Linkage methods

There is a wide variety of hierarchical algorithms available and it is impossible to discuss all of them here. Therefore, we shall only explain the most typical ones, namely the single linkage, the complete linkage and the average linkage methods. 

Single linkage methods have a tendency to chain together ill-defined clusters (see Fig. 30.8). This eventually leads to include rather different subjects (A to X of Fig. 30.8) into the same long drawn-out cluster. For that reason one sometimes... 

An example of an application is shown in Fig. 30.10. This concerns the classification of 42 solvents based on three solvatochromic parameters (parameters that describe the interaction of the solvents with solutes) [13]. Different methods were applied, among which was the average linkage method, the result of which is shown in the figure. According to the method applied, several clusterings can be found. For instance, the first cluster to split off from the majority of solvents consists of solvents 36, 37, 38, 39, 40, 41, 42 (t-butanol, isopropanol, n-butanol. 

Of the four different methods of cluster analysis applied, the method of Ward described in the Clustan User Manual (10), worked best when compared to the single-, complete-, or average-linkage methods. Using Ward s method, two clusters, Gn and Gm, are fused when by pooling the variance within two existing clusters the variance of the so formed clusters increases minimally. The variance or the sum of squares within the classes will be chosen as the index h of a partition. 

Protein Polymer and molecular weight Degree of amino group substitution and linkage method Stage in Clinical Trials Ref. 

Highly effective host molecules for metal ions have been designed with 2,9-bis(bro-momethyl)-l,10-phenanthroline (2) by the cross-linkage method [37]. By the reaction... 

There are a variety of ways to compute distances between data points and clusters in hierarchical clustering. A few are shown in Figure 9.7. The single-linkage method... 

There are numerous further linkage methods, but it would be rare that a chemist needs to use too many combination of similarity and linkage methods, however, a good rule of thumb is to check the result of using a combination of approaches. 

Labeling antibody with an enzyme can be accomplished rapidly and efficiently by the gluteraldehyde linkage method. Other widely used methods for labeling antibodies with enzymes include those of Nakane and Kawaoi and Engvall and Perlmann. Voller has described in techni-... 

Figure 2. Schematic representation of fragment linkage methods. In A a tricyclic ring linker connects three previously placed key fragments avoiding bumping the receptor. In B a bump occurs (signalled by the arrow).

Feuer, H., Hooz, J. The Chemistry of the Ether Linkage Methods of formation of the ether linkage, in The Chemistry of Functional Groups (ed. Patai, S.), 445-498 (Wiley, New York, 1967). 

The main step used in hierarchical clustering algorithm in analyzing gene expression data is to compare every entity with all the other entities by calculating a distance. The calculation of the distance depends on the linkage method being implemented and the method of calculation of the actual distances. There are three major... 

The HC algorithm requires choice of a distance measure and linkage method. The distance measure quantifies the similarity or dissimilarity between two gene expression profiles. The Euclidean distance and the Pearson correlation (PC) coefficient have been widely used as distance measures to quantify the similarity between profiles. The centered PC similarity measure, r, between any two series of numbers X = [Xt, X2,..., X and Y = Yi, Y2,..., Y is the familiar PC coefficient used in linear regression. The distance measure is obtained by subtracting the correlation value from unity. The uncentered PC is obtained from the centered PC by setting the means of X and Y to zero. The uncentered PC is defined as... 

Intramolecular Ring Closure to Form a C—O—C Linkage Method A-5... 

---