A comparison of algorithms for fitting the PARAFAC model

By Giorgio Tomasi, Rasmus Bro. 2006

407 citations recorded by the source corpus.

Subfields: Computational Mathematics, Signal Processing

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In Signal Processing

Citations in the corpus

Tensors : A brief introduction (2014, background): “[77], [65], [46], [21], [84]; they are widely used but their convergence towards a minimum is not guaranteed, because the objective function may have only an infimum.”
Unsupervised Multiway Data Analysis: A Literature Survey (2009, methodology): “Tomasi and Bro [57] highlight the advantages of SWATLD algorithm in the case of overfactoring and also suggest PMF3 [58] and Levenberg-Marquadt algorithm [58], [59] as alternative algorithms with better convergence properties than ALS for fitting a PARAFAC model.”
A scalable optimization approach for fitting canonical tensor decompositions (2011, methodology): “Likewise, CP is unchanged by scaling, e.g., [[ A (1) , A (2) ,... , A ( N ) ]] = 2 A (1) , 1 2 A (2) ,... , A ( N ) .”
Tensor Algebra and Multidimensional Harmonic Retrieval in Signal Processing for MIMO Radar (2010, background): “For a nondispersive propagation medium, the baseband received signal (3) after synchronization can be written on a per-pulse basis as [28] (12) where collects the samples observed by the antennas for the th pulse period, is the noise-term for the th pulse period.”
Efficient MATLAB Computations with Sparse and Factored Tensors (2007, positive): “Recent decades have seen tremendous growth in this area with a focus towards improved algorithms for computing the decompositions [13, 12, 58, 50].”
FFT-based Kronecker product approximation to micromagnetic long-range interactions (2012, methodology): “alternating least squares [22], gradient based or nonlinear least squares methods [3] or Gauss-Newton [30].”
Tensor decompositions, alternating least squares and other tales (2009, methodology): “One can mention in particular the Conjugate Gradient [46], Gauss-Newton and Levenberg-Marquardt [ 69 ] algorithms.”
A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition (2011, methodology): “The figures present convergence plots for a dense test problem that is a standard test case for CP decomposition from the literature [26, 2].”
Hadamard, Khatri-Rao, Kronecker and Other Matrix Products (2008, neutral): “…validation and constraints, and on other associated models, data analysis and applications in psychometrics, signal processing, chemometrics and food sciences, see e.g. Bro (1998), Ten Berge and Sidiropoulos (2002), Jiang and Sidiropoulos (2004), Smilde et al. (2004) and Tomasi and Bro (2006).”
Distributed large-scale tensor decomposition (2014, neutral): “[3, 4, 5]).”
All-at-once Optimization for Coupled Matrix and Tensor Factorizations (2011, background): “nating least squares approach and the numerical results show that all-at-once optimization is more robust to overfactoring as it has also been the case for fitting tensor models [2, 32].”