Combinative multivariate calibration that enhances prediction ability through removal of over-modeled regions
First Claim
1. A method of developing a calibration for predicting concentration of a target analyte in sample spectra, said method employing factor-based multivariate techniques, said method comprising the steps of:
- A. providing a matrix of calibration spectra;
B. modeling at least one spectral region using a first selected number of factors;
C. removing said modeled regions from said spectral matrix, so that, a residual matrix is generated;
D. modeling at least one region of said residual matrix using a further selected number of factors, wherein said further selected number of factors may be equal to or different from said first selected number;
E. repeating steps B through D, using said residual matrix as an input matrix for step B, until the number of factors employed for all iterations is equal to an optimal number of factors required to model at least a portion of said sample spectrum; and
F. generating a vector of calibration coefficients wherein said vector constitutes said calibration;
wherein a specific number of factors models at least one region of a spectrum independently of the number of factors used to model other spectral regions, thus minimizing prediction error.
10 Assignments
0 Petitions
Accused Products
Abstract
A novel multivariate model for analysis of absorbance spectra allows for each wavelength or spectral region to be modeled with just enough factors to fully model the analytical signal without the incorporation of noise by using excess factors. Each wavelength or spectral region is modeled utilizing its own number of factors independently of other wavelengths or spectral regions. An iterative combinative PCR algorithm allows a different number of factors to be applied to different wavelengths. In an exemplary embodiment, a three-factor model is applied over a given spectral region. The residual of the three-factor model is calculated and used as the input for an additional five-factor model. Prior to the additional five factors being applied, some of the wavelengths are removed. This leads to a three-factor model over the first region and an eight-factor model over the second region. This analysis of residuals can be repeated such that a one to n factor model could be applied to any given wavelength, or rather any number of factors may be employed to model any given frequency or spectral region. A method of predicting concentration of a target analyte from sample spectra applies a calibration developed using the inventive PCR algorithm to a matrix of sample spectral to generate a vector of predicted concentrations for the target analyte.
-
Citations
46 Claims
-
1. A method of developing a calibration for predicting concentration of a target analyte in sample spectra, said method employing factor-based multivariate techniques, said method comprising the steps of:
-
A. providing a matrix of calibration spectra;
B. modeling at least one spectral region using a first selected number of factors;
C. removing said modeled regions from said spectral matrix, so that, a residual matrix is generated;
D. modeling at least one region of said residual matrix using a further selected number of factors, wherein said further selected number of factors may be equal to or different from said first selected number;
E. repeating steps B through D, using said residual matrix as an input matrix for step B, until the number of factors employed for all iterations is equal to an optimal number of factors required to model at least a portion of said sample spectrum; and
F. generating a vector of calibration coefficients wherein said vector constitutes said calibration;
wherein a specific number of factors models at least one region of a spectrum independently of the number of factors used to model other spectral regions, thus minimizing prediction error. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
-
-
14. A method of predicting concentration of a target analyte from a prediction data set based on a multivariate calibration comprising steps of:
-
A. providing a prediction data set, said prediction data set comprising a matrix of sample spectra;
B. generating a calibration by modeling a calibration data set according to an iterative, combinative algorithm, wherein a specific number of factors models at least one region of a spectrum independently of the number of factors used to model other spectral regions; and
C. applying said calibration to said prediction data set, so that a prediction of a target analyte concentration is produced;
wherein prediction error is minimized. - View Dependent Claims (15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30)
-
-
31. An iterative, combinative algorithm for modeling a set of data, said algorithm comprising the steps of.
A. providing a data matrix containing an analytical signal, said data matrix comprising a plurality of samples and a plurality of variables; -
B. modeling at least one region of said data matrix, a region constituting at least one of said plurality of values, using a selected number of factors;
C. subtracting said modeled regions from said data matrix, so that a residual matrix is generated;
D. modeling at least one further region from said residual matrix after removal of a further selected number of values, wherein said further selected number equal to or different from said first number; and
E. repeating steps B through D, using said residual matrix as an input matrix for step B, until the number of factors employed for all iterations is equal to an optimal number of factors required to model said entire data set;
wherein a specific number of factors models at least one region of said data matrix independently of the number of factors used to model other regions of said data matrix so that said analytical signal is modeled. - View Dependent Claims (32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46)
-
Specification