Least squares estimation principal component analysis

Keywords soft-sensor, Just-In-Time modeling, recursive partial least squares regression, principal component analysis, estimation... 

For overlapping peaks the data matrix contains linear combinations of the pure spectra of the overlapping components in its rows, and combinations of the pure elution profiles in its columns. Multivariate analysis of the data matrix may allow extraction of useful information from either the rows or columns of the matrix, or an edited form of the data matrix [107,116-118]. Factor analysis approaches or partial least-squares analysis can provide information on whether a given spectrum (known compound) or several known compounds are present in a peak. Principal component analysis and factor analysis can be used to estimate the maximum number of probable (unknown) components in a peak cluster. Deconvolution or iterative target factor analysis can then be used to estimate the relative concentration of each component with known spectra in a peak cluster. 

Vajda, S., Valko, P. Godfrey, K. R. (1987). Direct and indirect least squares methods in continuous-time parameter estimation. Automatica, 23, 707-18. Vajda, S., Valko, P. Turanyi, T. (1985). Principal component analysis of kinetic models. Int. J. Chem. Kinet., 55-81. 

Wold H. Estimation of principal components and related models by iterative least squares. In Krishnaiah PR, editor, Multivariate analysis. New York Academic Press, 1966. p. 391 420. 

The effect of sugar and acid contents in fruit on the transmitted output power was fully examined and used to estimate the optical parameter preferable for detecting internal quality. The performances of multiple Unear regression (MLR), principal component regression (PCR), and partial least-squares regression (PLS) analysis by TOF-NIRS were also compared to those from normal methods using reflectance data. 

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