Hierarchical clustering methods

Several, but not all, of these mathematical methods (e.g. multicriteria decision making. Chapter 26) or problems (the non-hierarchical clustering methods of Chapter 30, which can be treated as allocation models) have been treated earlier. In this chapter, we will briefly discuss the methods that are relevant to chemo-metricians and have not been treated in earlier chapters yet. 

Non-hierarchical cluster methods have in common with classification methods that pre-information on the number of classes is needed or desired to start an iteration process. In the course of the clustering a rearrangement of objects between several clusters is possible. 

The typical output of hierarchical cluster methods is a so-called dendrogram, a treelike diagram which is very useful for discussing several possible results of the clustering process. For an illustration see Fig. 5-13 the underlying example will be explained in Section 5.3.4. 

The hierarchical clustering method uses the distances (or dissimilarities) between variables when forming the clusters. The distances that can be computed are based on a single dimension or multiple dimensions ... 

Massart, D.L. and Kaufman, L. (1983) Hierarchical clustering methods. In The Interpretation of Analytical Chemical Data by the Use of Cluster Analysis (ed. J.D. Winefordner), John Wiley and Sons, New York, pp. 75-99. 

The most commonly implemented hierarchical clustering methods are those belonging to the family of sequential agglomerative hierarchical nonoverlapping (SAHN) methods. These are traditionally implemented using... 

Comparison of Six Hierarchical Clustering Methods on Random Data. 

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. 

Jun, B.S., Ghosh, T.K., and Loyalka, S.K. (2000) Determination of CHF pattern using principal component analysis and the hierarchical clustering method (critical heat flux in reactors). Proceedings of the American Nuclear Society 2000 Summer Meeting, June 4-8, San Diego, CA. In Trans Am Nucl Soc, 82,250-251 (2000). 

The result of hierarchical clustering methods can be visualized in a dendrogram (Fig. 13.7). The higher two objects are connected in the dendrogram, the more dissimilar they are. The hierarchical analyses do not naturally recover... 

Algorithms for computing phylogenies are closely related to hierarchical clustering methods (Gusfield, 1997). 

An example of a non-hierarchical clustering method is the Jarvis-Patrick algorithm [Jarvis and Patrick 1973]. The Jarvis-Patrick method uses a nearest-neighbours approach. The nearest neighbours of each conformation are the conformations that are the shortest distance away. Two conformations are considered to be in the same cluster in the Jarvis-Patrick method if they satisfy the following criteria ... 

Jiang, D., Pei, J., and Zhang, A. (2003). DHC A density-based hierarchical clustering method for time-series gene expression data. In Proceedings of BIBE2003 3rd IEEE International Symposium on Bioinformatics and Bioengineering, March 10—12, 2003, Bethesda, MD. 

---