Multivariate statistical techniques clusters analysis

Throughout this chapter, reference will be made to techniques and approaches described elsewhere in this book, and a certain familiarity with these topics will be assumed Methods of representing molecular conformation, and different coordinate systems (Chapter 1), ways of dealing with symmetry aspects (Chapter 2), data retrieval from the Cambridge Structural Database (CSD Chapter 3) [3], and multivariate statistical techniques such as principal component analysis (PCA) and cluster analysis (CA Chapter 4). 

The data processing of the multivariate output data generated by the gas sensor array signals represents another essential part of the electronic nose concept. The statistical techniques used are based on commercial or specially designed software using pattern recognition routines like principal component analysis (PCA), cluster analysis (CA), partial least squares (PLSs) and linear discriminant analysis (LDA). 

Principal component analysis is a popular statistical method that tries to explain the covariance structure of data by means of a small number of components. These components are linear combinations of the original variables, and often allow for an interpretation and a better understanding of the different sources of variation. Because PCA is concerned with data reduction, it is widely used for the analysis of high-dimensional data, which are frequently encountered in chemometrics. PCA is then often the first step of the data analysis, followed by classification, cluster analysis, or other multivariate techniques [44], It is thus important to find those principal components that contain most of the information. 

There are several books on pattern recognition and multivariate analysis. An introduction to several of the main techniques is provided in an edited book [19]. For more statistical in-depth descriptions of principal components analysis, books by Joliffe [20] and Mardia and co-authors [21] should be read. An early but still valuable book by Massart and Kaufmann covers more than just its title theme cluster analysis [22] and provides clear introductory material. 

Cluster analysis is justifiably a popular and common technique for exploratory data analysis. Most commercial multivariate statistical software packages offer several algorithms, along with a wide range of graphical display facilities to aid the user in identifying patterns in data. Having indicated that... 

The chemo(bio)diversity analysis of maize landraces and propolis produced in southern regions of Brazil was successfully assessed by using a typical metabolomic platform involving spectroscopic techniques (FTIR, iR- and 13C-NMR, and UV-visible) and chemometrics. The huge amount of data afforded by those spectroscopic techniques was analyzed using multivariate statistical methods such as principal component analysis and cluster analysis allowing obtaining extra information on the metabolic profile of the complex matrices in study. 

Chatfield and Collins (1980), in the introduction to their chapter on cluster analysis, quote the first sentence of a review article on cluster analysis by Cormack (1971) The availability of computer packages of classification techniques has led to the waste of more valuable scientific time than any other statistical innovation (with the possible exception of multiple-regression techniques). This is perhaps a little hard on cluster analysis and, for that matter, multiple regression but it serves as a note of warning. The aim of this book is to explain the basic principles of the more popular and useful multivariate methods so that readers will be able to understand the results obtained from the techniques and, if interested, apply the methods to their own data. This is not a substitute for a formal training in statistics the best way to avoid wasting one s own valuable scientific time is to seek professional help at an early stage. 

One common query to the CSD (Table 2) involves the classification of fragment conformations - a recognition of the different 3-D shapes that are exhibited by a given 2-D chemical substructure. Here the number of geometrical parameters required to define the 3-D conformation is normally >2. For example, 15 distances or six torsion angles provide suitable descriptors for cyclohexane, and we must resort to multivariate statistical methods to analyse the appropriate G-matrix. Two techniques may be selected within GSTAT principal component analysis and cluster analysis. 

In both studies, nonmetric clustering outperformed the metric tests, although both principal components analysis and correspondence analysis yielded some additional insight into large-scaled patterns, which was not provided by the nonmetric clustering results. However, nonmetric clustering provided information without the use of inappropriate assumptions, data transformations, or other dataset manipulations that usually accompany the use of multivariate metric statistics. The success of these studies and techniques led to the examination of community dynamics in a series of two multispecies toxicity tests. 

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