Alternating coupled matrices resolution method for three-way arrays analysis

Abstract An alternating coupled matrices resolution (ACOMAR) method is developed for decomposition of three-way data arrays. By utilizing alternating least squares algorithm to minimize the proposed coupled matrices resolution error, the intrinsic profiles are found. Moreover, it yields simultaneously a numerically exact solution for all analytes present in the samples. This method retains the second-order advantage of quantization for analyte(s) of interest in the presence of potentially unknown interferents. The performance of a simulated experiment and a real analytical example shows that the proposed method works well when the number of components is chosen to be equal to or greater than the actual model dimensionality. The insensitivity of the ACOMAR method to the estimated component number escapes the difficulty of determining a proper component number for the model, which is hard to handle for the PARAFAC algorithm. Furthermore, this method circumvents the two-factor degeneracy, which is intrinsic in the PARAFAC algorithm.

[1]  Wilhelmus Petrus Krijnen,et al.  The analysis of three-way arrays by constrained parafac methods , 1993 .

[2]  Bruce R. Kowalski,et al.  Extension of Trilinear Decomposition Method with an Application to the Flow Probe Sensor , 1994 .

[3]  R. Bro.  PARAFAC. Tutorial and applications , 1997 .

[4]  Avraham Lorber,et al.  Generalized rank annihilation method: standard errors in the estimated eigenvalues if the instrumental errors are heteroscedastic and correlated , 1997 .

[5]  Sarah C. Rutan,et al.  Kinetic Detection of Overlapped Amino Acids in Thin-Layer Chromatography with a Direct Trilinear Decomposition Method , 1995 .

[6]  Age K. Smilde,et al.  Three-way analyses problems and prospects , 1992 .

[7]  Bruce R. Kowalski,et al.  Tensorial calibration: II. Second‐order calibration , 1988 .

[8]  Hai-Long Wu,et al.  An alternating trilinear decomposition algorithm with application to calibration of HPLC–DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons , 1998 .

[9]  Avraham Lorber,et al.  Quantifying chemical composition from two-dimensional data arrays , 1984 .

[10]  E. Davidson,et al.  Application of the method of rank annihilation to quantitative analyses of multicomponent fluorescence data from the video fluorometer , 1978 .

[11]  W. Rayens,et al.  Two-factor degeneracies and a stabilization of PARAFAC , 1997 .

[12]  Paul Geladi,et al.  Analysis of multi-way (multi-mode) data , 1989 .

[13]  Ben C. Mitchell,et al.  Slowly converging parafac sequences: Swamps and two‐factor degeneracies , 1994 .

[14]  A. Agresti,et al.  Multiway Data Analysis , 1989 .

[15]  Bruce R. Kowalski,et al.  Generalized rank annihilation factor analysis , 1986 .

[16]  B. Kowalski,et al.  Tensorial resolution: A direct trilinear decomposition , 1990 .