Multivariate unsupervised

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. 

Principal component analysis (PCA) can be considered as the mother of all methods in multivariate data analysis. The aim of PCA is dimension reduction and PCA is the most frequently applied method for computing linear latent variables (components). PCA can be seen as a method to compute a new coordinate system formed by the latent variables, which is orthogonal, and where only the most informative dimensions are used. Latent variables from PCA optimally represent the distances between the objects in the high-dimensional variable space—remember, the distance of objects is considered as an inverse similarity of the objects. PCA considers all variables and accommodates the total data structure it is a method for exploratory data analysis (unsupervised learning) and can be applied to practical any A-matrix no y-data (properties) are considered and therefore not necessary. 

Preliminary data analysis carried out for the spectral datasets were functional group mapping, and/or hierarchical cluster analysis (HCA). This latter method, which is well described in the literature,4,9 is an unsupervised approach that does not require any reference datasets. Like most of the multivariate methods, HCA is based on the correlation matrix Cut for all spectra in the dataset. This matrix, defined by Equation (9.1),... 

In this review, we demonstrate that excellent IR spectra from microscopic regions of cells and tissue can be collected. These spectra are extremely sensitive to variations in the biochemical composition of the pixels from which the spectra were acquired. Multivariate analyses of the spectra datasets of cells, cell smears and tissue sections produce pseudocolor maps in a totally unsupervised fashion that reproduce the histopathology of tissue sections and cytological features of cells and cell smears. 

Unsupervised multivariate statistical methods [CA, principal components analysis, Kohonen s self-organizing maps (SOMs), nonlinear mapping, etc.], which perform spontaneous data analysis without the need for special training (learning), levels of knowledge, or preliminary conditions. 

The main goal of this section is to provide a summary of several of the most widely used multivariate procedures in food authentication out of the vast array currently available. These are included in well-known computer packages such as BMDP, IMSL, MATLAB, NAG, SAS, SPSS and STATISTIC A. The first three subsections describe unsupervised procedures, also called exploratory data analysis, that can reveal hidden patterns in complex data by reducing data to more interpretable information, to emphasize the natural grouping in the data and show which variables most strongly influence these patterns. The fourth and fifth subsections are focused on the supervised procedures of discriminant analysis and regression. The former produces good information when applied under the strictness of certain tests, whereas the latter is mainly used when the objective is calibration. 

Analyses of the above type belong to the category of unsupervised learning , whereas discriminant analysis falls into the supervised analyses of multivariate... 

Unsupervised classification or projection can also be used for assessing the relationships between samples. In several studies, it has been shown that cell-type-specific MS profiles can be used to merge samples based on their multivariate molecular information to identify novel patient subgroupings with different clinical behavior (Figure 3B) (49,50). 

The choice of properties has a major influence on pattern recognition methods (unsupervised multivariate statistical or neural network methods) in particular and different property sets can resnlt in qnite different patterns of similarity between compounds. Several methods are available to make selections of subsets of uncorrelated properties which can be used... 

When performing an unsupervised multivariate analysis it is important to remember that it is a numerical analysis based on the variance of the data set Whenever the data set is manipulated, the results may change. Hence, it is imperative to verify the results with the original spectra to confirm the chemistry. Repetition is also a form of variance when there is more repetition of a spectral species, the loading will seem smoother. Conversely, even if the SNRs of the original spectra are similar the loading of a spectral species of less repehtion will seem noisier. 

The next example of an OTC map was treated first using a direct classic least square (DCLS) method, and then with more sophisticated multivariate analysis methods. The tablet was mapped over 800 X 800 gm with 10 gm steps. The data were baseline-corrected and normalized before being subjected to an unsupervised multivariate analysis. The first set of results was produced using univariate analysis (Figure 11.8a), when a manual exploration revealed three distinguishable and... 

An in-depth review of statistical methods for metabonomic data analysis is beyond the scope of this chapter. Briefly, there are a few main approaches to data analysis. Examples of multivariate data analyses include the so-called unsupervised analyses such as PCA, independent component analysis (ICA), and hierarchical clustering analysis (HCA), while partial least square differential analysis (PLS-DA) is... 

In analysing complex fermentor broths and supernatants, in contrast to the case for simple mixtures, the multivariate analysis approach not only monitors the infra-red spectral contribution of the target molecules per se but may also take into account other features associated with the metabolite concentration. In this way the use of unsupervised methods such as PCA and supervised methods such as PLS, and DFA can exploit differences in the organism (for example the mutant type) or the medium which correlate with metabolite overproduction. This can provide a useful amplification to the method when the target molecule concentrations are particularly low. 

Statistical Analysis and Reporting Methods for statistical analysis of metabonomics data sets include a variety of supervised and unsupervised multivariate techniques (Holmes et al., 2000) as well as univariate analysis strategies. These chemometric approaches have been recently reviewed (Holmes and Antti, 2002 Robertson et al., 2007), and a thorough discussion of these is outside the scope of this chapter. Perhaps the best known of the unsupervised multivariate techniques is principle component analysis (PCA) and is widely... 

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