Independent component analysis, a survey of some algebraic methods

By Jean-François Cardoso, Pierre Comon. 1996

Subfields: Representation & Self-Supervised Learning

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Citations in the corpus

Beyond CCA: Moment Matching for Multi-View Models (2016, positive): “As in Podosinnikova et al. (2015), we use as evaluation metric the normalized (cid:96) 1 - error between a recovered matrix (cid:98) D and the true matrix D with the best permutation of columns err 1 ( (cid:98) D, D ) := min π ∈ PERM The minimization is over the possible permutations π ∈ PERM of…”
Rethinking LDA: Moment Matching for Discrete ICA (2015, methodology): “In this section, (a) we compare experimentally the GP/DICA cumulants with the LDA moments and (b) the spectral algorithm [3], the tensor power method [4] (TPM), the joint diagonalization (JD) algorithm from Algorithm 1, and variational inference for LDA [1].”
Tensor decompositions for learning latent variable models (2012, methodology): “Tensor decompositions have been used in signal processing and computational neuroscience for blind source separation and independent component analysis (ICA) [CJ10].”
A Spectral Algorithm for Latent Dirichlet Allocation (2012, methodology): “These algebraic ideas are also used by [29, 30] for learning a linea r transformation (in a noiseless setting) and provides a different provably correct algorithm, based on a certain ascent algorithm (rather than joint diagonalization approach, as in [27]), and a provably correct algorithm for the n”
On the Best Rank-1 and Rank-(R1 , R2, ... , RN) Approximation of Higher-Order Tensors (2000, background): “Multilinear algebra is gaining more and more interest, largely due to its applications in the context of higher-order statistics (HOS) [17, 18, 2 , 4, 5, 7].”
A Multilinear Singular Value Decomposition (2000, methodology): “(for general aspects of HOS, the interested reader is referred to the tutorial papers [34, 37, 38, 30] and the bibliography [41]; for the use of tensor decompositions as a basic tool in HOS-based signal processing, we refer to [11, 12, 9 , 19]).”
A Framework for Robust Subspace Learning (2003, methodology): “Other multi-linear models include tensorial approaches to structure from motion [33] or Independent Component Analysis (ICA) [12].”
On the Best Rank-1 and Rank-( (2004, background): “Multilinear algebra is gaining more and more interest, largely due to its applications in the context of higher-order statistics (HOS) [17, 18, 2, 4, 5, 7].”
Learning mixtures of spherical gaussians: moment methods and spectral decompositions (2012, methodology): “The Gaussian mixture model shares some similarities to a standard model for independent component analysis (ICA) [11, 8, 18, 12].”