Multivariate analysis clustering

Chatfield C and A J CoHns 1980. Introduction to Multivariate Analysis. London, Chapman Hall. Desiraju G R 1997. Crystal Gazing Structure Prediction and Polymorphism. Sdence 278 404-405. Everitt B.S. 1993 Cluster Analysis. Chichester, John Wiley Sons. 

McCombie G, Staab D, Stoeckli M, et al. Spatial and spectral correlations in MALDI mass spectrometry images by clustering and multivariate analysis. Anal. Chem. 2005 77 6118-6124. 

One has to keep in mind that groups of objects found by any clustering procedure are not statistical samples from a certain distribution of data. Nevertheless the groups or clusters are sometimes analyzed for their distinctness using statistical methods, e.g. by multivariate analysis of variance and discriminant analysis, see Section 5.6. As a result one could then discuss only those clusters which are statistically different from others. 

Marco, V R., Young, D. M., Turner, D. W. Commun. Statist. - Simula. 16 (1987) 485 Mardia, K.V, Kent, J.T., Bibby, J.M. Multivariate Analysis, Academic Press, London, 1979, pp. 191 Massart, D.L., Kaufman, L. The Interpretation of Analytical Data by the Lise of Cluster Analysis, Wiley, New York, 1983... 

Combination of Cluster Analysis, and Multivariate Analysis of Variance and Discriminant Analysis... 

The application of methods of multivariate statistics (here demonstrated with examples of cluster analysis, multivariate analysis of variance and discriminant analysis, and principal components analysis) enables clarification of the lateral structure of the types of feature change within a test area. 

Reasonable noise in the spectral data does not affect the clustering process. In this respect, cluster analysis is much more stable than other methods of multivariate analysis, such as principal component analysis (PCA), in which an increasing amount of noise is accumulated in the less relevant clusters. The mean cluster spectra can be extracted and used for the interpretation of the chemical or biochemical differences between clusters. HCA, per se, is ill-suited for a diagnostic algorithm. We have used the spectra from clusters to train artificial neural networks (ANNs), which may serve as supervised methods for final analysis. This process, which requires hundreds or thousands of spectra from each spectral class, is presently ongoing, and validated and blinded analyses, based on these efforts, will be reported. 

Principal component analysis (PCA), factor analysis (FA) and cluster analysis (CA) are some of the most widely used multivariate analysis techniques applied to... 

To investigate relationships between crustacean grazing rates on Phaeocystis and experimental conditions, a multiple correspondence analysis (MCA) followed by a hierarchical cluster analysis (HCA) was performed using SPAD 3.5 software (Lebart et al. 1988). The combination of MCA and cluster analysis is a common way to explore relationships among a large number of variables and to facilitate interpretation of the correspondence analysis results (Lebart et al. 2000). MCA uses a contingency table as data, which provides a simultaneous representation of the observations (rows) and variables (column) in a factorial space. This form of multivariate analysis describes the total inertia (or variability) of a multidimensional... 

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. 

Among the multivariate methods the most important are principal components analysis (PCA), factor analysis, cluster analysis and the pattern recognition method, from which only PCA will be briefly described below. PCA is used to find such a system of new variables, called principal components (PC), which explains the variation of a given data set in a more convenient way than the original system of variables, e.g. xl9...,Xj,...,xm. The greater convenience of PC consists mainly in a reduction of dimensions, m, in which the data were originally described, because the PC variables are chosen so that only two or three of them should be sufficient to characterize the variation of the data. The PC are linear combinations of the original variables, xj9 used to characterize the set of objects,... 

As a first test of the use of multivariate analysis in the interpretation of multispecies toxicity tests, the dataset used to analyze the CR microcosm experiment was presented in a blind fashion for analysis. Neither the purpose nor the experimental setup was provided for the analysis. Nonmetric clustering was used to rank variables in terms of contribution and to set clusters. 

Statistical analyses were performed using the change scores from the NBAS evaluation (Time 2-Time 1). Multivariate analysis of covariance (MANCOVA) was performed for each of the NBAS clusters with group membership (high, low, and no fish consumption) as the independent variable and the 24 components representing potential confounders as covariates. Approximately 75% of each fish consumption group was included in the analysis (n=416). The loss of subjects occurred because only subjects with data for all variables were included. Multiple regression was also performed for each of the NBAS clusters with inclusion of component covariates for confounder control. 

Data sets can be analyzed by exploratory data analysis, usually based on multivariate techniques, such as principal component analysis cluster analysis allows the evaluation of... 

According to Ennis (1988), the application of the various multivariate analysis techniques (factor, cluster, discriminant analysis, multidimensional scaling) to classification in sensory analysis has been very valuable but is of little help for understanding the modes of perception. Mathematical models are proposed for predicting human sensory responses and the author concludes that they need development before they are able to improve the understanding of the complex perceptions associated with foods and beverages . 

---