How 3-MFA data can cause degenerate parafac solutions, among other relationships
Multiway data analysis
Cramer-Rao lower bounds for low-rank decomposition ofmultidimensional arrays
IEEE Transactions on Signal Processing
Blind PARAFAC signal detection for polarization sensitive array
EURASIP Journal on Applied Signal Processing
Editorial: Special Issue on Statistical Algorithms and Software
Computational Statistics & Data Analysis
Blind Joint Symbol Detection and DOA Estimation for OFDM System with Antenna Array
Wireless Personal Communications: An International Journal
Scenario Discovery Using Nonnegative Tensor Factorization
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Adaptive algorithms to track the PARAFAC decomposition of a third-order tensor
IEEE Transactions on Signal Processing
Blind multiuser detection for MC-CDMA with antenna array
Computers and Electrical Engineering
Sequential unfolding SVD for tensors with applications in array signal processing
IEEE Transactions on Signal Processing
Hierarchical multilinear models for multiway data
Computational Statistics & Data Analysis
Batch and adaptive PARAFAC-based blind separation of convolutive speech mixtures
IEEE Transactions on Audio, Speech, and Language Processing
Classification with sums of separable functions
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
Tensor algebra and multidimensional harmonic retrieval in signal processing for MIMO radar
IEEE Transactions on Signal Processing
Novel blind carrier frequency offset estimation for OFDM system with multiple antennas
IEEE Transactions on Wireless Communications
SIAM Journal on Matrix Analysis and Applications
Speech separation via parallel factor analysis of cross-frequency covariance tensor
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Computing the polyadic decomposition of nonnegative third order tensors
Signal Processing
PARAFAC algorithms for large-scale problems
Neurocomputing
Fast metadata-driven multiresolution tensor decomposition
Proceedings of the 20th ACM international conference on Information and knowledge management
SIAM Journal on Matrix Analysis and Applications
Block component analysis, a new concept for blind source separation
LVA/ICA'12 Proceedings of the 10th international conference on Latent Variable Analysis and Signal Separation
Robust tensor classifiers for color object recognition
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
MultiAspectForensics: mining large heterogeneous networks using tensor
International Journal of Web Engineering and Technology
Computational Statistics & Data Analysis
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A multitude of algorithms have been developed to fit a trilinear PARAFAC model to a three-way array. Limits and advantages of some of the available methods (i.e. GRAM-DTLD, PARAFAC-ALS, ASD, SWATLD, PMF3 and dGN) are compared. The algorithms are explained in general terms together with two approaches to accelerate them: line search and compression. In order to compare the different methods, 720 sets of artificial data were generated with varying level and type of noise, collinearity of the factors and rank. Two PARAFAC models were fitted on each data set: the first having the correct number of factors F and the second with F+1 components (the objective being to assess the sensitivity of the different approaches to the over-factoring problem, i.e. when the number of extracted components exceeds the rank of the array). The algorithms have also been tested on two real data sets of fluorescence measurements, again by extracting both the right and an exceeding number of factors. The evaluations are based on: number of iterations necessary to reach convergence, time consumption, quality of the solution and amount of resources required for the calculations (primarily memory).