Scale dendrogram

Fig. 6 Classification at different levels of resolution. When the resolution is low it is still possible to distinguish between the elephant and. something that is as. small as a dog. If we want to discriminate between a dog and a wolf, we need higher resolution. The right-hand side of the figure shows a scale dendrogram which is used to summarise the qualitative properties of the classification of the objects.

Scale dendrograms can in principle be applied to both unsupervised and supervised classification, however in this chapter only examples from unsupervised classification are included. 

A scale dendrogram for the same analysis is shown in the upper part of Fig. 22. 

Fig. 22 This figure shows a. scale dendrogram for each of the two data sets analysed ( UTI and Eubacterium). Scale dendrograms as used here efficiently summarise the qualitative change of the overlap. structure of the clusters involved after adding the different wavelet scales. Note that other measures than duster overlap could have been u.sed in the. scale dendrogram. Another possible measure would be the cluster area or shape.

Let s first suppose we knew that we can consider things on a pairwise basis. The attraction of metric distance, principal component analysis, multidimensional scaling, clustering, and dendrograms is that they consider the mere N(N - 2)12 parameters for an N parameter problem. The approaches are powerful and persuasive. But we just illustrated above that this is not justified in general. You just never get to miss the more complicated relationships because you never get to see them. 

Figure 16.13. Multidimensional scaling plot of the same data represented in Figure 16.12. Note that the samples that fall closely together in the dendrogram also plot near to one another in the MDS plot. Ideally, this plot should be viewed in three dimensions on a computer screen so that it can be rotated to allow better inspection of the distances between the data points.

The Pearson correlation coefficient is used to represent the scale of a dendrogram constructed with TreeView after phylogenetic analysis with Cluster. For a pairwise comparison, a coefficient of 1 indicates absolute identity and zero indicates complete independence. 

Fig. 22.1. PCA and hierarchical clustering example shown on a kidney sample, (a) Optical image of the kidney section prior to matrix application, (b) Scores of first principal component. The image is in agreement with the anatomy of the kidney, with the renal pelvis and part of the cortex showing the hot colors, (c) Clustering result Renal cortex, medulla, and pelvis are defined by the highest level clusters. The advantage of this type of analysis is that the dendrogram nodes can be expanded and highlighted until the desired molecular structure is found. Scale bar 2 mm.

Fig. 22.2. PCA and hierarchical clustering for a gastric cancer section, (a) H E-stained tissue section after MALDI imaging measurement, (b) Scores of the first principal component show the hot colors in the tumor area, (c) Hierarchical clustering Top dendrogram nodes differentiate tumor (green and magenta) versus non-tumor (blue, squamous epitheiium in red), (d) The dendrogram can be expanded down the tumor node to evaluate the moiecuiar differentiation inside the tumor. This can also be directly correlated with the histoiogy. This workflow enables the fast and concise selection of mass spectra representative for specific tissue states. Scale bar 2 mm.

---