K-means method

The method used here is called Forgy s method [25], This is one of the K-center or K-centroid methods, another well-known variant of which is MacQueen s K-means method [26]. Forgy s method involves the following steps. 

The K-Means method can be rather efficient for a large number of objects, but requires a priori selection of the number of clusters K, and thus is less exploratory in nature than the HCA methods discussed earlier. In addition, its outcome depends on the initial selection of targets. As a result, one can do a smart selection of the initial targets based on their uniqueness in the data set, for example those objects with the highest Hotelling P value (Section 12.2.5) obtained from a PCA analysis of the data. 

The best-known relocation method is the k-means method, for which there exist many variants and different algorithms for its implementation. The k-means algorithm minimizes the sum of the squared Euclidean distances between each item in a cluster and the cluster centroid. The basic method used most frequently in chemical applications proceeds as follows ... 

The principal aim of performing a cluster analysis is to permit the identification of similar samples according to their measured properties. Hierarchical techniques, as we have seen, achieve this by linking objects according to some formal rule set. The K-means method on the other hand seeks to partition the pattern space containing the objects into an optimal predefined number of... 

A hybrid method, bisecting K-means, combines the divisive hierarchical and K-means methods to produce a controlled number of hierarchical document clusters. It has been shown to perform as good as or better than hierarchical methods while retaining the performance of the K-means approach [32]. The process of this method involves bisecting a selected cluster of documents (biggest or poorest quality) into two smaller clusters but optimizing the centroids to obtain new clusters with the best possible quality. An example of an implementation of this type of method is the Oracle Text hierarchical K-means algorithm. 

A. We projected the 42-dimensional space of the bispectrum—which corresponds to j < 4—to the two-dimensional plane and clustered the points using the k-means algorithm [18]. In Fig. 2.7, we show the result of the principle component analysis. Different colours are assigned to each cluster identified by the k-means method, and we coloured the atoms with respect to the cluster they belong. This example demonstrates that the bispectmm can be used to identify atomic environments in an automatic way. 

The method of cluster analysis described here is hierarchical, meaning that once an object has been assigned to a group the process cannot be reversed. For non-hierarchical methods the opposite is the case. One such method is the k-means method which is available, for example, in Minitab. This starts by either dividing the points into k clusters or alternatively choosing k seed points. Then each individual is... 

Nonhierarchical relocation methods, such as the k-means method, start with a user-defined number of seed clusters and iteratively reassign molecules between clusters to see if better clusters result, where the success of the solution is measured by some parameter such as the ratio of the mean intercluster similarity to the mean intracluster similarity, The methods can be quite... 

Figure 2.7 shows the results of a partition clustering method on a kidney calculus image by k-means method. On the left, segmentation schemes obtained by... 

Figure 2.7 Results of image segmentation by k-means method (hard ciustering approach) for a Raman kidney caicuius. (A) segmentation schemes (B) ciass centroids.

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