Application of robust eigenvectors to the compression of infrared spectral libraries

Abstract

Robust eigenvectors are Insensitive to nonnormal data. An algorithm was devised to calculate robust eigenvectors for the specific purpose of compressing spectral libraries. All spectral entries Including outlying or atypical spectra will maintain a minimum retained variance. Infrared libraries compressed with robust eigenvectors were compared to libraries compressed with conventional eigenvectors and a noncompressed library. A method for locating poor quality Infrared spectra In large databases Is also discussed.

Nonlinear least-squares fitting of multivariate absorption data

“…Data reduction through SVD has been used in very different fields of chemistry (25, 26,35). The basic steps are briefly repeated: Y in eq 1 is replaced by its SVD (eq 3) to yield…”

“…Reasonable models or hypotheses can further be tested by target factor analysis (32)(33)(34). An additional feature of factor analysis is the possibility of data reduction which is important from the point of view of memory allocation and speeds up the calculations considerably (25,26,35). Even a completely model-free analysis of the original measurement is possible under certain conditions (1)(2)(3)(4)11,36,37).…”

“…A primary goal of factor analysis is the determination of the number of TV of components or factors in the system under investigation. Many different methods have been developed to answer this purely statistical question (27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37); it is assumed here that TV has been determined and is identical with the number of absorbing species. Noise reduction is another important feature of factor analysis: by representing Y by USV the information content of Y is retained whereas most of the noise component is rejected (27).…”

“…Noise reduction is another important feature of factor analysis: by representing Y by USV the information content of Y is retained whereas most of the noise component is rejected (27). Data reduction through SVD has been used in very different fields of chemistry (25,26,35). The basic steps are briefly repeated: Y in eq 1 is replaced by its SVD (eq 3) to yield…”

Regularized Linear Discriminant Analysis of Wavelet Compressed Ion Mobility Spectra

“…The mean and principal components from the training model were used to compress the test set spectra before prediction. 29,30 This approach was used to verify that the wavelet compression was de-noising the data and not m erely compressing the data. Selected prediction results of this evaluation are given in Table II.…”