Capability of Urine Analysis for the Disease Blastomycosis Using Infrared Spectroscopy with Eigenvector Signal to Noise Assessment

2003

Appl Spectrosc

Recent work has shown that ridge regression (RR) is Pareto to partial least squares (PLS) and principal component regression (PCR) when the variance indicator Euclidian norm of the regression coefficients, //p//, is plotted against the bias indicator root mean square error of calibration (RMSEC). Simplex optimization demonstrates that RR is Pareto for several other spectral data sets when //p// is used with RMSEC and the root mean square error of evaluation (RMSEE) as optimization criteria. From this investigation, it was observed that while RR is Pareto optimal, PLS and PCR harmonious models are near equivalent to harmonious RR models. Additionally, it was found that RR is Pareto robust, i.e., models formed at one temperature were then used to predict samples at another temperature. Wavelength selection is commonly performed to improve analysis results such that bias indicators RMSEC, RMSEE, root mean square error of validation, or root mean square error of cross-validation decrease using a subset of wavelengths. Just as critical to an analysis of selected wavelengths is an assessment of variance. Using wavelengths deemed optimal in a previous study, this paper reports on the variance/bias tradeoff. An approach that forms the Pareto model with a Pareto wavelength subset is suggested.

Section: Introductionmentioning

confidence: 99%

Assessment of Pareto Calibration, Stability, and Wavelength Selection

Anderson

2003

Appl Spectrosc

“…18,19 Thus, the goal is to not only determine the m odel with an acceptable bias level as evaluated by an error criterion (RMSECV, etc), but also the model with suitable variance is needed where \p \ or the A-optimal criterion can be used as an indicator of the representative size of the model. 17,20,21 For further discussion on parsimonious and harmonious concepts, see Refs. 1,15, and 17-19. Other studies have also suggested that the regression vector norm should be inspected to assist in model evaluation.…”

Section: Introductionmentioning

confidence: 99%

Pareto Optimal Multivariate Calibration for Spectroscopic Data

Green

2001

Appl Spectrosc

Multivariate calibration of spectra l data is considered with an emphasis on prediction. An abundance of methods are available to develop such calibration m odels. Using a harmonious approach with target vector optimization, the best calibration models are identi ed relative to the criteria used. Criteria utilized to determine the adequacy of models are minimization of the root mean square error of calibration (RMSEC) and the norm of the regressio n vector. Because of the simplicity of the optimization response surfaces, the method of sim plex was found to function much faster than generalized simulated annealing. Using a near infrared spectral example to demonstrate concepts, a family of models are established to be good, i.e., Pareto optimal models. For the data set investigated, it is found that the Pareto optimal models are essentially the same as models obtained by ridge regression and generalized ridge regression and are more harmonious than models obtained by principal component regressio n (PCR), partial least-squares (PLS), continuum regression, and cyclic subspace regression as the Pareto optimal models have smaller regressio n vector norms, RMSEC, and root mean square error of validation (RMSEV) values. The PLS models are found to be Pareto optimal relative to the PCR models. The paper presents an explanation of when the RR model will not be acceptable.

“…Said another way, when the correlation of an eigenvector is small and not well known, the eigenvector contains little useful modeling information and is unreliable. Similar arguments are presented in Reference [15], where RSDs of eigenvector weights were used to assist in determining prediction ranks. 0⋅069 0⋅97 0⋅92 78⋅3 779 12 0⋅110 0⋅054 0⋅90 0⋅93 209⋅0 6082 21 0⋅070 0⋅400 0⋅91 0⋅94 579⋅0 108340 18 0⋅069 0⋅208 0⋅91 0⋅94 696⋅4 162280 Table III.…”

Section: Soy Datamentioning

confidence: 92%

“…The prediction property of interest is moisture content. The second data set examined contains infrared (IR) spectra of canine urine measured as absorbance from 1800 to 1000 cm 71 at 3 cm 71 intervals for 36 samples [15]. The analyte of interest is concentration of the infectious disease Blastomyces dermatitidis (blastomycosis).…”

Section: Datamentioning

confidence: 99%

“…Two of these are the root mean square error of cross-validation (RMSECV) based on a leave-one-out process, and the coefficient of determination (R 2 ). Two variance indicators are also used and are computed by the regression vector norm kp n k and trR T n R n , where 'tr' signifies the trace operation, R n is the projection of R using n eigenvectors, and denotes the Moore-Penrose generalized inverse [14,15]. Minimization of the variance indicator trR T n R n is known as A-optimal in experimental design [16].…”

Section: Introduction Principal Component Regression (Pcr) Is a Widelmentioning

confidence: 99%

See 1 more Smart Citation

PCR eigenvector selection based on correlation relative standard deviations

Fairchild

Journal of Chemometrics

2001

SUMMARYWhile principal component regression (PCR) is often performed with eigenvectors ordered by decreasing singular values, PCR models have been formed using other eigenvector arrangements. A common criterion for organizing eigenvectors involves absolute correlations between respective eigenvectors and the prediction property being modeled. However, correlation cut-off values for eigenvector selection are inconsistent between data sets, and additional criteria are needed such as the root mean square error of cross-validation (RMSECV). Furthermore, correlations for some selected eigenvectors are often extremely low (e.g. values of 0⋅1 have been considered acceptable) and it is difficult to justify inclusion of these eigenvectors. Relative standard deviations (RSDs) of correlations are evaluated in this paper as an alternative method of eigenvector selection. This paper reveals distinct advantages for using eigenvectors ordered by RSDs of correlations compared to eigenvectors ordered by absolute correlations. In particular, RSDs can be used to determine significant eigenvectors without resorting to additional criteria such as the RMSECV. Additionally, inspection of RSD values explains why different correlation cut-off values are obtained for different data sets as well as why correlations can be small.