Quadratic optimization for simultaneous matrix diagonalization

Vollgraf, Roland; Obermayer, Klaus

doi:10.1109/tsp.2006.877673

Cited by 93 publications

(90 citation statements)

References 13 publications

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“…Interestingly, the estimation of the optimal parameters is the same as the one we obtained before when using the matrix transformation in (16).…”

Section: Proofmentioning

confidence: 84%

“…Many other algorithms have been developed by considering specific criteria or constraints in order to avoid trivial and degenerate solutions [14] [15]. These algorithms can be listed as follow: QDiag [16] (Quadratic Diagonalization algorithm) developed by Vollgraf and Obermayer where the JD criterion is rearranged as a quadratic cost function; FAJD [17] (Fast Approximative Joint Diagonalization) developed by Li and Zhang where the diagonalizing matrix is estimated column by column; UWEDGE [14] (UnWeighted Exhaustive joint Diagonalization with Gauss itErations) developed by Tichavsky and Yeredor where numerical optimization is used to get the JD solution; JUST [18] (Joint Unitary and Shear Transformations) developed by Iferroudjene, Abed-Meraim and Belouchrani where the algebraic joint diagonalization is considered; CVFFDiag [19] [20] (Complex Valued Fast Frobenius Diagonalization) developed by Xu, Feng and Zheng where first order of Taylor expansion is used to minimize the JD criterion; ALS [21] (Alternating Least Squares) developed by Trainini and Moreau where the mixing and diagonal matrices are estimated alternatively by using least squares criterion and LUCJD [22] [23] (LU decomposition for Complex Joint Diagonalization) developed by Wang, Gong and Lin where the diagonalizing matrix is estimated by LU decomposition.…”

Section: Introductionmentioning

confidence: 99%

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A New Algorithm for Complex Non-Orthogonal Joint Diagonalization Based on Shear and Givens Rotations

Mesloub

Abed-Meraim²,

Belouchrani³

2014

IEEE Trans. Signal Process.

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This paper introduces a new algorithm to approximate non orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the JD problem and takes advantage from combining Givens and Shear rotations to attempt the approximate joint diagonalization (JD). It represents a non trivial generalization of the JDi (Joint Diagonalization) algorithm (Souloumiac 2009) to the complex case. The JDi is first slightly modified then generalized to the CJDi (i.e. Complex JDi) using complex to real matrix transformation. Also, since several methods exist already in the literature, we propose herein a brief overview of existing NOJD algorithms then we provide an extensive comparative study to illustrate the effectiveness and stability of the CJDi w.r.t. various system parameters and application contexts.Index Terms-Non orthogonal joint diagonalization, Performance comparison of NOJD algorithm, Givens and Shear rotations.

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“…Interestingly, the estimation of the optimal parameters is the same as the one we obtained before when using the matrix transformation in (16).…”

Section: Proofmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

A New Algorithm for Complex Non-Orthogonal Joint Diagonalization Based on Shear and Givens Rotations

Mesloub

Abed-Meraim²,

Belouchrani³

2014

IEEE Trans. Signal Process.

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“…We compare our LSDIC algorithm to the well-established FFDIAG algorithm of [10] and QDIAG of [9]. We plan to perform a more comprehensive comparison and to publish that in a longer article elsewhere.…”

Section: Simulationmentioning

confidence: 99%

“…Mean and standard deviation (in parentheses) of the performance index (7) attained by QDIAG [9], FFDIAG [10] and our LSDIC algorithm across 250 repetitions of the simulation with K = 15 and N = 30. The higher the mean and the lower the standard deviation, the better the performance.…”

Section: Orthogonal Mixingmentioning

confidence: 99%

“…This restriction allows BSS only after whitening the sensor measurements, but whitening is known to affect adversely the quality of the separation forcing the data covariance to be exactly diagonal at the expenses of the input matrix set. In [9,5] it is required instead that Diag(B T C 0 B) = I, with C 0 being some positive definite matrix, Diag denoting the operator which cancels the off diagonal elements of its matrix argument. This amounts to a normalization of the columns of B (a scaling).…”

Section: Introductionmentioning

confidence: 99%

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Least Square Joint Diagonalization of Matrices under an Intrinsic Scale Constraint

Pham¹,

Congedo²

2009

Independent Component Analysis and Signal Separation

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To cite this version:Abstract. We present a new algorithm for approximate joint diagonalization of several symmetric matrices. While it is based on the classical least squares criterion, a novel intrinsic scale constraint leads to a simple and easily parallelizable algorithm, called LSDIC (Least squares Diagonalization under an Intrinsic Constraint). Numerical simulations show that the algorithm behaves well as compared to other approximate joint diagonalization algorithms.

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Co‐channel interference cancellation based on BSS for multi‐satellite MIMO communication systems with FFR

Qin,

Zhang,

et al. 2024

Satell Commun Network

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SummaryMultiple‐input multiple‐output (MIMO) technology can boost the capacity of conventional satellite communications, and full frequency reuse (FFR) can further improve the capacity by making full use of frequency resources. However, FFR will cause severe co‐channel interference and lead to a degradation of channel capacity. Blind source separation (BSS) algorithm can be used to eliminate co‐channel interference and does not require prior information, which avoids the extra occupation of channel frequency resources. While the multi‐satellite MIMO communication system have delay mixing characteristic, the separation performance will be degraded if the delay is ignored. In this paper, DMBSS algorithm for delay mixing is proposed. Firstly, the DMBSS algorithm utilizes Taylor expansion to achieve dimension expansion of observed signals and so as to transform the delay mixing into instantaneous mixing with extended dimension. Secondly, complex non‐orthogonal joint diagonalization algorithm is used to solve the separation matrix equation of extended observation signals and extended source signals and thus to eliminate the co‐channel interference. Simulation results show that for multi‐satellite MIMO communication scenarios with FFR, the proposed algorithm can effectively improve the performance of co‐channel interference cancellation and reduce the value of BER. Furthermore, the influence of order of Taylor expansion on the separation performance is also analyzed and simulated in this paper to show the cost performance of the proposed algorithm.

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Quadratic optimization for simultaneous matrix diagonalization

Cited by 93 publications

References 13 publications

A New Algorithm for Complex Non-Orthogonal Joint Diagonalization Based on Shear and Givens Rotations

A New Algorithm for Complex Non-Orthogonal Joint Diagonalization Based on Shear and Givens Rotations

Least Square Joint Diagonalization of Matrices under an Intrinsic Scale Constraint

Co‐channel interference cancellation based on BSS for multi‐satellite MIMO communication systems with FFR

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