Dendrogram plot

Figure 16.12. Hierarchical clustering dendrogram plotted from the Pearson correlation coefficients calculated across a series of experiments (Khan et al., 1998).

Figure 9.25 shows the MANOVA cluster (dendrogram plot) for stress data. 

The dendrogram plot where groups are paired based upon their normalized mean values... 

P.J. Lewi, H. Moereels and D. Adriaensen, Combination of dendrograms with plots of latent variables. Application of G-protein coupled receptor sequences. Chemom. Intell. Lab. Syst., 16 (1992) 145-154. 

Figure 11.3 Positive ion FIESMS spectra of crude cell extracts from Escherichia coli HB101 (A), Bacillus sphaericus DSM 28 (B), and Bacillus licheniformis NTCC 10341 (C). (D) A pseudo-3D plot of the first three discriminant functions (DF1-3) obtained from positive ion whole-cell DIESMS spectra of seven Bacillus subtilis strains (a-g) (E) the corresponding abridged dendrogram obtained from the same information as in D. (Adopted from Vaidyanathan et al.57)...

Due to the mainly qualitative nature of PCA, DFA, and HCA, the role of PyMS in microbiology has been somewhat restricted. For example, using these clustering methods, the use of PyMS to identify microorganisms can be a subjective process because it relies on the interpretation of complex scatter plots and dendrograms. Furthermore the qualitative nature of PCA, DFA, and FICA prevents the application of PyMS to quantitative microbial analysis, while limitations also arise from batch-to-batch variation of PyMS data.80... 

X clust <- hclust (X dist) hierarchical clustering plot (X clust) plots a dendrogram... 

For comparison also a dendrogram (Figure 3.28) and a nonlinear mapping (NLM) (Figure 3.29) have been performed on the PAH data. Results from these methods show a clear separation of the samples from Linz and Vienna, but not much more details. The clusters in the NLM plots are very similar to the clusters in the PCA score plots. Thus, preserving the distances using two dimensions—the goal of... 

PCA and NLM—can give very similar results for a linear method (like PCA) and in a nonlinear method (like NLM). Note that neither the dendrogram nor the NLM plots allow a direct interpretation of the PAHs responsible for the origin of pollution. 

Depending on the clustering method, cluster results can be displayed in the form of a dendrogram or in a PCA score plot (Section 3.8.2). Such graphic allows abetter visual impression about the relations between the variables and about the clustering structure. It is thus a suitable tool for selecting the variables. 

Figure 4.16. dendrogram for the data plotted in Figure 4.14. with class identification labels. 

Hierarchical cluster analysis (HCA) is an unsupervised technique that examines the inteipoint distances between all of the samples and represents that information in the form of a twcKlimensional plot called a dendrogram. These dendrograms present the data from high-dimensional row spaces in a form that facilitates the use of human pattern-recognition abilities. 

Summary of Validation Diagnostic Tools for HCA The row space plot for this example is shown in Figure 4.17 with the class information included (remember that in most cases it is not possible to obtain this plot). This plot verifies the conclusion drawn from the dendrogram, that is,... 

The HCA technique examines the interpoint distances between the samples in a data set and represents that information in the form of a two-dimensional plot called a dendrogram. The HCA method is an excellent tool for preliminary data analysis. It is useful for examining data sets for expected or unexpected clusters, including the presence of outliers. It is informative to examine the dendrogram in conjunction with PCA because they give similar information in different forms. 

One ad antage of HCA over PCA is that the dendrogram represents ail of the variation in the original data set. Tliis is in contrast to PCA. which n pically only presents some fraction of the total variation in the scores plots. 

The two unsupervised methods examined are HCA and PCA. HCA calculates the interpoint distances between all of the rows and represents that information in the form of a two-dimensional plot called a dendrogram. PCA calculates a new axis system that maximally describes the variation in the data set. Our recommendation is to use both of the methods whe " they are available. HCA gives a broader view of the data and PCA can be used to further investigate samples and dusters that are highlighted in HCA. 

The results can be visualized in a plot called a dendrogram, in which the similarity or distance values corresponding to each fusion /partition step are represented. One of the two axes corresponds to the similarity. 

N represents the number of sensors in the array. For p = 2, the distance in (10.10) is Euclidian. The protocol is relatively simple. The distance matrix is created from the datapoints and scanned for the smallest values that are then arranged and displayed in the form of a dendrogram (Fig. 10.9 Suslick, 2004) in which the dissimilarity is plotted on the horizontal axis. In a dendrogram, each horizontal line segment represents the distance—that is, the similarity—between samples. Thus, if we want... 

Figure 5. Logarithmic plot of the ratios of chromium to iron for the samples from sherds in group A and group B of the cluster dendrogram shown in Figure 4. Key , archaeological samples attributed to Mexico City production A, archaeological samples attributed to Puebla production +, modem majolica produced in Puebla.

The bidimensional methods of representation most used by multivariate techniques are direct methods, such as matricial dispersion diagrams, and icon plots based on histograms, profiles or stars projection approach techniques, that represent observations in the new variables obtained, and which fulfil a specific objective (principal components, canonical variables, etc.) and dendrograms that inform about the similarity of observations or variables (Krzanowski 1988). 

NMR peaks. Samples with the same letters belong to the same cultivar. In the TCA dendrogram all samples start as individual clusters. Three levels of discrimination in the TCA analysis are marked. The 3D scores plot (dimensions 1,2, and 3) obtained from LDA reveals good separation of the different cultivars, with the different symbols denoting oil samples from the same cultivar O, NO, Nocellara , BI, Biancolilla O, CE, Cerasuola A, TI, Tonda Iblea. Adapted figure reprinted with permission from Hanneguelle et Copyright 2003 American Chemical Society. 

---