Mlpca: Difference between revisions
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===Purpose=== | ===Purpose=== | ||
Maximum likelihood principal components analysis (user contributed). | Maximum likelihood principal components analysis (user contributed). | ||
===Synopsis=== | ===Synopsis=== | ||
:[U,S,V,SOBJ,ErrFlag] = mlpca(x,stdx,p) | :[U,S,V,SOBJ,ErrFlag] = mlpca(x,stdx,p) | ||
===Description=== | ===Description=== | ||
MLPCA performs maximum likelihood principal components analysis assuming uncorrelated measurement errors. This is a method that attempts to provide an optimal estimation of the ''p''-dimensional subspace containing the data by taking into account uncertainties in the measurements, thereby dealing with those cases that cannot be treated by simple scaling. Inputs are x (''m'' by ''n'') the data matrix to be decomposed, stdx (''m'' by ''n'') matrix of standard deviations corresponding to the observations in x, and the number of factors into which the data is decomposed p. The outputs are U (''m'' by ''p'') orthonormal, S (''p'' by ''p'') diagonal, and V (''n'' by ''p'') orthonormal. The ML scores are given by U\*S. Additional output SOBJ is the value of the objective function for the best model. For exact uncertainty estimates, this should follow a chi-squared distribution with (m-p)\*(n-p) degrees of freedom. Additional output ErrFlag indicates the termination conditions of the function; | |||
MLPCA performs maximum likelihood principal components analysis assuming uncorrelated measurement errors. This is a method that attempts to provide an optimal estimation of the ''p''-dimensional subspace containing the data by taking into account uncertainties in the measurements, thereby dealing with those cases that cannot be treated by simple scaling. | |||
Inputs are x (''m'' by ''n'') the data matrix to be decomposed, stdx (''m'' by ''n'') matrix of standard deviations corresponding to the observations in x, and the number of factors into which the data is decomposed p. | |||
The outputs are U (''m'' by ''p'') orthonormal, S (''p'' by ''p'') diagonal, and V (''n'' by ''p'') orthonormal. The ML scores are given by U\*S. Additional output SOBJ is the value of the objective function for the best model. For exact uncertainty estimates, this should follow a chi-squared distribution with (m-p)\*(n-p) degrees of freedom. Additional output ErrFlag indicates the termination conditions of the function; | |||
ErrFlag = 0: normal termination (convergence), or | ErrFlag = 0: normal termination (convergence), or | ||
ErrFlag = 1: maximum number of iterations exceeded. | ErrFlag = 1: maximum number of iterations exceeded. | ||
'''Further Reference:''' | |||
P.D. Wentzell and M.T. Lohnes, "Maximum Likelihood Principal Component Analysis with Correlated Measurement Errors Theoretical and Practical Considerations", Chemom. Intell. Lab. Syst., '''45''', 65-85 (1999). | P.D. Wentzell and M.T. Lohnes, "Maximum Likelihood Principal Component Analysis with Correlated Measurement Errors Theoretical and Practical Considerations", Chemom. Intell. Lab. Syst., '''45''', 65-85 (1999). | ||
P.D. Wentzell, D.T. Andrews, D.C. Hamilton, K. Faber, and B.R. Kowalski, "Maximum likelihood principal component analysis", J. Chemometrics '''11'''(4), 339-366 (1997). | P.D. Wentzell, D.T. Andrews, D.C. Hamilton, K. Faber, and B.R. Kowalski, "Maximum likelihood principal component analysis", J. Chemometrics '''11'''(4), 339-366 (1997). | ||
P.D. Wentzell, D.T. Andrews, and B.R. Kowalski, "Maximum likelihood multivariate calibration", Anal. Chem., '''69''', 2299-2311 (1997). | P.D. Wentzell, D.T. Andrews, and B.R. Kowalski, "Maximum likelihood multivariate calibration", Anal. Chem., '''69''', 2299-2311 (1997). | ||
D.T. Andrews and P.D. Wentzell, "Applications of maximum likelihood principal components analysis: Incomplete data and calibration transfer", Anal. Chim. Acta, '''350''', 341-352 (1997). | D.T. Andrews and P.D. Wentzell, "Applications of maximum likelihood principal components analysis: Incomplete data and calibration transfer", Anal. Chim. Acta, '''350''', 341-352 (1997). | ||
===See Also=== | ===See Also=== | ||
[[analysis]], [[mcr]], [[parafac]], [[pca]] | [[analysis]], [[mcr]], [[parafac]], [[pca]] | ||
Latest revision as of 14:53, 7 October 2008
Purpose
Maximum likelihood principal components analysis (user contributed).
Synopsis
- [U,S,V,SOBJ,ErrFlag] = mlpca(x,stdx,p)
Description
MLPCA performs maximum likelihood principal components analysis assuming uncorrelated measurement errors. This is a method that attempts to provide an optimal estimation of the p-dimensional subspace containing the data by taking into account uncertainties in the measurements, thereby dealing with those cases that cannot be treated by simple scaling.
Inputs are x (m by n) the data matrix to be decomposed, stdx (m by n) matrix of standard deviations corresponding to the observations in x, and the number of factors into which the data is decomposed p.
The outputs are U (m by p) orthonormal, S (p by p) diagonal, and V (n by p) orthonormal. The ML scores are given by U\*S. Additional output SOBJ is the value of the objective function for the best model. For exact uncertainty estimates, this should follow a chi-squared distribution with (m-p)\*(n-p) degrees of freedom. Additional output ErrFlag indicates the termination conditions of the function;
ErrFlag = 0: normal termination (convergence), or
ErrFlag = 1: maximum number of iterations exceeded.
Further Reference:
P.D. Wentzell and M.T. Lohnes, "Maximum Likelihood Principal Component Analysis with Correlated Measurement Errors Theoretical and Practical Considerations", Chemom. Intell. Lab. Syst., 45, 65-85 (1999).
P.D. Wentzell, D.T. Andrews, D.C. Hamilton, K. Faber, and B.R. Kowalski, "Maximum likelihood principal component analysis", J. Chemometrics 11(4), 339-366 (1997).
P.D. Wentzell, D.T. Andrews, and B.R. Kowalski, "Maximum likelihood multivariate calibration", Anal. Chem., 69, 2299-2311 (1997).
D.T. Andrews and P.D. Wentzell, "Applications of maximum likelihood principal components analysis: Incomplete data and calibration transfer", Anal. Chim. Acta, 350, 341-352 (1997).