Review on multiway analysis in chemistry - 2000-2005

Critical Reviews in Analytical Chemistry

Volumn 36, Issue 3-4, 2006, Pages 279-293

  Bro, Rasmus ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

PARAFAC; Tensor; Three way; Tucker

Indexed keywords

DATA REDUCTION; PHYSICAL CHEMISTRY; RESEARCH;

MULTIWAY ANALYSIS;

CHEMICAL ANALYSIS;

CHEMICAL ANALYSIS; DATA REDUCTION; PHYSICAL CHEMISTRY; RESEARCH;

CHEMICAL ANALYSIS; STATISTICAL ANALYSIS;

EID: 33845429108     PISSN: 10408347     EISSN: 15476510     Source Type: Journal    
DOI: 10.1080/10408340600969965     Document Type: Review

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244. Xie, H. and Jiang, J. and Long, N. and Shen, G. and Wu, H. and Yu, R. (2003) Estimation of chemical rank of a three-way array using a two-mode subspace comparison approach Chemometrics and Intelligent Laboratory Systems, 66(2), pp. 101-115.
245. Xie, H. and Jiang, J. and Chu, X. and Cui, H. and Wu, H. and Shen, G. and Yu, R. (2002) Competitive interaction of the antitumor drug daunorubicin and the fluorescence probe ethidium bromide with DNA as studied by resolving trilinear fluorescence data: The use of PARAFAC and its modification Analytical and Bioanalytical Chemistry, 373(3), pp. 159-162.
246. ten Berge, J. and Sidiropoulos, N. (2002) On uniqueness in Candecomp/ Parafac Psychometrika, 67(3), pp. 399-409.
247. Ten Berge, J. and Sidiropoulos, N. (2002) Some new results on uniqueness in CANDECOMP/PARAFAC Psychometrika, 67, pp. 399-409.
248. Henrion, R. (2000) On global, local and stationary solutions in three-way data analysis Journal of Chemometrics, 14(3), pp. 261-274.
249. Zijlstra, B. and Kiers, H. (2002) Degenerate solutions obtained from several variants of factor analysis Journal of Chemometrics, 16(11), pp. 596-605.
250. Abrescia, S. (2004) A characterization of degenerate tridimensional tensors Journal of Pure and Applied Algebra, 187(1-3), pp. 1-17.
251. De Lathauwer, L. and Vandewalle, J. (2004) Dimensionality reduction in higher-order signal processing and rank- (R-1, R-2,..., R-N) reduction in multilinear algebra Linear Algebra and its Applications, 391, pp. 31-55.
252. De Lathauwer, L. and Vandewalle, J. (2004) Dimensionality reduction in ICA and rank- (R-1, R-2,..... R-N) reduction in multilinear algebra Independent Component Analysis and Blind Signal Separation, 3195, pp. 295-302.
253. De Lathauwer, L. (2004) First-order perturbation analysis of the best rank- (R-1, R-2, R-3) approximation in multilinear algebra Journal of Chemometrics, 18(1), pp. 2-11.
254. Paatero, P. (2000) Construction and analysis of degenerate PARAFAC models Journal of Chemometrics, 14(3), pp. 285-299.
255. ten Berge, J. and Smilde, A. (2002) Non-triviality and identification of a constrained Tucker3 analysis Journal of Chemometrics, 16(12), pp. 609-612.
256. Rocci, R. and ten Berge, J. (2002) Transforming three-way arrays to maximal simplicity Psychometrika, 67(3), pp. 351-365.
257. ten Berge, J. and Kiers, H. and Murakami, T. and van der Heijden, R. (2000) Transforming three-way arrays to multiple orthonormality Journal of Chemometrics, 14(3), pp. 275-284.
258. ten Berge, J. and Sidiropoulos, N. and Rocci, R. (2004) Typical rank and indscal dimensionality for symmetric three-way arrays of order Ix2x2 or Ix3x3 Linear Algebra and its Applications, 388, pp. 363-377.
259. ten Berge, J. (2000) The typical rank of tall three-way arrays Psychometrika, 65(4), pp. 525-532.
260. Kiers, H. and TenBerge, J. and Rocci, R. (1997) Uniqueness of three-mode factor models with sparse cores: The 3x3x3 case Psychometrika, 62, pp. 349-374.
261. Kiers, H. (2000) Some procedures for displaying results from three-way methods Journal of Chemometrics, 14(3), pp. 151-170.
262. Geladi, P. and Manley, M. and Lestander, T. (2003) Scatter plotting in multivariate data analysis Journal of Chemometrics, 17(8-9), pp. 503-511.
263. Bro, R. and Smilde, A. (2003) Centering and scaling in component analysis Journal of Chemometrics, 17(1), pp. 16-33.
264. Bylund, D. and Danielsson, R. and Malmquist, G. and Markides, K. (2002) Chromatographic alignment by warping and dynamic programming as a pre-processing tool for PARAFAC modelling of liquid chromatography-mass spectrometry data Journal of Chromatography A, 961(2), pp. 237-244.
265. Wu, W. and Guo, Q. and Massart, D. and Boucon, C. and de Jong, S. (2003) Structure preserving feature selection in PARAFAC using a genetic algorithm and Procrustes analysis Chemometrics and Intelligent Laboratory Systems, 65(1), pp. 83-95.
266. Cao, Y. and Chen, H. and Wu, H. and Yu, R. (2003) An algorithm for three-way data analysis that alternatively minimizes coupled vector (COV) resolution error and PARAFAC error Analytical Sciences, 19(5), pp. 753-756.
267. Cao, Y. and Chen, Z. and Mo, C. and Wu, H. and Yu, R. (2000) A PARAFAC algorithm using penalty diagonalization error (PDE) for three-way data array resolution Analyst, 125(12), pp. 2303-2310.
268. Chen, Z. and Wu, H. and Li, Y. and Yu, R. (2000) Novel constrained PARAFAC algorithm for second-order linear calibration Analytica Chimica Acta, 423(2), pp. 187-196.
269. Chen, Z. and Wu, H. and Jiang, J. and Li, Y. and Yu, R. (2000) A novel trilinear decomposition algorithm for second-order linear calibration Chemometrics and Intelligent Laboratory Systems, 52(1), pp. 75-86.
270. Chen, Z. and Wu, H. and Yu, R. (2001) On the self-weighted alternating trilinear decomposition algorithm - the property of being insensitive to excess factors used in calculation Journal of Chemometrics, 15(5), pp. 439-453.
271. Chen, Z. and Li, Y. and Yu, R. (2001) Pseudo alternating least squares algorithm for trilinear decomposition Journal of Chemometrics, 15(3), pp. 149-167.
272. Li, Y. and Jiang, J. and Wu, H. and Chen, Z. and Yu, R. (2000) Alternating coupled matrices resolution method for three-way arrays analysis Chemometrics and Intelligent Laboratory Systems, 52(1), pp. 33-43.
273. Jiang, H. and Wu, H. and Li, Y. and Yu, R. (1999) Alternating coupled vectors resolution (ACOVER) method for trilinear analysis of three-way data Journal of Chemometrics, 13(6), pp. 557-578.
274. Mo, C. and Cao, Y. (2005) An alternatively minimising covariant matrix error algorithm for three-way data resolution Chemia Analityczna, 50(4), pp. 673-683.
275. Lu, J. and Wu, H. and Jiang, J. and Long, N. and Mo, C. and Yu, R. (2003) An improved trilinear decomposition algorithm based on a Lagrange operator Analytical Sciences, 19(7), pp. 1037-1043.
276. Tomasi, G. and Bro, R. (2006) A comparison of algorithms for fitting the PARAFAC model Computational Statistics and Data Analysis, 50(7), pp. 1700-1734.
277. Faber, N. and Bro, R. and Hopke, P. (2003) Recent developments in CANDECOMP/ PARAFAC algorithms: A critical review Chemometrics and Intelligent Laboratory Systems, 65, pp. 119-137.
278. Timmerman, M. and Kiers, H. (2002) Three-way component analysis with smoothness constraints Computational Statistics and Data Analysis, 40(3), pp. 447-470.
279. Reis, M. and Ferreira, M. (2002) PARAFAC with splines: A case study Journal of Chemometrics, 16(8-10), pp. 444-450.
280. Tomasi, G. and Bro, R. (2005) PARAFAC and missing values Chemometrics and Intelligent Laboratory Systems, 75, pp. 163-180.
281. Wang, J. and Hopke, P. (2001) Equation-oriented system: An efficient programming approach to solve multilinear and polynomial equations by the conjugate gradient algorithm Chemometrics and Intelligent Laboratory Systems, 55(1-2), pp. 13-22.
282. Vega-Montoto, L. and Wentzell, P. (2006) Approaching the direct exponential curve resolution algorithm from a maximum likelihood perspective Analytica Chimica Acta, 556(2), pp. 383-399.
283. Vega-Montoto, L. and Wentzell, P. (2005) Mathematical improvements to maximum likelihood parallel factor analysis: Experimental studies Journal of Chemometrics, 19(4), pp. 236-252.
284. Vega-Montoto, L. and Gu, H. and Wentzell, P. (2005) Mathematical improvements to maximum likelihood parallel factor analysis: Theory and simulations Journal of Chemometrics, 19(4), pp. 216-235.
285. Vega-Montoto, L. and Wentzell, P. (2003) Maximum likelihood parallel factor analysis (MLPARAFAC) Journal of Chemometrics, 17(4), pp. 237-253.
286. Bro, R. and Sidiropoulos, N. and Smilde, A. (2002) Maximum likelihood fitting using simple least squares algorithms Journal of Chemometrics, 16(8-10), pp. 387-400.
287. Riu, J. and Bro, R. (2003) Jack-knife technique for outlier detection and estimation of standard errors in PARAFAC models Chemometrics and Intelligent Laboratory Systems, 65(1), pp. 35-49.
288. Kiers, H. (2004) Bootstrap confidence intervals for three-way methods Journal of Chemometrics, 18(1), pp. 22-36.
289. Serneels, S. and Van Espen, P. (2005) Bootstrap confidence intervals for trilinear partial least squares regression Analytica Chimica Acta, 544(1-2), pp. 153-158.
290. Liu, X. and Sidiropoulos, N. (2001) Cramer-Rao lower bounds for low-rank decomposition of multidimensional arrays IEEE Transactions on Signal Processing, 49(9), pp. 2074-2086.
291. Faber, N. (2001) Comment on a recently proposed resampling method Journal of Chemometrics, 15(3), pp. 169-188.
292. Olivieri, A. (2004) Sample-specific standard prediction errors in three-way parallel factor analysis (PARAFAC) exploiting the second-order advantage Journal of Chemometrics, 18(7-8), pp. 363-371.
293. Bro, R. and Rinnan, A. and Faber, N. (2005) Standard error of prediction for multilinear PLS - 2. Practical implementation in fluorescence spectroscopy Chemometrics and Intelligent Laboratory Systems, 75(1), pp. 69-76.
294. Faber, N. and Bro, R. (2002) Standard error of prediction for multiway PLS 1. Background and a simulation study Chemometrics and Intelligent Laboratory Systems, 61(1-2), pp. 133-149.
295. Serneels, S. and Lemberge, P. and Van Espen, P. (2004) Calculation of PLS prediction intervals using efficient recursive relations for the Jacobian matrix Journal of Chemometrics, 18(2), pp. 76-80.
296. Linder, M. and Sundberg, R. (2002) Precision of prediction in second-order calibration, with focus on bilinear regression methods Journal of Chemometrics, 16(1), pp. 12-27.
297. Olivieri, A. (2005) Computing sensitivity and selectivity in parallel factor analysis and related multiway techniques: The need for further developments in net analyte signal theory Analytical Chemistry, 77(15), pp. 4936-4946.
298. Boque, R. and Ferre, J. and Faber, N. and Rius, F. (2002) Limit of detection estimator for second-order bilinear calibration Analytica Chimica Acta, 451(2), pp. 313-321.
299. Andersson, C. and Bro, R. (2000) The N-way Toolbox for MATLAB Chemometrics and Intelligent Laboratory Systems, 52(1), pp. 1-4.
300. de Juan, A. (2000) N-way toolbox for MATLAB Journal of Chemometrics, 14(4), pp. 379-380.
301. Gourvénec, S. and Tomasi, G. and Durville, C. and Di Crescenzo, E. and Saby, C. and Massart, D. and Bro, R. and Oppenheim, G. (2005) CuBatch, a MATLAB interface for n-mode data analysis Chemometrics and Intelligent Laboratory Systems, 77, pp. 122-130.
302. Kiers, H. and ten Berge, J. and Bro, R. (1999) PARAFAC2 - Part I. A direct fitting algorithm for the PARAFAC2 model Journal of Chemometrics, 13, pp. 275-294.
303. Bro, R. and Andersson, C. and Kiers, H. (1999) PARAFAC2 - Part II. Modeling chromatographic data with retention time shifts Journal of Chemometrics, 13, pp. 295-309.
304. Bro, R. and Sidiropoulos, N. and Giannakis, G.(1999). A Fast Least Squares Algorithm for Separating Trilinear Mixtures. Proc. ICA99 - Int. Workshop on Independent Component Analysis and Blind Signal Separation AussoisFranceJan.11-15. In [pp. 289-294].