Ward’s algorithm

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]...

We applied three hierarchical clustering methods to the same 32 data sets used in the previous section for partitional clustering (1) simulated annealing with the criterion in equation (11) (2) simulated annealing with the criterion in equation (12) and (3) Ward s algorithm. Each method generated a separate dendrogram for each data set. 

A dendrographic analysis of all FTIR measurements at sites of atheromas (employing the d-value distances measure. Ward s algorithm, together with the... 

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