Nonhierarchical clustering algorithm

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. 

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]. 

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. 

If different partitions are obtained in an independent way by varying some parameter, nonhierarchic clustering is used. In so-called partitionmaking algorithms, such as A-means or Forgy s... 

The trained map can be graphically presented by 2D planes for each variable, with the variable distribution values being indicated by different colors on the different regions of the map. Additionally, the node coordinates (vectors) can be clustered by the nonhierarchical A -means classification algorithm. 

Nonhierarchical or partitional clustering uses algorithms, which determine all clusters at once. 

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