Principal component analysis noise factors

Factor spaces are a mystery no more We now understand that eigenvectors simply provide us with an optimal way to reduce the dimensionality of our spectra without degrading them. We ve seen that, in the process, our data are unchanged except for the beneficial removal of some noise. Now, we are ready to use this technique on our realistic simulated data. PCA will serve as a pre-processing step prior to ILS. The combination of Principal Component Analysis with ILS is called Principal Component Regression, or PCR. 

Because of the relatively small number of experiments done on commercial-scale equipment before submission, and the often very narrow factor ranges (Hi/Lo might differ by only 5-10%), if conditions are not truly under control, high-level models (multi-variate regressions, principal components analysis, etc.) will pick up spurious signals due to noise and unrecognized drift. For example, Fig. 4.43 summarizes the yields achieved for... 

In some cases a principal components analysis of a spectroscopic- chromatographic data-set detects only one significant PC. This indicates that only one chemical species is present and that the chromatographic peak is pure. However, by the presence of noise and artifacts, such as a drifting baseline or a nonlinear response, conclusions on peak purity may be wrong. Because the peak purity assessment is the first step in the detection and identification of an impurity by factor analysis, we give some attention to this subject in this chapter. 

Irrespective of the method chosen, meaningful data can only be obtained if the appropriate level of signal to noise (S/N) is reached in the spectrum of each analyte. This has been achieved for Raman measurements through short data acquisition times (<1 s) and application of mathematical approaches such as If-harmonic means clustering (KHMC), factor analysis [57] and principal component analysis (PCA) [58] to the data set. Ultimately the sample response to the excitation energy determines the speed that a measurement can be made. 

Principal component regression and partial least squares are two widely used methods in the factor analysis category. PCR decomposes the matrix of calibration spectra into orthogonal principal components that best capture the variance in the data. These new variables eliminate redundant information and, by using a subset of these principal components, filter noise from the original data. With this compacted and simplified form of the data, equation (12.7) may be inverted to arrive at b. 

In this paper the PLS method was introduced as a new tool in calculating statistical receptor models. It was compared with the two most popular methods currently applied to aerosol data Chemical Mass Balance Model and Target Transformation Factor Analysis. The characteristics of the PLS solution were discussed and its advantages over the other methods were pointed out. PLS is especially useful, when both the predictor and response variables are measured with noise and there is high correlation in both blocks. It has been proved in several other chemical applications, that its performance is equal to or better than multiple, stepwise, principal component and ridge regression. Our goal was to create a basis for its environmental chemical application. 

Briefly, PCA models the data in terms of the significant factors, or principal components, which describe the systematic variability of the data. PCA also describes the data in terms of residuals that represent the noise in the system. PLS may be described as a method for constructing predictive models from data sets with many collinear factors. Both have received considerable attention in the analysis of multivariate data. 

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