Nonhierarchical clustering, hierarchical

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 ... 

Other distance measures include the Canberra metric and the Czekanowski coefficient [126]. Clustering can be hierarchical such as grouping of species and subspecies in biology or nonhierarchical such as grouping of items. For fault diagnosis nonhierarchical clustering is used to group data to k clusters... 

D. L. Massart, L. Kaufman, and K. H. Esbensen, Anal. Chem., 54, 911 (1982). Hierarchical Nonhierarchical Clustering Strategy and Application to Classification of Iron Meteorites According to Their Trace Element Patterns. 

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. 

Cluster-Based Methods. Clustering methods have a long history of application in chemical information (60). Any set of descriptors can be used in the clustering, but most typically some form of structural fingerprint is used in conjunction with a similarity measure such as the Tanimoto coefficient (see Section 2.1.4.1). The methods fall into two broad classes, hierarchical and nonhierarchical. 

The traditional hierarchical and nonhierarchical (e.g., fc-means) clustering algorithms [69] have a number of drawbacks that require caution in their implementation for time series data. The hierarchical clustering algorithms assume an implicit parent-child relationship between the members of a cluster which may not be relevant for time series data. However, they can provide good initial estimates of patterns that may exist in the data set. The fc-means algorithm requires the estimate of the number of clusters (i.e., k) and its solution depends on the initial assignments as the optimization... 

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]. 

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. 

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