Clustering tendency

If there is no structure will be more or less equal to and H not far from 0.5. If there is clustering tendency, then Sm > and H will be higher than 0.5. 

J. Jurs and R.G. Lawson, New index for clustering tendency and its application to chemical problems. Chemom. Intell. Lab. Syst., 10 (1991) 81-83. 

Many other subjects are important to achieve successful pattern recognition. To name only two, it should be investigated to what extent outliers are present, because these can have a profound influence on the quality of a model and to what extent clusters occur in a class (e.g. using the index of clustering tendency of Section 30.4.1). When clusters occur, we must wonder whether we should not consider two (or more) classes instead of a single class. These problems also affect multivariate calibration (Chapter 36) and we have discussed them to a somewhat greater extent in that chapter. 

Since cluster analysis will only give sensible results if there is a grouping structure inherent in the data, methods have been developed that check the clustering tendency, that is, they check for the existence of subgroups with higher... 

In presence of clustering tendency, dydi) will tend to be smaller than du(i), and thus H will be larger than 0.5 and at most be 1. Practically, the Hopkins statistic is computed for several random selections of points, and the average of all results for H is used for a decision if this average is greater than 0.75 then the null hypothesis can be rejected with a high confidence. 

A very different approach to characterize clustering tendency is based on the frequency distributions of the lengths of the edges in the minimum spanning tree connecting the objects in the real data and in uniformly distributed data (Forina et al. 2001). 

Fernandez Piema, J. A., Massart, D. L. Anal. Chim. Acta 408, 2000, 13-20. Improved algorithm for clustering tendency. 

Forina, M., Lanteri, S., Esteban Diez, I. Anal. Chim. Acta 446, 2001, 59-70. New index for clustering tendency. 

A considerable solvent dependence has been reported by Debye and coworkers32 33 in their already mentioned study of a-monoglycerides in benzene, chlorobenzene, and chloroform. The authors found a correlation between the cohesive energy densities of the solvents and the clustering tendency of the nonionic surfactants with decreasing cohesive energy the aggregation increased. In chloroform no micelles were found. 

An expression for the clustering tendency of a monomer in a multi-component copolymerization, that is its tendency to add to a growing chain ending in a monomer unit of the same type, has been proposed by Seiner (42). 

Seiner, J. A. Clustering tendency in multicomponent polymerisation systems. Polymer Letters 2, 985 (1964). 

Further, Zimm and Zimm and Lundberg introduced the notion of cluster integral G lv to characterize the solvent clustering in the systems solvent (1)—polymer (protein) (2). They called G v a cluster integral , because the quantity q> G lv is the mean number of type 1 molecules in excess of the mean concentration of type 1 molecules in the neighborhood of a given type 1 molecule thus, it measures the clustering tendency of the type 1 molecules . 

The physical picture is as follows a batch of A and B particles have been mixed until equilibrium has been reached. There are no segregating or clustering tendencies therefore, A is considered to be randomly distributed throughout the mixture. If this is true, then the probability of finding a particle of type A at any point in the mixture is a constant equal to the proportion of that kind of particle in the whole mixture. This key statement immediately identifies the distribution of spot sample compositions (expressed in terms of number of A particles or particle... 

Statistical methods were used by O Kelly and Fortune (1983) to relate microscopically determined silicate percentages and clustering tendencies to grindability. 

The result we have obtained expresses a clustering tendency of molecules of the same mass. This clustering tendency may also be obtained by calculating the force between two light isotopes imbedded in a matrix of heavy isotopes (or inversely). This point of view has been considered recently by Montroix and Potts [1955]. 

In-line monitoring of EVA extrusion was carried out using in-line fibre optic Raman spectroscopy. Vinyl acetate content in the random copolymer and melt indices of various grades of the EVA were determined and vinyl acetate content in the samples correlated using linear least squares andPLS analysis. Hierarchical Cluster analysis was employed as a pattern recognition technique to follow the natural clustering tendencies of the EVA samples. 10 refs. 

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