Optimized quantum singular value thresholding algorithm based on a hybrid quantum computer

2021 ◽  
Author(s):  
Yangyang Ge ◽  
Zhimin Wang ◽  
Wen Zheng ◽  
Yu Zhang ◽  
Xiangmin Yu ◽  
...  
Keyword(s):  
Quantum Computer ◽  
Singular Values ◽  
Singular Value ◽  
Low Rank ◽  
Continuous Variables ◽  
Rank Matrix ◽  
Near Term ◽  
Thresholding Algorithm ◽  
Low Rank Matrix ◽  
Singular Value Thresholding

Abstract Quantum singular value thresholding (QSVT) algorithm, as a core module of many mathematical models, seeks the singular values of a sparse and low rank matrix exceeding a threshold and their associated singular vectors. The existing all-qubit QSVT algorithm demands lots of ancillary qubits, remaining a huge challenge for realization on near-term intermediate-scale quantum computers. In this paper, we propose a hybrid QSVT (HQSVT) algorithm utilizing both discrete variables (DVs) and continuous variables (CVs). In our algorithm, raw data vectors are encoded into a qubit system and the following data processing is fulfilled by hybrid quantum operations. Our algorithm requires O[log(MN)] qubits with O(1) qumodes and totally performs O(1) operations, which significantly reduces the space and runtime consumption.

scholarly journals A Singular Value Thresholding with Diagonal-Update Algorithm for Low-Rank Matrix Completion

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yong-Hong Duan ◽  
Rui-Ping Wen ◽  
Yun Xiao
Keyword(s):  
Matrix Completion ◽  
Arithmetic Operation ◽  
Computational Cost ◽  
Singular Value ◽  
Low Rank ◽  
Simple Arithmetic ◽  
Rank Matrix ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix ◽  
Singular Value Thresholding

The singular value thresholding (SVT) algorithm plays an important role in the well-known matrix reconstruction problem, and it has many applications in computer vision and recommendation systems. In this paper, an SVT with diagonal-update (D-SVT) algorithm was put forward, which allows the algorithm to make use of simple arithmetic operation and keep the computational cost of each iteration low. The low-rank matrix would be reconstructed well. The convergence of the new algorithm was discussed in detail. Finally, the numerical experiments show the effectiveness of the new algorithm for low-rank matrix completion.

scholarly journals Sign Inference for Dynamic Signed Networks via Dictionary Learning

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yi Cen ◽  
Rentao Gu ◽  
Yuefeng Ji
Keyword(s):  
Online Social Network ◽  
Research Area ◽  
Singular Value ◽  
Low Rank ◽  
Estimation Accuracy ◽  
Inference Problem ◽  
Matrix Estimation ◽  
Rank Matrix ◽  
Low Rank Matrix ◽  
Singular Value Thresholding

Mobile online social network (mOSN) is a burgeoning research area. However, most existing works referring to mOSNs deal with static network structures and simply encode whether relationships among entities exist or not. In contrast, relationships in signed mOSNs can be positive or negative and may be changed with time and locations. Applying certain global characteristics of social balance, in this paper, we aim to infer the unknown relationships in dynamic signed mOSNs and formulate this sign inference problem as a low-rank matrix estimation problem. Specifically, motivated by the Singular Value Thresholding (SVT) algorithm, a compact dictionary is selected from the observed dataset. Based on this compact dictionary, the relationships in the dynamic signed mOSNs are estimated via solving the formulated problem. Furthermore, the estimation accuracy is improved by employing a dictionary self-updating mechanism.

scholarly journals Image Denoising Using Low Rank Matrix Approximation in Singular Value Decomposition

2021 ◽  
Vol 11 (2) ◽  
pp. 1430-1446
Author(s):  
Satyanarayana Tallapragada V.V.
Keyword(s):  
Singular Value Decomposition ◽  
Image Denoising ◽  
Singular Values ◽  
Singular Value ◽  
Low Rank ◽  
Lower Rank ◽  
Rank Matrix ◽  
Wide Range ◽  
Value Decomposition ◽  
Low Rank Matrix

The factorization of a matrix into lower rank matrices give solutions to a wide range of computer vision and image processing tasks. The inherent patches or the atomic patches can completely describe the whole image. The lower rank matrices are obtained using different tools including Singular Value Decomposition (SVD), which is typically found in minimization problems of nuclear norms. The singular values obtained will generally be a thresholder to realize the nuclear norm minimization. However, soft-thresholding is performed uniformly on all the singular values that lead to a similar importance to all the patches whether it is principal/useful or not. Our observation is that the decision on a patch (to be principal/useful or not) can be taken only when the application of this minimization is taken into consideration. Thus, in this paper, we propose a new method for image denoising by choosing variable weights to different singular values with a deep noise effect. Experimental results illustrate that the proposed weighted scheme performs better than the state-of-the-art methods.

scholarly journals On critical points of quadratic low-rank matrix optimization problems

2020 ◽  
Vol 40 (4) ◽  
pp. 2626-2651
Author(s):  
André Uschmajew ◽  
Bart Vandereycken
Keyword(s):  
Critical Points ◽  
Optimization Problems ◽  
Quadratic Function ◽  
Singular Values ◽  
Positive Semidefinite ◽  
Optimization Methods ◽  
Low Rank ◽  
Local Minima ◽  
Rank Matrix ◽  
Low Rank Matrix

Abstract The absence of spurious local minima in certain nonconvex low-rank matrix recovery problems has been of recent interest in computer science, machine learning and compressed sensing since it explains the convergence of some low-rank optimization methods to global optima. One such example is low-rank matrix sensing under restricted isometry properties (RIPs). It can be formulated as a minimization problem for a quadratic function on the Riemannian manifold of low-rank matrices, with a positive semidefinite Riemannian Hessian that acts almost like an identity on low-rank matrices. In this work new estimates for singular values of local minima for such problems are given, which lead to improved bounds on RIP constants to ensure absence of nonoptimal local minima and sufficiently negative curvature at all other critical points. A geometric viewpoint is taken, which is inspired by the fact that the Euclidean distance function to a rank-$k$ matrix possesses no critical points on the corresponding embedded submanifold of rank-$k$ matrices except for the single global minimum.

scholarly journals Guarantees of Fast Band Restricted Thresholding Algorithm for Low-Rank Matrix Recovery Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Fujun Zhao ◽  
Jigen Peng ◽  
Kai Sun ◽  
Angang Cui
Keyword(s):  
Combinatorial Problem ◽  
Low Rank ◽  
Linear Measurements ◽  
Matrix Recovery ◽  
Rank Matrix ◽  
Restricted Isometry Constant ◽  
Wide Range ◽  
Thresholding Algorithm ◽  
Low Rank Matrix Recovery ◽  
Low Rank Matrix

Affine matrix rank minimization problem is a famous problem with a wide range of application backgrounds. This problem is a combinatorial problem and deemed to be NP-hard. In this paper, we propose a family of fast band restricted thresholding (FBRT) algorithms for low rank matrix recovery from a small number of linear measurements. Characterized via restricted isometry constant, we elaborate the theoretical guarantees in both noise-free and noisy cases. Two thresholding operators are discussed and numerical demonstrations show that FBRT algorithms have better performances than some state-of-the-art methods. Particularly, the running time of FBRT algorithms is much faster than the commonly singular value thresholding algorithms.

scholarly journals Fabric defect detection based on deep-handcrafted feature and weighted low-rank matrix representation

2021 ◽  
Vol 16 ◽  
pp. 155892502110084
Author(s):  
Chunlei Li ◽  
Ban Jiang ◽  
Zhoufeng Liu ◽  
Yan Dong ◽  
Shuili Tang ◽  
...  
Keyword(s):  
Defect Detection ◽  
Matrix Representation ◽  
Singular Values ◽  
Low Rank ◽  
Fabric Defect Detection ◽  
Rank Matrix ◽  
Fabric Defect ◽  
The Matrix ◽  
Low Rank Representation ◽  
Low Rank Matrix

In the process of textile production, automatic defect detection plays a key role in controlling product quality. Due to the complex texture features of fabric image, the traditional detection methods have poor adaptability, and low detection accuracy. The low rank representation model can divide the image into the low rank background and sparse object, and has proven suitable for fabric defect detection. However, how to further effectively characterize the fabric texture is still problematic in this kind of method. Moreover, most of them adopt nuclear norm optimization algorithm to solve the low rank model, which treat every singular value in the matrix equally. However, in the task of fabric defect detection, different singular values of feature matrix represent different information. In this paper, we proposed a novel fabric defect detection method based on the deep-handcrafted feature and weighted low-rank matrix representation. The feature characterization ability is effectively improved by fusing the global deep feature extracted by VGG network and the handcrafted low-level feature. Moreover, a weighted low-rank representation model is constructed to treat the matrix singular values differently by different weights, thus the most distinguishing feature of fabric texture can be preserved, which can efficiently outstand the defect and suppress the background. Qualitative and quantitative experiments on two public datasets show that our proposed method outperforms the state-of-the-art methods.

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