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．

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

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 Correlated Spatio-Temporal Data Collection in Wireless Sensor Networks Based on Low Rank Matrix Approximation and Optimized Node Sampling

Sensors ◽  
2014 ◽  
Vol 14 (12) ◽  
pp. 23137-23158 ◽  
Author(s):  
Xinglin Piao ◽  
Yongli Hu ◽  
Yanfeng Sun ◽  
Baocai Yin ◽  
Junbin Gao
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Data Collection ◽  
Low Rank ◽  
Wireless Sensor ◽  
Temporal Data ◽  
Matrix Approximation ◽  
Rank Matrix ◽  
Spatio Temporal ◽  
Low Rank Matrix

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.

Active Subspace: Toward Scalable Low-Rank Learning

2012 ◽  
Vol 24 (12) ◽  
pp. 3371-3394 ◽  
Author(s):  
Guangcan Liu ◽  
Shuicheng Yan
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Low Rank ◽  
Small Scale ◽  
Large Solution ◽  
Rank Matrix ◽  
Low Rank Matrix ◽  
Active Subspace ◽  
Solution Matrix

We address the scalability issues in low-rank matrix learning problems. Usually these problems resort to solving nuclear norm regularized optimization problems (NNROPs), which often suffer from high computational complexities if based on existing solvers, especially in large-scale settings. Based on the fact that the optimal solution matrix to an NNROP is often low rank, we revisit the classic mechanism of low-rank matrix factorization, based on which we present an active subspace algorithm for efficiently solving NNROPs by transforming large-scale NNROPs into small-scale problems. The transformation is achieved by factorizing the large solution matrix into the product of a small orthonormal matrix (active subspace) and another small matrix. Although such a transformation generally leads to nonconvex problems, we show that a suboptimal solution can be found by the augmented Lagrange alternating direction method. For the robust PCA (RPCA) (Candès, Li, Ma, & Wright, 2009 ) problem, a typical example of NNROPs, theoretical results verify the suboptimality of the solution produced by our algorithm. For the general NNROPs, we empirically show that our algorithm significantly reduces the computational complexity without loss of optimality.

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