Objectives of Cluster Analysis

If the aim of the data analysis or the question asked about the data is clearly fixed and the result is obtained the next question will be what is the cause of the structure found This in turn may lead to new hypotheses about the data. Hence, methods of confirmatory data analysis ( usual statistics ) may subsequently be necessary in the next step. Sometimes in recognition processes the problem of the adequate selection of objects will arise. Then an additional problem may consist in the proper choice of features to be measured in order to characterize the objects correctly. 

Let us assume that a reasonable number of objects, n, and their m features have been selected and are arranged in a measuring data matrix X like  

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Analytical results are often represented in a data table, e.g., a table of the fatty acid compositions of a set of olive oils. Such a table is called a two-way multivariate data table. Because some olive oils may originate from the same region and others from a different one, the complete table has to be studied as a whole instead as a collection of individual samples, i.e., the results of each sample are interpreted in the context of the results obtained for the other samples. For example, one may ask for natural groupings of the samples in clusters with a common property, namely a similar fatty acid composition. This is the objective of cluster analysis (Chapter 30), which is one of the techniques of unsupervised pattern recognition. The results of the clustering do not depend on the way the results have been arranged in the table, i.e., the order of the objects (rows) or the order of the fatty acids (columns). In fact, the order of the variables or objects has no particular meaning. 

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