Block Power Method for SVD Decomposition

Bentbib, Abdeslem Hafid; Kanber, A.

doi:10.1515/auom-2015-0024

Cited by 23 publications

(19 citation statements)

References 8 publications

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“…Figure 1: Geometric interpretation of one step of projector-splitting optimization procedure: the gradient step an the retraction of the high-rank matrix X i +∇F (X i ) to the manifold of low-rank matrices M d . also quite intuitive: instead of computing the full SVD of X i + ∇F (X i ) according to the gradient projection method, we use just one step of the block power numerical method (Bentbib and Kanber, 2015) which computes the SVD, what reduces the computational complexity.…”

Section: Discussionmentioning

confidence: 99%

Riemannian Optimization for Skip-Gram Negative Sampling

Fonarev¹,

Grinchuk²,

Gusev

et al. 2017

Proceedings of the 55th Annual Meeting of the Association For Computational Linguistics (Volume 1: Long Papers)

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Skip-Gram Negative Sampling (SGNS) word embedding model, well known by its implementation in "word2vec" software, is usually optimized by stochastic gradient descent. However, the optimization of SGNS objective can be viewed as a problem of searching for a good matrix with the low-rank constraint. The most standard way to solve this type of problems is to apply Riemannian optimization framework to optimize the SGNS objective over the manifold of required low-rank matrices. In this paper, we propose an algorithm that optimizes SGNS objective using Riemannian optimization and demonstrates its superiority over popular competitors, such as the original method to train SGNS and SVD over SPPMI matrix.

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Section: Discussionmentioning

confidence: 99%

Riemannian Optimization for Skip-Gram Negative Sampling

Fonarev¹,

Grinchuk²,

Gusev

et al. 2017

Proceedings of the 55th Annual Meeting of the Association For Computational Linguistics (Volume 1: Long Papers)

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“…Then, the contribution of each derived RF precoding vector was iteratively cancelled to form the residual optimal covariance matrix G n (Line 9 of Algorithm 3). Because only the first singular vector was required, we used the power SVD method [13] (Algorithm 4) to avoid the complete SVD processing. The accuracy of u (Np) increases along with N p .…”

Section: B Kkt-condition-based Algorithmmentioning

confidence: 99%

“…13: end for Output: FRF Algorithm 4 Power Method for SVD [13] Input: A square matrix G ∈ C n×n , iteration Np 1:…”

Section: B Kkt-condition-based Algorithmmentioning

confidence: 99%

Low-Complexity Wideband Hybrid Precoding for mmWave MIMO-OFDM

Fang

Tso

et al. 2021

2021 IEEE International Symposium on Circuits and Systems (ISCAS)

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Hybrid RF and baseband precoding can not only deal with low-scattering problem caused by severe signal attenuation of mmWave but also significantly reduce the power and cost of radio frequency (RF) chains and data converters in the massive MIMO transceiver. However, its baseband complexity is still very high for frequency-selective multi-carrier system such as orthogonal frequency division multiplexing (OFDM). Therefore, this paper proposes a computationally-efficient hybrid precoding algorithm for mmWave MIMO-OFDM systems. By decomposing the optimization of spectrum efficiency into many sub-optimization problems, we developed an iterative matrixinversion-bypass algorithm to reduce the complexity. The baseband precoder was also designed to further reduce total complexity. The simulation and complexity analysis results showed that we can significantly reduce computational complexity for mmWave MIMO with negligible performance degradation compared to a state-of-the-art work in the literature.

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“…Following the sole objective of image compression using SVD, the most problem is which K rank to use for giving a better image compression. For this reason, the method presented in El Asnaoui et al, [14], introduces two new approaches: The first one is an improvement of the Block Truncation Coding method that overcomes the disadvantages of the classical Block Truncation Coding, while the second one describes how to obtain a new rank of SVD method, which gives a better image compression.…”

Section: Lossy Compression Is Another Type Of Image Compressionmentioning

confidence: 99%

Image Compression Techniques Using Linear Algebra with SVD Algorithm

Selvam¹,

Selvam²

2021

AJEAT

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In recent days, the data are transformed in the form of multimedia data such as images, graphics, audio and video. Multimedia data require a huge amount of storage capacity and transmission bandwidth. Consequently, data compression is used for reducing the data redundancy and serves more storage of data. In this paper, addresses the problem (demerits) of the lossy compression of images. This proposed method is deals on SVD Power Method that overcomes the demerits of Python SVD function. In our experimental result shows superiority of proposed compression method over those of Python SVD function and some various compression techniques. In addition, the proposed method also provides different degrees of error flexibility, which give minimum of execution of time and a better image compression.

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Block Power Method for SVD Decomposition

Cited by 23 publications

References 8 publications

Riemannian Optimization for Skip-Gram Negative Sampling

Riemannian Optimization for Skip-Gram Negative Sampling

Low-Complexity Wideband Hybrid Precoding for mmWave MIMO-OFDM

Image Compression Techniques Using Linear Algebra with SVD Algorithm

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