Nonnegative PARAFAC2: A Flexible Coupling Approach

Modeling variability in tensor decomposition methods is one of the challenges of source separation. One possible solution to account for variations from one data set to another, jointly analysed, is to resort to the PARAFAC2 model. However, so far imposing constraints on the mode with variability has not been possible. In the following manuscript, a relaxation of the PARAFAC2 model is introduced, that allows for imposing nonnegativity constraints on the varying mode. An algorithm to compute the proposed flexible PARAFAC2 model is derived, and its performance is studied on both synthetic and chemometrics data.

[1]  Barry M. Wise,et al.  Application of PARAFAC2 to fault detection and diagnosis in semiconductor etch , 2001 .

[2]  R. Harshman.  The differences between analysis of covariance and correlation , 2001 .

[3]  R. Bro,et al.  PARAFAC2—Part I. A direct fitting algorithm for the PARAFAC2 model , 1999 .

[4]  R. Bro,et al.  Solving GC-MS problems with PARAFAC2 , 2008 .

[5]  Pierre Comon,et al.  Exploring Multimodal Data Fusion Through Joint Decompositions with Flexible Couplings , 2015, IEEE Transactions on Signal Processing.

[6]  R. Harshman,et al.  Shifted factor analysis—Part I: Models and properties , 2003 .

[7]  R. Bro,et al.  Gas chromatography - mass spectrometry data processing made easy. , 2017, Journal of chromatography. A.

[8]  Nicolas Gillis,et al.  Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization , 2011, Neural Computation.

[9]  Nicolas Gillis,et al.  Two algorithms for orthogonal nonnegative matrix factorization with application to clustering , 2012, Neurocomputing.

[10]  P. Comon,et al.  Tensor decompositions, alternating least squares and other tales , 2009 .

[11]  Rasmus Bro,et al.  A new approach for modelling sensor based data , 2005 .

[12]  Lars Kai Hansen,et al.  Shift-invariant multilinear decomposition of neuroimaging data , 2008, NeuroImage.

[13]  Luis A. Sarabia,et al.  Building robust calibration models for the analysis of estrogens by gas chromatography with mass spectrometry detection , 2004 .

[14]  Rasmus Bro,et al.  Classification of GC‐MS measurements of wines by combining data dimension reduction and variable selection techniques , 2008 .