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Manifold Constrained Low-Rank Decomposition [article]

Chen Chen and Baochang Zhang and Alessio Del Bue and Vittorio Murino
2017 arXiv   pre-print
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling.  ...  The proposed approach is successfully used to calculate low-rank models from face images, hand-written digits and planar surface images.  ...  Figure 1 . 1 The framework of the proposed manifold constrained low-rank decomposition.  ... 
arXiv:1708.01846v1 fatcat:4m6bk2xjrfgvbh6miqsxffuugy

Manifold Constrained Low-Rank Decomposition

Chen Chen, Baochang Zhang, Alessio Del Bue, Vittorio Murino
2017 2017 IEEE International Conference on Computer Vision Workshops (ICCVW)  
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling.  ...  The proposed approach is successfully used to calculate low-rank models from face images, hand-written digits and planar surface images.  ...  Figure 1 . 1 The framework of the proposed manifold constrained low-rank decomposition.  ... 
doi:10.1109/iccvw.2017.213 dblp:conf/iccvw/0001ZBM17 fatcat:mfm3ln4nq5e75clwhksivayjmq

ManiDec: Manifold Constrained Low-Rank and Sparse Decomposition

Jingjing Liu, Donghui He, Xiaoyang Zeng, Mingyu Wang, Xianchao Xiu, Wanquan Liu, Wenhong Li
2019 IEEE Access  
Therefore, this novel manifold constrained low-rank and sparse decomposition (ManiDec) can consistently integrate the manifold constraint during the non-convex optimization process, and it can contribute  ...  INDEX TERMS Low-rank and sparse decomposition, image alignment, manifold constraint, non-convex optimization.  ...  FIGURE 1 . 1 The framework of manifold constrained model. (a) The framework of manifold embedding. (b) The framework of manifold constrained low-rank and sparse decomposition in this paper.  ... 
doi:10.1109/access.2019.2935235 fatcat:uil4rowd4jb3rl426qgrl2b4g4

Manifold Constrained Low-rank and Joint Sparse Learning for Dynamic Cardiac MRI

Qingmin Meng, Xianchao Xiu, Yan Li
2020 IEEE Access  
In this paper, we propose a manifold constrained low-rank and joint sparse learning model that embeds the manifold priors into lowrank and joint sparse decomposition.  ...  The application of low-rank and sparse matrix decomposition to MRI can improve imaging speed and efficiency.  ...  This illustrates the advantages of our approach with manifold constrained low-rank and joint sparse learning.  ... 
doi:10.1109/access.2020.3014236 fatcat:s2jy3xqpsrhnda46oswkk3b5hu

A literature survey of low-rank tensor approximation techniques [article]

Lars Grasedyck and Daniel Kressner and Christine Tobler
2013 arXiv   pre-print
During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable  ...  Initially proposed for low-rank matrix manifolds in [166] , dynamical low-rank methods have been extended to low-rank tensors in Tucker [167, 199] , TT/MPS [118, 123, 163, 186] , and HT [9, 186, 255  ...  As for the TT decomposition, the set of tensors having fixed HT-rank forms a smooth manifold [83, 254, 255] .  ... 
arXiv:1302.7121v1 fatcat:qxxl4n4le5h33krvmsch2pxwgi

The condition number of many tensor decompositions is invariant under Tucker compression [article]

Nick Dewaele, Paul Breiding, Nick Vannieuwenhoven
2021 arXiv   pre-print
These decompositions include canonical polyadic decompositions, block term decompositions, and sums of tree tensor networks.  ...  We give the example of an 265× 371× 7 tensor of rank 3 from a food science application whose condition number was computed in 6.9 milliseconds by exploiting our new theorem, representing a speedup of four  ...  ., [20, 31] and the references therein), one seeks a decomposition that expresses a tensor A as a sum of R elementary terms: (1.1) A " A 1`¨¨¨`AR , where A r P M r and M r is a low-dimensional manifold  ... 
arXiv:2106.13034v1 fatcat:a6b3wfovrzcmdla7djqeremmta

Fixed-rank matrix factorizations and Riemannian low-rank optimization [article]

B. Mishra, G. Meyer, S. Bonnabel, R. Sepulchre
2013 arXiv   pre-print
We make connections with existing algorithms in the context of low-rank matrix completion and discuss relative usefulness of the proposed framework.  ...  We adopt the geometric framework of optimization on Riemannian quotient manifolds.  ...  From an optimization point to view this corresponds to finding a low-rank coefficient matrix. The papers [YELM07, AFSU07] , thus, motivate the rank-constrained optimization problem formulation.  ... 
arXiv:1209.0430v2 fatcat:6riq4ml5mres5owb3x636mi3ee

Foreword to the Special Issue on Hyperspectral Remote Sensing and Imaging Spectroscopy

S. Prasad, W. Liao, M. He, J. Chanussot
2018 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing  
Wang et al. present an approach to hyperspectral image restoration based on total variation regularized low-rank tensor decomposition.  ...  In Zhang et al. image fusion of multispectral and hyperspectral imagery is undertaken via a spatial-spectral graph-regularized low-rank tensor decomposition.  ...  Wang et al. present an approach to hyperspectral image restoration based on total variation regularized low-rank tensor decomposition.  ... 
doi:10.1109/jstars.2018.2820938 fatcat:pqu6zhrl3rc3tm7tqpi4p4t34m

Geometric Methods on Low-Rank Matrix and Tensor Manifolds [chapter]

André Uschmajew, Bart Vandereycken
2020 Handbook of Variational Methods for Nonlinear Geometric Data  
on Low-Rank Matrix and Tensor Manifolds Geometric Methods on Low-Rank Matrix and Tensor Manifolds Geometric Methods on Low-Rank Matrix and Tensor Manifolds  ...  Geometric Methods on Low-Rank Matrix and Tensor Manifolds Geometric Methods on Low-Rank Matrix and Tensor Manifolds Geometric Methods on Low-Rank Matrix and Tensor Manifolds We remark that  ... 
doi:10.1007/978-3-030-31351-7_9 fatcat:d2ztbg2objbdnldo34dd64dxhe

Sparse Subspace Clustering-Based Feature Extraction for PolSAR Imagery Classification

Bo Ren, Biao Hou, Jin Zhao, Licheng Jiao
2018 Remote Sensing  
Those learned matrices, that are constrained by the sparsity and low rank terms can search for a few points from the samples and capture the global structure.  ...  In this paper, based on the subspace clustering algorithms, we combine sparse representation, low-rank representation, and manifold graphs to investigate the intrinsic property of PolSAR data.  ...  regularized Low Rank Subspace Clustering (LapLRSC) [35] under the constraint of sparsity, low-rank and manifold regularization to find a reasonable representation of data.  ... 
doi:10.3390/rs10030391 fatcat:mscslz6bureldmxrtq2haswv4q

Riemannian preconditioned coordinate descent for low multi-linear rank approximation [article]

Mohammad Hamed Firouzehtarash, Reshad Hosseini
2021 arXiv   pre-print
This paper presents a fast, memory efficient, optimization-based, first-order method for low multi-linear rank approximation of high-order, high-dimensional tensors.  ...  In our method, we exploit the second-order information of the cost function and the constraints to suggest a new Riemannian metric on the Grassmann manifold.  ...  Low-rank tensor decomposition methods can serve for purposes like, dimensionality reduction, denoising and latent variable analysis.  ... 
arXiv:2109.01632v1 fatcat:gz35vsecvndgzce4be5k7qs7ay

Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold [article]

Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
2022 arXiv   pre-print
Our result is the first to partially overcome the incompleteness of the low-rank matrix manifold without changing the vanilla Riemannian gradient descent algorithm.  ...  the manifold.  ...  The low-rank matrix manifold [10, 11] has gained popularity in recent years since it gives a neat description of low-rank matrices.  ... 
arXiv:2107.09207v2 fatcat:yx2fksiby5galjj3jubsfbmnvq

Dynamic MRI using deep manifold self-learning [article]

Abdul Haseeb Ahmed, Hemant Aggarwal, Prashant Nagpal, Mathews Jacob
2019 arXiv   pre-print
We propose a deep self-learning algorithm to learn the manifold structure of free-breathing and ungated cardiac data and to recover the cardiac CINE MRI from highly undersampled measurements.  ...  Results show the ability of our method to better capture the manifold structure, thus providing us reduced spatial and temporal blurring as compared to the SToRM reconstruction.  ...  Low-rank/Subspace constrained dynamic MRI We now briefly review the low-rank/subspace approach, where the voxel time profiles are constrained to be in a subspace, to set the stage for the proposed scheme  ... 
arXiv:1911.02492v1 fatcat:x723kopumzaxzotiojxsif3ps4

Nonnegative Low Rank Matrix Approximation for Nonnegative Matrices [article]

Guang-Jing Song, Michael Kwok-Po Ng
2020 arXiv   pre-print
The proposed NLRM approximation algorithm was derived using the alternating projection on the low rank matrix manifold and the non-negativity property.  ...  (ii) Our low rank matrix admits a matrix singular value decomposition automatically which provides a significant index based on singular values that can be used to identify important singular basis vectors  ...  Then some constrained optimization problems can be rewritten as optimizing a real-valued function f (x) on a manifold M: min x∈M f (x). (4) Here, M can be the Stiefel manifold, the Grassmann manifold and  ... 
arXiv:1912.06836v4 fatcat:e6q7iczupzfaldcogeixzy4zbe

A dual framework for low-rank tensor completion [article]

Madhav Nimishakavi, Pratik Jawanpuria, Bamdev Mishra
2018 arXiv   pre-print
We develop a dual framework for solving the low-rank tensor completion problem.  ...  One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors.  ...  Each of these individual tensors is constrained to have a low-rank in one mode. The low-rank constraint is enforced on a different mode for each tensor.  ... 
arXiv:1712.01193v4 fatcat:xlvuq6mp3rgabgd7bmmug6wkqm
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