Nonhierarchical cluster analysis

P Willett, V Wmterman, D Bawden. Implementation of nonhierarchic cluster analysis methods m chemical information systems Selection of compounds for biological testing and clustering of substiaictures search output. I Chem Inf Comput Sci 26 109-118, 1986. 

There are three steps to nonhierarchical cluster analysis. The first is to dioose seedpoints these are approximate points compositions from which to start cluster analysis. Choosing seedpoints is by far the most critical step. Secondly, a cluster-analysis algorithm is applied to define the clusters. Finally, the statistical significance of the clusters must be determined. In other words, are the clusters well resolved or do they overlap The three steps are detailed below. 

Willett, P., Winterman, V., and Bawden, D. (1986) Implementation of nonhierarchic cluster analysis methods in chemical information systems selection of compounds for bilogical testing and clustering of substructures search output. J. Chem. Inf. Comput. Sci. 26, 109-118. 

A basic question of whether hierarchical or nonhierarchical cluster analysis is used deals with the correct or best number of groups in a data set. The notion of best relates not only to a criterion value or large break in a dendrogram, but to the research objectives as well. We can not resist quoting from Everitt (48) what is probably the ultimate word regarding the number of groups ... 

Implementation of Nonhierarchic Cluster-Analysis Methods in Chemical Information Systems Selection of Compounds for Biological Testing and Clustering of Substructure Search Output. 

Commonly in nonhierarchical cluster analysis, one starts with an initial partitioning of objects to the different clusters. After that, the membership of the objects to the clusters, for example, to the cluster centroids, is determined and the objects are newly partitioned. We consider here a general method for nonhierarchical clustering that can be used for both crisp (classical) and fuzzy clustering, the c-means algorithm. 

P. Willett, V. Winterman, and D. Bawden, ]. Chem. Inf. Comput. Set., 26, 109 (1986). Implementation of Nonhierarchical Cluster Analysis Methods in Chemical Information Systems Selection of Compounds for Biological Testing and Clustering of Substructure Search Output. 

There are two main types of clustering techniques hierarchical and nonhierarchical. Hierarchical cluster analysis may follow either an agglomerative or a divisive scheme agglomerative techniques start with as many clusters as objects and, by means of repeated similarity-based fusion steps, they reach a final situation with a unique cluster containing all of the objects. Divisive methods follow exactly the opposite procedure they start from an all-inclusive cluster and then perform a number of consecutive partitions until there is a bijective correspondence between clusters and objects (see Fig. 2.12). In both cases, the number of clusters is defined by the similarity level selected. 

Grouping. The most commonly employed techniques of data analysis in compositional investigations are those that seek to partition a data set into smaller groups that contain samples that are more similar to others in the group than to other samples in the data set. Cluster analysis, including both hierarchical and nonhierarchical variants, encompasses virtually the full range of grouping procedures used in compositional data analysis. 

The second strategy of unsupervised learning is based on cluster analysis. With this method, the objects are aggregated stepwise according to the similarity of their features. As a result, hierarchically or nonhierarchically ordered clusters are formed. In order to describe the similarity of objects, we need to learn about appropriate similarity measures. 

Clustering algorithms can be classified into four major approaches hierarchical methods, partitioning-based methods, density-based methods, and grid-based methods. Here, we will focus on the hierarchical cluster approach because it is often used in the context of structure-activity analysis. Recent research has suggested that hierarchical methods perform better than the more commonly used nonhierarchical methods in separating known actives and inactives [41]. 

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