Cluster hierarchical techniques

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... 

Hierarchical clustering procedures iteratively partition the item set into disjointed subsets. There are top-down and bottom-up techniques. The top-down techniques partition can be into two or more subsets, and the number of subsets can be fixed or variable. The aim is to maximize the similarity of the items within the subset or to maximize the difference of the items between subsets. The bottom-up techniques work the other way around and build a hierarchy by assembling iteratively larger clusters from smaller clusters until the whole item set is contained in a single cluster. A popular hierarchical technique is nearest-neighbor clustering, a technique that works bottom up by iteratively joining two most similar clusters to a new cluster. 

There are basically two approaches to data clustering, dynamic methods and hierarchical techniques. 

In hierarchical clustering one can obtain any number of clusters K,lhierarchical clustering, with the difference that there K is defined a priori by the user. The question then arises which A -clustering is significant. To introduce the problem let us first consider a technique that was proposed for the non-hierarchical method MASLOC [27], which selects so-called robust clusters. 

One of the most used techniques of non-hierarchical cluster analysis is the density method (potential method). The high density of objects in the m-dimension that characterizes clusters is estimated by means of a density function (potential function) P. For this, the objects are modelled by Gaus-... 

Another very useful exploration technique is cluster analyis, which quantifies similarities by calculating mathematic distances. The typical graphic output is a dendrogram. A common method of cluster analysis is Hierarchical cluster analysis (HCA). 

The bottleneck in utilizing Raman shifted rapidly from data acquisition to data interpretation. Visual differentiation works well when polymorph spectra are dramatically different or when reference samples are available for comparison, but is poorly suited for automation, for spectrally similar polymorphs, or when the form was previously unknown [231]. Spectral match techniques, such as are used in spectral libraries, help with automation, but can have trouble when the reference library is too small. Easily automated clustering techniques, such as hierarchical cluster analysis (HCA) or PCA, group similar spectra and provide information on the degree of similarity within each group [223,230]. The techniques operate best on large data sets. As an alternative, researchers at Pfizer tested several different analysis of variance (ANOVA) techniques, along with descriptive statistics, to identify different polymorphs from measurements of Raman... 

Cluster analysis is far from an automatic technique each stage of the process requires many decisions and therefore close supervision by the analyst. It is imperative that the procedure be as interactive as possible. Therefore, for this study, a menu-driven interactive statistical package was written for PDP-11 and VAX (VMS and UNIX) series computers, which includes adequate computer graphics capabilities. The graphical output includes a variety of histograms and scatter plots based on the raw data or on the results of principal-components analysis or canonical-variates analysis (14). Hierarchical cluster trees are also available. All of the methods mentioned in this study were included as an integral part of the package. 

Median partitioning is another statistical method distinct from RR The development of this methodology was driven by the need to select representative subsets from very large compound pools. Hierarchical clustering techniques... 

Hierarchical cluster analysis (HCA) is an unsupervised technique that examines the inteipoint distances between all of the samples and represents that information in the form of a twcKlimensional plot called a dendrogram. These dendrograms present the data from high-dimensional row spaces in a form that facilitates the use of human pattern-recognition abilities. 

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. 

So, clustering techniques have been used for classification. Piepponen et al. applied a hierarchical cluster analysis (CLUSTAN) to the classification of food oils (groundnut, soya, sunflower and maize) by their fatty acid composition. The dendrogram of the distances shows four weU-separated clusters. Some suspect commercial samples of sunflower oil fall near the cluster of soya oils, so far from the clainud class that they cannot be consider i genuine. 

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