scholarly journals Matrix Optimization Over Low-Rank Spectral Sets: Stationary Points and Local and Global Minimizers

2019 ◽  
Vol 184 (3) ◽  
pp. 895-930
Author(s):  
Xinrong Li ◽  
Naihua Xiu ◽  
Shenglong Zhou
Keyword(s):  
Low Rank ◽  
Stationary Points ◽  
Spectral Sets ◽  
Global Minimizers ◽  
Matrix Optimization

scholarly journals Radar Target and Moving Clutter Separation Based on the Low-Rank Matrix Optimization

2018 ◽  
Vol 56 (8) ◽  
pp. 4765-4780 ◽  
Author(s):  
Jiapeng Yin ◽  
Christine Unal ◽  
Marc Schleiss ◽  
Herman Russchenberg
Keyword(s):  
Low Rank ◽  
Radar Target ◽  
Matrix Optimization ◽  
Rank Matrix ◽  
Low Rank Matrix

scholarly journals Low-rank Matrix Optimization for Video Segmentation Research

2017 ◽  
Vol 6 (1) ◽  
pp. 36
Author(s):  
Caiyun Huang ◽  
Guojun Qin
Keyword(s):  
Video Segmentation ◽  
Optimal Solution ◽  
Low Rank ◽  
Superior Performance ◽  
Closed Form Solutions ◽  
Matrix Optimization ◽  
Rank Matrix ◽  
Low Rank Representation ◽  
Spatio Temporal ◽  
Low Rank Matrix

This paper investigates how to perform robust and efficient unsupervised video segmentation while suppressing the effects of data noises and/or corruptions. The low-rank representation is pursued for video segmentation. The supervoxels affinity matrix of an observed video sequence is given, low-rank matrix optimization seeks a optimal solution by making the matrix rank explicitly determined. We iteratively optimize them with closed-form solutions. Moreover, we incorporate a discriminative replication prior into our framework based on the obervation that small-size video patterns, and it tends to recur frequently within the same object. The video can be segmented into several spatio-temporal regions by applying the Normalized-Cut algorithm with the solved low-rank representation. To process the streaming videos, we apply our algorithm sequentially over a batch of frames over time, in which we also develop several temporal consistent constraints improving the robustness. Extensive experiments are on the public benchmarks, they demonstrate superior performance of our framework over other approaches．

An exact penalty method for semidefinite-box-constrained low-rank matrix optimization problems

2018 ◽  
Vol 40 (1) ◽  
pp. 563-586
Author(s):  
Tianxiang Liu ◽  
Zhaosong Lu ◽  
Xiaojun Chen ◽  
Yu-Hong Dai
Keyword(s):  
Penalty Method ◽  
Original Problem ◽  
Optimization Problems ◽  
Rank Correlation ◽  
Low Rank ◽  
Matrix Optimization ◽  
Rank Constraint ◽  
Rank Matrix ◽  
Adaptive Penalty ◽  
Low Rank Matrix

Abstract This paper considers a matrix optimization problem where the objective function is continuously differentiable and the constraints involve a semidefinite-box constraint and a rank constraint. We first replace the rank constraint by adding a non-Lipschitz penalty function in the objective and prove that this penalty problem is exact with respect to the original problem. Next, for the penalty problem we present a nonmonotone proximal gradient (NPG) algorithm whose subproblem can be solved by Newton’s method with globally quadratic convergence. We also prove the convergence of the NPG algorithm to a first-order stationary point of the penalty problem. Furthermore, based on the NPG algorithm, we propose an adaptive penalty method (APM) for solving the original problem. Finally, the efficiency of an APM is shown via numerical experiments for the sensor network localization problem and the nearest low-rank correlation matrix problem.

scholarly journals Global Optimality in Low-Rank Matrix Optimization

2018 ◽  
Vol 66 (13) ◽  
pp. 3614-3628 ◽  
Author(s):  
Zhihui Zhu ◽  
Qiuwei Li ◽  
Gongguo Tang ◽  
Michael B. Wakin
Keyword(s):  
Low Rank ◽  
Global Optimality ◽  
Matrix Optimization ◽  
Rank Matrix ◽  
Low Rank Matrix

scholarly journals The Global Optimization Geometry of Low-Rank Matrix Optimization

2021 ◽  
pp. 1-1
Author(s):  
Zhihui Zhu ◽  
Qiuwei Li ◽  
Gongguo Tang ◽  
Michael B. Wakin
Keyword(s):  
Global Optimization ◽  
Low Rank ◽  
Matrix Optimization ◽  
Rank Matrix ◽  
Low Rank Matrix

The Influences of the Rank of Coal on Methane Sorption Capacity in Coals/Wpływ Rzędu Węgla Na Pojemność Sorpcyjną Metanu W Węglach

2014 ◽  
Vol 59 (2) ◽  
pp. 509-516
Author(s):  
Andrzej Olajossy
Keyword(s):  
Sorption Capacity ◽  
Coalbed Methane ◽  
Vitrinite Reflectance ◽  
Sorption Isotherms ◽  
Volatile Matter ◽  
Low Rank ◽  
Hard Coal ◽  
Petrographic Composition ◽  
Methane Sorption ◽  
Indian Coals

Abstract Methane sorption capacity is of significance in the issues of coalbed methane (CBM) and depends on various parameters, including mainly, on rank of coal and the maceral content in coals. However, in some of the World coals basins the influences of those parameters on methane sorption capacity is various and sometimes complicated. Usually the rank of coal is expressed by its vitrinite reflectance Ro. Moreover, in coals for which there is a high correlation between vitrinite reflectance and volatile matter Vdaf the rank of coal may also be represented by Vdaf. The influence of the rank of coal on methane sorption capacity for Polish coals is not well understood, hence the examination in the presented paper was undertaken. For the purpose of analysis there were chosen fourteen samples of hard coal originating from the Upper Silesian Basin and Lower Silesian Basin. The scope of the sorption capacity is: 15-42 cm3/g and the scope of vitrinite reflectance: 0,6-2,2%. Majority of those coals were of low rank, high volatile matter (HV), some were of middle rank, middle volatile matter (MV) and among them there was a small number of high rank, low volatile matter (LV) coals. The analysis was conducted on the basis of available from the literature results of research of petrographic composition and methane sorption isotherms. Some of those samples were in the form (shape) of grains and others - as cut out plates of coal. The high pressure isotherms previously obtained in the cited studies were analyzed here for the purpose of establishing their sorption capacity on the basis of Langmuire equation. As a result of this paper, it turned out that for low rank, HV coals the Langmuire volume VL slightly decreases with the increase of rank, reaching its minimum for the middle rank (MV) coal and then increases with the rise of the rank (LV). From the graphic illustrations presented with respect to this relation follows the similarity to the Indian coals and partially to the Australian coals.

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