescence may now take on mechanisms more related to those operative in the thinning of foams. 

Another important characteristic of the late stages of phase separation kinetics, for asynnnetric mixtures, is the cluster size distribution fimction of the minority phase clusters n(R,z)dR is the number of clusters of minority phase per unit volume with radii between R and + cW. Its zeroth moment gives the mean number of clusters at time r and the first moment is proportional to die mean cluster size. 

One of the motivations for studying Van der Waals complexes and clusters is that they are floppy systems with similarities to the transition states of chemical reactions. This can be taken one stage further by studying clusters that actually are precursors for chemical reactions, and can be broken up to make more than one set of products. A good example of this is H2-OH, which can in principle dissociate to fonn either H2 + OH or H2O + H. Indeed, dissociation to H2 O -t H is energetically favoured the reaction H2 + OH—> H2 O -t H is exothennic by about 5000... 

In dissimilarity-based compound selection the required subset of molecules is identified directly, using an appropriate measure of dissimilarity (often taken to be the complement of the similarity). This contrasts with the two-stage procedure in cluster analysis, where it is first necessary to group together the molecules and then decide which to select. Most methods for dissimilarity-based selection fall into one of two categories maximum dissimilarity algorithms and sphere exclusion algorithms [Snarey et al. 1997]. 

Fig. I. Experimental setup the clusters are emitted from the cluster condensation cell, passing as a particle beam through a differential pumping stage into the focus of a time-of-flight mass spectrometer, where they are ionized by a laser pulse.

After condensation, the clusters are transported by the He-flow through a nozzle and a differential pumping stage into a high vacuum chamber. For ionization of the clusters, we used excimer and dye laser pulses at various wavelengths. The ions were then mass analyzed by a time-of-flight mass spectrometer, having... 

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