Unsupervised techniques component analysis

Multiple linear regression is strictly a parametric supervised learning technique. A parametric technique is one which assumes that the variables conform to some distribution (often the Gaussian distribution) the properties of the distribution are assumed in the underlying statistical method. A non-parametric technique does not rely upon the assumption of any particular distribution. A supervised learning method is one which uses information about the dependent variable to derive the model. An unsupervised learning method does not. Thus cluster analysis, principal components analysis and factor analysis are all examples of unsupervised learning techniques. 

Fig. 10.11 Representation of hybrid approach in which Kohonen maps, neural nets, multiple component analysis, and pattern recognition are combined to create a complex data evaluation cascade. Within this cascade supervised (quantitative) and unsupervised (qualitative) techniques are combined (Hierlemann et al., 1996)...

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... 

In this chapter, we will show altered composition of metabolites in the cancerous tissue revealed by IMS, with both manual data processing and statistic data management. In particular, as a statistical strategy, an unsupervised multivariate data analysis technique that enables us to sort the data sets without any reference information is described. A major method that is related to IMS, namely principal component analysis (PCA), will be described in detail. 

While principal components models are used mostly in an unsupervised or exploratory mode, models based on canonical variates are often applied in a supervisory way for the prediction of biological activities from chemical, physicochemical or other biological parameters. In this section we discuss briefly the methods of linear discriminant analysis (LDA) and canonical correlation analysis (CCA). Although there has been an early awareness of these methods in QSAR [7,50], they have not been widely accepted. More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR. Nevertheless, the early pattern recognition techniques have prepared the minds for the introduction of modem chemometric approaches. 

In complex systems where the number of groups to be separated during classification becomes larger, the performance of simple unsupervised methods (Section 3) degrades, requiring the use of more sophisticated supervised chemometric techniques. Additionally, in fields such a process NMR where there is a need for quantifying a component, the use of supervised methods becomes necessary. The different supervised methods described in the sections below have all been utilized in the chemometric analysis of NMR data for classification and/or quantitation. Examples utilizing these different techniques are discussed in Section 5. 

Ann X m matrix can be considered n points in the m-dimensional space (or m points in the n-dimensional space). The points can be projected into a smaller dimensional subspace (smaller than n or m, whichever is the smaller) using proper techniques as PCA. Therefore, PCA is often called as a projection method. Projecting the points, dimension reduction of the data can be achieved. The principal components are often called underlying components their values are the scores. The principal components are, in fact, linear combinations of the original variables. PCA is an unsupervised method of pattern recognition in the sense that no grouping of the data has to be known before the analysis. Still the data structure can be revealed easily and class membership is easy to assiga... 

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