Ward s clustering

Wild DJ, Blankley J. Comparison of 2D fingerprint types and hierarchy level selection methods for structural grouping using Ward s clustering. J Chem Inf Comput Sci 2000 40 155-62. 

D Fingerprint Types and Hierarchy Level Selection Methods for Structural Grouping Using Ward s Clustering. 

Table 9.3 A comparison of the single-linkage, complete-linkage and average-linkage cluster methods using the data in Table 92 The figures in parentheses indicate the distance between the clusters as they are formed In this particular case Ward s clustering follows the same order of cluster formation as the group average method.

Fig. 22.17 Comparison of (a) principal components analysis, (b) non-linear mapping, (c) Ward s cluster analysis and (d) Kohonen mapping to display similarity of 15 substituents characterized by five para substituent constants (tt, F, R, MR and /.).

A fourth hierarchical method that is quite popular is Ward s method [Ward 1963]. This method merges those two clusters whose fusion minimises the information toss due to the fusion. Information loss is defined in terms of a function rvhich fdr each cluster i corresponds to the total sum of squared deviations from the mean of the cluster ... 

Fig. 8.8. Result of cluster analysis of 88 German wines according to Ward s method (Thiel et al. [2004])...

There exist several methods of hierarchical clustering which use diverse measures of distance or similarity, respectively, e.g., single linkage, complete linkage, average linkage, centroid linkage, and Ward s method (Sharaf et al. [1986], Massart et al. [1988], Otto [1998] Danzer et al. [2001]). 

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. 

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

Prior to analysis, the Raman shift axes of the spectra were calibrated using the Raman spectrum of 4-acetamidophenol. Pretreatment of the raw spectra, such as vector normalization and calculation of derivatives were done using Matlab (The Mathworks, Inc.) or OPUS (Bruker) software. OPUS NT software (Bruker, Ettlingen, Germany) was used to perform the HCA. The first derivatives of the spectra were used over the range from 380 cm-1 to 1700 cm-1. To calculate the distance matrix, Euclidean distances were used and for clustering, Ward s algorithm was applied [59]. 

Fig. 4.3. Dendrogram resulting from cluster analysis containing 91 spectra from 15 tree species (see also Table 4.2). Cluster analysis was done on first derivatives over the spectral range 380 cm-1 to 1700 cm-1). The distance matrix was calculated using Euclidean distance and Ward s algorithm was applied for clustering. Spectra were measured after decomposition of carotenoid molecules with 633 nm irradiation. For example, spectra of each species are shown in Fig. 4.1. Reprinted with permission from [52]...

Figure 7.1 Authentication of monovarietal virgin olive oils results of applying clustering analysis to volatile compounds. The Mahattan (city block) distance metric and Ward s amalgamation methods were used in (a) the Squared Euclidean distance and (b) complete linkage amalgamation methods. Note A, cv. Arbequina (6) C, cv. Coratina (6) K, cv. Koroneiki (6) P, cv. Picual (6) 1, harvest 1991 2, harvest 1992. Olives were harvested at three levels of maturity (unripe, normal, overripe) (source SEXIA Group-Instituto de la Grasa, Seville, Spain).

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