Efficient FPGA Implementation of Conjugate Gradient Methods for Laplacian System using HLS

Rampalli, Sahithi; Sehgal, Natasha; Bindlish, Ishita; Tyagi, Tanya; Kumar, Pawan

doi:10.48550/arxiv.1803.03797

Cited by 2 publications

(2 citation statements)

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“…The problem (11) can be solved alternatively for Z and S. Then the resulting problem in Z is unconstrained least-squares problem, which can be solved using linear conjugate gradient algorithm (For various preconditioned CG approaches, see [4][5][6][7][8][9][12][13][14][15][16][17][18][19][20][21][22][23][24]), and over S it is non-negative leastsquares problem which can be solved using [37]. The cost g(U ) and the gradient ∇g(U ) can be easily computed following Lemma 3, hence, we employ Riemannian conjugate gradient to solve the outer optimization problem over U .…”

Section: Nonnegative Tensor Completionmentioning

confidence: 99%

Generalized Structured Low-Rank Tensor Learning

Naram

Sinha

Kumar

2023

Proceedings of the 6th Joint International Conference on Data Science &Amp; Management of Data (10th ACM IKDD CODS and 28th COM

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We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an optimization problem on manifolds. We develop first-order and second-order Riemannian optimization algorithms to solve it. The duality gap for the resulting problem is derived, and we experimentally verify the correctness of the proposed algorithm. We demonstrate the algorithm on nonnegative constraints and Hankel constraints.

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Section: Nonnegative Tensor Completionmentioning

confidence: 99%

Generalized Structured Low-Rank Tensor Learning

Naram

Sinha

Kumar

2023

Proceedings of the 6th Joint International Conference on Data Science &Amp; Management of Data (10th ACM IKDD CODS and 28th COM

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“…This is a sparse linear system in Z, which can be solved using linear conjugate gradient method. For various preconditioned CG approaches, see [53,33,34,35,36,37,38,42,48,52,41,43,44,45,46,47,49,50,51]. Problem (9) has only one term involving S. Hence, the optimization problem over S reduces to…”

Section: Convex Optimization Problemmentioning

confidence: 99%

Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion

Sinha

Naram

Kumar

2022

2022 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)

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Recent approaches to the tensor completion problem have often overlooked the nonnegative structure of the data. We consider the problem of learning a nonnegative lowrank tensor, and using duality theory, we propose a novel factorization of such tensors. The factorization decouples the nonnegative constraints from the low-rank constraints. The resulting problem is an optimization problem on manifolds, and we propose a variant of Riemannian conjugate gradients to solve it. We test the proposed algorithm across various tasks such as colour image inpainting, video completion, and hyperspectral image completion. Experimental results show that the proposed method outperforms many state-of-the-art tensor completion algorithms.

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Efficient FPGA Implementation of Conjugate Gradient Methods for Laplacian System using HLS

Cited by 2 publications

References 0 publications

Generalized Structured Low-Rank Tensor Learning

Generalized Structured Low-Rank Tensor Learning

Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion

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