DLSLA 3-D SAR Imaging via Sparse Recovery Through Combination of Nuclear Norm and Low-Rank Matrix Factorization

2021 ◽  
pp. 1-13
Author(s):  
Tong Gu ◽  
Guisheng Liao ◽  
Yachao Li ◽  
Yifan Guo ◽  
Yongjun Liu
Keyword(s):  
Matrix Factorization ◽  
Sparse Recovery ◽  
Nuclear Norm ◽  
Low Rank ◽  
Rank Matrix ◽  
Sar Imaging ◽  
Low Rank Matrix

Semi-Orthogonal Low-Rank Matrix Factorization for Deep Neural Networks

2018 ◽  
Author(s):  
Daniel Povey ◽  
Gaofeng Cheng ◽  
Yiming Wang ◽  
Ke Li ◽  
Hainan Xu ◽  
...  
Keyword(s):  
Neural Networks ◽  
Matrix Factorization ◽  
Deep Neural Networks ◽  
Low Rank ◽  
Rank Matrix ◽  
Low Rank Matrix

scholarly journals Single-cell data clustering based on sparse optimization and low-rank matrix factorization

2021 ◽  
Author(s):  
Yinlei Hu ◽  
Bin Li ◽  
Falai Chen ◽  
Kun Qu
Keyword(s):  
Single Cell ◽  
Rna Sequencing ◽  
Matrix Factorization ◽  
Data Clustering ◽  
Cell Types ◽  
Low Rank ◽  
Sequencing Data ◽  
Rank Matrix ◽  
Single Cell Rna Sequencing ◽  
Low Rank Matrix

Abstract Unsupervised clustering is a fundamental step of single-cell RNA sequencing data analysis. This issue has inspired several clustering methods to classify cells in single-cell RNA sequencing data. However, accurate prediction of the cell clusters remains a substantial challenge. In this study, we propose a new algorithm for single-cell RNA sequencing data clustering based on Sparse Optimization and low-rank matrix factorization (scSO). We applied our scSO algorithm to analyze multiple benchmark datasets and showed that the cluster number predicted by scSO was close to the number of reference cell types and that most cells were correctly classified. Our scSO algorithm is available at https://github.com/QuKunLab/scSO. Overall, this study demonstrates a potent cell clustering approach that can help researchers distinguish cell types in single-cell RNA sequencing data.

Structural Identifiability in Low-Rank Matrix Factorization

Algorithmica ◽  
2009 ◽  
Vol 56 (3) ◽  
pp. 313-332 ◽  
Author(s):  
Epameinondas Fritzilas ◽  
Martin Milanič ◽  
Sven Rahmann ◽  
Yasmin A. Rios-Solis
Keyword(s):  
Matrix Factorization ◽  
Low Rank ◽  
Structural Identifiability ◽  
Rank Matrix ◽  
Low Rank Matrix

scholarly journals A non-convex optimization framework for large-scale low-rank matrix factorization

2020 ◽  
Author(s):  
Sajad Fathi Hafshejani ◽  
Saeed Vahidian ◽  
Zahra Moaberfard ◽  
Reza Alikhani ◽  
Bill Lin
Keyword(s):  
Matrix Factorization ◽  
Large Scale ◽  
Significant Loss ◽  
Low Rank ◽  
Function Evaluation ◽  
Dimensional Manifold ◽  
Step Size ◽  
Rank Matrix ◽  
Real World Datasets ◽  
Low Rank Matrix

Low-rank matrix factorization problems such as non negative matrix factorization (NMF) can be categorized as a clustering or dimension reduction technique. The latter denotes techniques designed to find representations of some high dimensional dataset in a lower dimensional manifold without a significant loss of information. If such a representation exists, the features ought to contain the most relevant features of the dataset. Many linear dimensionality reduction techniques can be formulated as a matrix factorization. In this paper, we combine the conjugate gradient (CG) method with the Barzilai and Borwein (BB) gradient method, and propose a BB scaling CG method for NMF problems. The new method does not require to compute and store matrices associated with Hessian of the objective functions. Moreover, adopting a suitable BB step size along with a proper nonmonotone strategy which comes by the size convex parameter $\eta_k$, results in a new algorithm that can significantly improve the CPU time, efficiency, the number of function evaluation. Convergence result is established and numerical comparisons of methods on both synthetic and real-world datasets show that the proposed method is efficient in comparison with existing methods and demonstrate the superiority of our algorithms.

Low rank matrix completion using truncated nuclear norm and sparse regularizer

2018 ◽  
Vol 68 ◽  
pp. 76-87 ◽  
Author(s):  
Jing Dong ◽  
Zhichao Xue ◽  
Jian Guan ◽  
Zi-Fa Han ◽  
Wenwu Wang
Keyword(s):  
Matrix Completion ◽  
Nuclear Norm ◽  
Low Rank ◽  
Rank Matrix ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix ◽  
Truncated Nuclear Norm

Multi-view low-rank matrix factorization using multiple manifold regularization

2019 ◽  
Vol 335 ◽  
pp. 143-152 ◽  
Author(s):  
Shengxiang Gao ◽  
Zhengtao Yu ◽  
Taisong Jin ◽  
Ming Yin
Keyword(s):  
Matrix Factorization ◽  
Low Rank ◽  
Manifold Regularization ◽  
Rank Matrix ◽  
Low Rank Matrix

scholarly journals s-Goodness for Low-Rank Matrix Recovery

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Lingchen Kong ◽  
Levent Tunçel ◽  
Naihua Xiu
Keyword(s):  
Linear Transformation ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Nuclear Norm ◽  
Low Rank ◽  
Matrix Recovery ◽  
Rank Matrix ◽  
Necessary And Sufficient ◽  
Low Rank Matrix Recovery ◽  
Low Rank Matrix

Low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, and system identification and control. This class of optimization problems is generally𝒩𝒫hard. A popular approach replaces the rank function with the nuclear norm of the matrix variable. In this paper, we extend and characterize the concept ofs-goodness for a sensing matrix in sparse signal recovery (proposed by Juditsky and Nemirovski (Math Program, 2011)) to linear transformations in LMR. Using the two characteristics-goodness constants,γsandγ^s, of a linear transformation, we derive necessary and sufficient conditions for a linear transformation to bes-good. Moreover, we establish the equivalence ofs-goodness and the null space properties. Therefore,s-goodness is a necessary and sufficient condition for exacts-rank matrix recovery via the nuclear norm minimization.

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