Use of eigenvalues for determining the number of components in window factor analysis of spectroscopic and chromatographic data

Abstract Three methods for determining eigenvalues, namely (1) mean-centred sequential scores, (2) mean-centred sequential loadings and (3) uncentred data, are described, and compared on simulations and real data of two-way data matrices. The sequential direction may be time (high-performance liquid chromatography (HPLC)) or wavelength (infrared spectroscopy (IR)), with the non-sequential direction wavelength (HPLC) or sample number (IR). It is shown that method 1 is very dependent on peak shapes. Method 2 works well except when there is low variability in the non-sequential direction. Method 3 performs poorly in the presence of heteroscedastic noise. It is concluded that standard statistical approaches for eigenanalysis must be used with caution in chemometric methods for window factor analysis (WFA).

[1]  Edmund R. Malinowski,et al.  Investigation of window factor analysis and matrix regression analysis in chromatography , 1993 .

[2]  H. R. Keller,et al.  Evolving factor analysis , 1991 .

[3]  H. R. Keller,et al.  Evolving factor analysis in the presence of heteroscedastic noise , 1992 .

[4]  T. A. Bancroft,et al.  Research papers in statistics , 1966 .

[5]  Stephen P. Gurden,et al.  Resolution of infrared spectra of mixtures of potential organic workplace pollutants by factor analysis , 1994 .

[6]  R. Brereton,et al.  Resolution of strongly overlapping two‐way multicomponent data by means of heuristic evolving latent projections , 1993 .

[7]  R. Shrager.  Chemical transitions measured by Spectra and resolved using singular value decomposition , 1986 .

[8]  Olav M. Kvalheim,et al.  Eigenstructure tracking analysis for revealing noise pattern and local rank in instrumental profiles: application to transmittance and absorbance IR spectroscopy , 1993 .

[9]  H. R. Keller,et al.  Peak purity control in liquid chromatography with photodiode-array detection by a fixed size moving window evolving factor analysis , 1991 .

[10]  Paul Geladi,et al.  Principal Component Analysis , 1987, Comprehensive Chemometrics.

[11]  R. Brereton,et al.  Use of chemometric factor analysis for chromatographic integration: application to diode-array high-performance liquid chromatography of mixtures of chlorophyll a degradation products , 1993 .

[12]  Richard G. Brereton,et al.  Chemometrics: Applications of Mathematics and Statistics to Laboratory Systems , 1991 .

[13]  Edmund R. Malinowski,et al.  Determination of the number of factors and the experimental error in a data matrix , 1977 .

[14]  G. Dunteman.  Principal Components Analysis , 1989 .

[15]  R. Brereton,et al.  INVESTIGATION OF THE ALLOMERIZATION REACTION OF CHLOROPHYLL a: USE OF DIODE ARRAY HPLC, MASS SPECTROMETRY AND CHEMOMETRIC FACTOR ANALYSIS FOR THE DETECTION OF EARLY PRODUCTS , 1994 .

[16]  M. Maeder.  Evolving factor analysis for the resolution of overlapping chromatographic peaks , 1987 .

[17]  Yizeng Liang,et al.  Heuristic evolving latent projections: resolving two-way multicomponent data. 1. Selectivity, latent-projective graph, datascope, local rank, and unique resolution , 1992 .