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 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.

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 Robust low-rank matrix estimation

2018 ◽  
Vol 46 (6B) ◽  
pp. 3481-3509 ◽  
Author(s):  
Andreas Elsener ◽  
Sara van de Geer
Keyword(s):  
Low Rank ◽  
Matrix Estimation ◽  
Rank Matrix ◽  
Low Rank Matrix

scholarly journals Channel Covariance Matrix Estimation via Dimension Reduction for Hybrid MIMO MmWave Communication Systems

Sensors ◽  
2019 ◽  
Vol 19 (15) ◽  
pp. 3368
Author(s):  
Rui Hu ◽  
Jun Tong ◽  
Jiangtao Xi ◽  
Qinghua Guo ◽  
Yanguang Yu
Keyword(s):  
Covariance Matrix ◽  
Communication Systems ◽  
Low Complexity ◽  
Low Rank ◽  
Covariance Matrix Estimation ◽  
Hardware Complexity ◽  
Matrix Estimation ◽  
Planar Arrays ◽  
Rank Matrix ◽  
Low Rank Matrix

Hybrid massive MIMO structures with lower hardware complexity and power consumption have been considered as potential candidates for millimeter wave (mmWave) communications. Channel covariance information can be used for designing transmitter precoders, receiver combiners, channel estimators, etc. However, hybrid structures allow only a lower-dimensional signal to be observed, which adds difficulties for channel covariance matrix estimation. In this paper, we formulate the channel covariance estimation as a structured low-rank matrix sensing problem via Kronecker product expansion and use a low-complexity algorithm to solve this problem. Numerical results with uniform linear arrays (ULA) and uniform squared planar arrays (USPA) are provided to demonstrate the effectiveness of our proposed method.

scholarly journals Numerical Comparisons Between Bayesian and Frequentist Low-Rank Matrix Completion: Estimation Accuracy and Uncertainty Quantification

2021 ◽  
Author(s):  
The Tien Mai
Keyword(s):  
Confidence Intervals ◽  
Estimation Error ◽  
Matrix Completion ◽  
Low Rank ◽  
Small Samples ◽  
Estimation Accuracy ◽  
Bayesian Approaches ◽  
Rank Matrix ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix

In this paper we perform numerous numerical studies for the problem of low-rank matrix completion. We compare the Bayesian approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optimal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesian estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. However, we also find that the length of the confidence intervals revealed by the de-biased estimator for an entry is absolutely shorter than the length of the considered credible interval. These suggest further theoretical studies on the estimation error and the concentration for Bayesian methods as they are being quite limited up to present.

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