CONFAC Decomposition Approach to Blind Identification of Underdetermined Mixtures Based on Generating Function Derivatives

Almeida, André L. F. de; Luciani, Xavier; Stegeman, Alwin; Comon, Pierre

doi:10.1109/tsp.2012.2208956

Cited by 18 publications

(14 citation statements)

References 52 publications

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“…For this simple case, we can express the factor matrix as X = [X] (1,2) We now show that G can be estimated using a GEVD, and A is a solution to a quadratic programming problem with quadratic constraints. Our proposed algorithm alternates the estimation of G and A.…”

Section: Generalized Eigenvalue Decomposition With Eigen Matrix Of Lomentioning

confidence: 97%

“…Symmetric tensors can be cumulant tensors, or derivative tensors of the second Generalised Characteristic Functions Performance comparison in solving the QP with three quadratic constraints. [1,10,20,34], or tensors representing similarity or interaction between groups of identities used for clustering [24,31]. We consider an order-4 tensor Y which is symmetric, i.e., y(i 1 , i 2 , i 3 , i 4 ) = y( j 1 , j 2 , j 3 , j 4 ), where [ j 1 , j 2 , j 3 , j 4 ] is any permutation of indices [i 1 , i 2 , i 3 , i 4 ].…”

Section: Best Rank-1 Tensor Approximation To Symmetric Tensor Of Order-4mentioning

confidence: 99%

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Quadratic programming over ellipsoids with applications to constrained linear regression and tensor decomposition

Phan

Yamagishi

Mandic

et al. 2019

Neural Comput & Applic

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A novel algorithm to solve the quadratic programming problem over ellipsoids is proposed. This is achieved by splitting the problem into two optimisation subproblems, quadratic programming over a sphere and orthogonal projection. Next, an augmented-Lagrangian algorithm is developed for this multiple constraint optimisation. Benefit from the fact that the QP over a single sphere can be solved in a closed form by solving a secular equation [14] and [16], we derive a tighter bound of the minimiser of the secular equation. We also propose to generate a new psd matrix with a low condition number from the matrices in the quadratic constraints. This correction method improves convergence of the proposed augmented-Lagrangian algorithm. Finally, applications of the quadratically constrained QP to bounded linear regression and tensor decompositions are presented.

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Section: Generalized Eigenvalue Decomposition With Eigen Matrix Of Lomentioning

confidence: 97%

Section: Best Rank-1 Tensor Approximation To Symmetric Tensor Of Order-4mentioning

confidence: 99%

Quadratic programming over ellipsoids with applications to constrained linear regression and tensor decomposition

Phan

Yamagishi

Mandic

et al. 2019

Neural Comput & Applic

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“…In this case, even if the mixing matrix is known or has been estimated, it is impossible to estimate the source signals directly. Therefore, in order to realize the source extraction from the mixed signals, some a priori knowledge about the whole system must to be exploited, such as independence or sparsity [25,26].…”

Section: Introductionmentioning

confidence: 99%

Blind Nonparametric Determined and Underdetermined Signal Extraction Algorithm for Dependent Source Mixtures

Wang

et al. 2015

Intelligent Computing Theories and Methodologies

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Abstract. Blind extraction or separation statistically independent source signals from linear mixtures have been well studied in the last two decades by searching for local extrema of certain objective functions, such as nonGaussianity (NG) measure. Blind source extraction (BSE) algorithm from underdetermined linear mixtures of the statistically dependent source signals is derived using nonparametric NG measure in this paper. After showing that maximization of the NG measure can also separate or extract the statistically weak dependent source signals, the nonparametric NG measure is defined by statistical distances between different source signals distributions based on the cumulative density function (CDF) instead of traditional probability density function (PDF), which can be estimated by the quantiles and order statistics using the L 2 norm efficiently. The nonparametric NG measure can be optimized by a deflation procedure to extract or separate the dependent source signals. Simulation results for synthesis and real world data show that the proposed nonparametric extraction algorithm can extract the dependent signals and yield ideal performance.

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“…The classical alternating least squares (ALS) method is used to compute CP decomposition. For the past few years, some new strategies have presented to improve these algorithms for better identification performance [8,9].…”

Section: Introductionmentioning

confidence: 99%

Underdetermined blind identification based on charrelation matrix and tucker decomposition

Luo

Zhu

2014

2014 Sixth International Conference on Wireless Communications and Signal Processing (WCSP)

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A novel underdetermined blind identification algorithm based on charrelation matrix and tucker decomposition is developed. The charrelation matrix is a generalization of covariance matrix, encompassing statistical information beyond second-order while maintaining a convenient 2-dimensional structure. The core functions of charrelation matrices in different processing-points are stacked as a three-order tensor, and then tucker decomposition of tensor is executed to estimate the mixing matrix. Theoretical analysis and simulation results illustrate the proposed algorithm perform better than the representative underdetermined blind identification algorithm based CP (CANDECOM/PARAFAC) decomposition in computational complexity and identification performance.

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CONFAC Decomposition Approach to Blind Identification of Underdetermined Mixtures Based on Generating Function Derivatives

Cited by 18 publications

References 52 publications

Quadratic programming over ellipsoids with applications to constrained linear regression and tensor decomposition

Quadratic programming over ellipsoids with applications to constrained linear regression and tensor decomposition

Blind Nonparametric Determined and Underdetermined Signal Extraction Algorithm for Dependent Source Mixtures

Underdetermined blind identification based on charrelation matrix and tucker decomposition

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