Flag Manifolds for Subspace ICA Problems

Nishimori, Yasunori; Akaho, Shotaro; Abdallah, Samer A.; Plumbley, Mark D.

doi:10.1109/icassp.2007.367345

Cited by 9 publications

(6 citation statements)

References 9 publications

(5 reference statements)

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“…Manifolds of this type are used, among others, in invariant subspace analysis, application-driven dimension reduction and subspace tracking [24,25]. When there is a need for a simultaneous (parallel) subspace extraction, as is the case in independent subspace analysis (ISA), one resorts to the concept of generalized flag manifold, which is a manifold consisting of orthogonal subspaces that constitutes a generalization of both Stiefel and Grassmann manifolds [26][27][28]. The generalized flag manifold Fl(n, d 1 , .…”

Section: Geometry Of Ica Isa and Other Bsp Modelsmentioning

confidence: 99%

Lie Group Methods in Blind Signal Processing

Mika

Jóźwik

2020

Sensors

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This paper deals with the use of Lie group methods to solve optimization problems in blind signal processing (BSP), including Independent Component Analysis (ICA) and Independent Subspace Analysis (ISA). The paper presents the theoretical fundamentals of Lie groups and Lie algebra, the geometry of problems in BSP as well as the basic ideas of optimization techniques based on Lie groups. Optimization algorithms based on the properties of Lie groups are characterized by the fact that during optimization motion, they ensure permanent bonding with a search space. This property is extremely significant in terms of the stability and dynamics of optimization algorithms. The specific geometry of problems such as ICA and ISA along with the search space homogeneity enable the use of optimization techniques based on the properties of the Lie groups O ( n ) and S O ( n ) . An interesting idea is that of optimization motion in one-parameter commutative subalgebras and toral subalgebras that ensure low computational complexity and high-speed algorithms.

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Section: Geometry Of Ica Isa and Other Bsp Modelsmentioning

confidence: 99%

Lie Group Methods in Blind Signal Processing

Mika

Jóźwik

2020

Sensors

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“…For solving the optimization problem in (24), we will use an iterative algorithm based on Riemannian optimization method [26], which can be considered as a generalization of the standard euclidean optimization by formulating the optimization problem over smooth manifolds instead of the standard euclidean space [27][28][29]. The update rule for the IA iterative algorithm that based on maximizing the sum-rate is given by the Riemannian optimization over the Grassmann manifold and based on geodesics of a straight line in the euclidean space to the manifold.…”

Section: Sum-rate Maximization Approachmentioning

confidence: 99%

“…The update rule for the iterative algorithm that computes the decoding matrices U m is derived by substituting (28) and (30) in (27).…”

Section: Sum-rate Maximization Approachmentioning

confidence: 99%

Joint interference alignment and power allocation for NOMA-based multi-user MIMO systems

Rihan

Zhang

2018

J Wireless Com Network

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Interference alignment (IA) and non-orthogonal multiple access (NOMA) are key technologies for achieving the capacity scaling required by next generation networks to overcome the unprecedented growth of data network traffic. Each of these technologies was proved to present excellent performance for MIMO systems. In this article, we propose a joint IA and power allocation (PA) framework for NOMA-based multiuser MIMO (MU-MIMO) systems. Different approaches for applying IA in downlink NOMA-based MU-MIMO systems will be addressed while implementing a PA technique that fully exploits the characteristics of NOMA-based systems. The proposed framework aims to maximize the sum-rate of the NOMA-based MU-MIMO system through combining IA with PA. The process begins by initially grouping the system users into clusters for optimum implementation of NOMA. The sum-rate maximization is carried out under cluster power budget, user quality-of-service (QoS), and robust successive interference cancellation (SIC) constraints. Meanwhile, it uses the power domain multiplexing strategy to allow the users within each cluster to share the data streams without exerting interference to one another. Three iterative joint IA and PA algorithms are proposed for NOMA-based MU-MIMO systems. Moreover, these algorithms are compared with orthogonal multiple access (OMA)-based MU-MIMO counterpart as well as the state-of-the-art techniques presented for NOMA-based MU-MIMO systems. Numerical simulations verify that the proposed framework can greatly improve the performance of NOMA-based MU-MIMO systems in terms of the achievable sum-rate when compared with OMA-based MU-MIMO and the state-of-the-art NOMA-based MU-MIMO systems.

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“…, 2d r ; R). Thus, the formula for the natural gradient and geodesics of real flag manifolds we obtained in [14] can also be complexified by replacing the real Euclidean gradient by the complex gradient and the transpose operator by the Hermitian transpose operator;…”

Section: Geometry Of Complex Flag Manifoldsmentioning

confidence: 99%

Natural Conjugate Gradient on Complex Flag Manifolds for Complex Independent Subspace Analysis

Nishimori

Akaho

Plumbley

2008

Artificial Neural Networks - ICANN 2008

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Abstract.We study the problem of complex-valued independent subspace analysis (ISA). We introduce complex flag manifolds to tackle this problem, and, based on Riemannian geometry, propose the natural conjugate gradient method on this class of manifolds. Numerical experiments demonstrate that the natural conjugate gradient method yields better convergence compared to the natural gradient geodesic search method.

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Flag Manifolds for Subspace ICA Problems

Cited by 9 publications

References 9 publications

Lie Group Methods in Blind Signal Processing

Lie Group Methods in Blind Signal Processing

Joint interference alignment and power allocation for NOMA-based multi-user MIMO systems

Natural Conjugate Gradient on Complex Flag Manifolds for Complex Independent Subspace Analysis

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