Principle component analysis , input

The most common algorithms used in the analysis of multivariate process and spectroscopic data are principle component analysis (PCA) and PLS. PLS and PCA are similar in that they are both factor analysis methods, and they both significantly reduce the dimensionality of the variable space. This is done by representing the data matrix (X) with a few orthogonal variables that explain most of the variance. The main difference between PLS and PCA is that PLS can be referred to as a supervised technique that maximizes the covariance between the response (Y) and input variables (X) in as few factors as possible while PCA... 

Fig. 5 a, b. Illustration of the computation principles for (a) artificial neural networks with input signals (array signals), hidden nodes chosen during the training of the net, and output signals (the parameters to be predicted) and (b) principal component analysis with two principal components (PC 1 and PC 2) based on three sensor signals (represented by the x, y and z axes). Normally reduces from approximately 100 signals down to two or three PCs... 

PCA is a statistical technique that has been used ubiquitously in multivariate data analysis." Given a set of input vectors described by partially cross-correlated variables, the PCA will transform them into a set that is described by a smaller number of orthogonal variables, the principle components, without a significant loss in the variance of the data. The principle components correspond to the eigenvectors of the covariance matrix, m, a symmetric matrix that contains the variances of the variables in its diagonal elements and the covariances in its off-diagonal elements (15) ... 

One commercially available sensor array analysis system, offered by Mosaic Industries [51], is Rhino , a microprocessor-based instrument with an array composed of discrete, resistive gas sensors. An artificial neural network processes sensor inputs and relates them to patterns established by training the instrument with gas components and mixtures of interest for a specific application. In principle, each system is customized for an application by the choice of sensors and the gas detection needs. Potential applications for this system are limited by the availability of suitable sensors and the complexity needed for discrimination. 

The balancing procedures described above start with a raw output composition vector and seek to produce a corrected output composition vector whose molar contents and atomic balances are such that they present a solution closest to a perfect balance in each of the components. The adjustments made to the raw data will in principle remove the analytical error present in the raw data and will quickly alert the operator to the presence of systematic or unusual random errors in the analysis. The procedures used for this purpose are based cm the self-evident proposition that mass and atomic balances must all close between the input and the output of the reactor. 

This is sufficient in dealing with the important input-response relationship, but does not enable the effect of specific disposition changes to be considered. The disposition decomposition analysis (DDA) methodology overcomes this problem. DDA is based on a most fnndamental principle of dividing the disposition into two fundamental components namely, an elimination component and a distribution component (Figure 16.3). 

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