Abstract
An alternating trilinear decomposition algorithm based on simultaneously minimizing diagonal matrix error and covariant matrix error (ADCE) is developed for three-way data analysis. By alternatively optimizing three objective functions with intrinsic relationships, ADCE algorithm keeps the ‘second-order advantage’ of second-order calibration methods and provides a natural way to avoid the two-factor degeneracies, which is intrinsic in the traditional PARAFAC algorithm. The simulated results and real experimental results show ADCE algorithm has the features of fast convergence rate as well as insensitivity to the overestimated factor number, in other words, it not only avoids the dilemma of identifying the actual component number accurately in practical problem but also converges fast, which is rather difficult to handle for the traditional PARAFAC algorithm.
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References
Sanchez, E., Kowalski, B.R.: Tensorial calibration: II. Second-order calibration. J. Chemom. 2(4), 265–280 (1988)
Olivieri, A.C.: On a versatile second-order multivariate calibration method based on partial least-squares and residual bilinearization: Second-order advantage and precision properties. J. Chemom. 19(7), 253–265 (2005)
Harshman, R.A.: Foundations of the PARAFAC procedure: models and conditions for an exploratory multimode factor analysis. UCLA Working Papers Phonetics 16, 1–84 (1970)
Bro, R.: Tutorial and applications. Chemom. Intell. Lab. Syst. 38(2), 149–171 (1997)
Wu, H.L., Shibukawa, M., Oguma, K.: An alternating trilinear decomposition algorithm with application to calibration of HPLC-DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons. J. Chemom. 12(1), 1–26 (1998)
Xia, A.L., Wu, H.L., Fang, D.M., Ding, Y.J., Hu, L.Q., Yu, R.Q.: Alternating penalty trilinear decomposition algorithm for second-order calibration with application to interference-free analysis of excitation–emission matrix fluorescence data. J. Chemom. 19(2), 65–76 (2005)
Bosco, M.V., Garrido, M., Larrechi, M.S.: Determination of phenol in the presence of its principal degradation products in water during a TiO2-photocatalytic degradation process by three dimensional excitation-emission matrix fluorescence and parallel factor analysis. Anal. Chim. Acta. 559(2), 240–247 (2006)
Mitchell, B.C., Burdick, D.S.: Slowly converging PARAFAC sequences: swamps and two-factor degeneracies. J. Chemom. 8(2), 155–168 (1994)
Rayens, W.S., Mitchell, B.C.: Two-factor degeneracies and a stabilization of PARAFAC. Chemom. Intell. Lab. Syst. 38(2), 173–181 (1997)
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Sun, J. (2012). An Alternating Simultaneously Minimizing Diagonal Matrix Error and Covariant Matrix Error Trilinear Decomposition Algorithm for Second-Order Calibration. In: Tan, H. (eds) Knowledge Discovery and Data Mining. Advances in Intelligent and Soft Computing, vol 135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27708-5_6
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DOI: https://doi.org/10.1007/978-3-642-27708-5_6
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