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Nearly-optimal Robust Matrix Completion [article]

Yeshwanth Cherapanamjeri, Kartik Gupta, Prateek Jain
2016 arXiv   pre-print
Our algorithm solves RMC using nearly optimal number of observations as well as nearly optimal number of corruptions.  ...  In this paper, we consider the problem of Robust Matrix Completion (RMC) where the goal is to recover a low-rank matrix by observing a small number of its entries out of which a few can be arbitrarily  ...  In this work, we studied the Robust Matrix Completion problem.  ... 
arXiv:1606.07315v3 fatcat:syxxscwky5f5lhes2dkmgu44ci

Hyperspectral Image Recovery Using Non-Convex Low-Rank Tensor Approximation

Hongyi Liu, Hanyang Li, Zebin Wu, Zhihui Wei
2020 Remote Sensing  
Firstly, a non-convex approximation of tensor nuclear norm (NCTNN) is introduced to the low-rank tensor completion.  ...  To achieve an unbiased approximation and improve the robustness, this paper develops a non-convex relaxation approach for low-rank tensor approximation.  ...  As such, the derived matrix -norm defined by the MCP function with regard to singular values generates a nearly optimal non-convex approximation to low-rank (NRLR).  ... 
doi:10.3390/rs12142264 fatcat:v35ea5egwjhtveuqby7j45gsc4

A note on robustness of D-optimal block designs for two-colour microarray experiments

R.A. Bailey, Katharina Schiffl, Ralf-Dieter Hilgers
2013 Journal of Statistical Planning and Inference  
As an extension of Latif et al. (2009) , we define the optimal breakdown number for a collection of designs to describe the robustness, and we calculate the breakdown number for various D-optimal block  ...  Due to the high risk of missing observations in microarray experiments, it is fundamental to concentrate not only on optimal designs but also on designs which are robust against missing observations.  ...  Theorem 2 suggests that nearly equireplicate designs are good candidates for robust designs.  ... 
doi:10.1016/j.jspi.2013.01.005 fatcat:rctzadrhh5dtheex2rmmokupzy

Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping

Carlos Ignacio Hernández Castellanos, Oliver Schütze, Jian-Qiao Sun, Guillermo Morales-Luna, Sina Ober-Blöbaum
2020 Mathematics  
In this paper, we present a novel algorithm for the computation of lightly robust optimal solutions for multi-objective optimization problems.  ...  Figure 4 shows the Pareto optimal solutions. Figure 5 shows the nearly optimal solutions.  ...  matrix, 0 is an r by ts zero matrix, and I is the r by r identity matrix.  ... 
doi:10.3390/math8111959 fatcat:ccfehbpwl5g6pjbho3weemfwbi

Factor Group-Sparse Regularization for Efficient Low-Rank Matrix Recovery [article]

Jicong Fan, Lijun Ding, Yudong Chen, Madeleine Udell
2019 arXiv   pre-print
Experiments show promising performance of factor group-sparse regularization for low-rank matrix completion and robust principal component analysis.  ...  We provide generalization error bounds for low-rank matrix completion which show improved upper bounds for Schatten-p norm reglarization as p decreases.  ...  Application to robust PCA Suppose a fraction of entries in a matrix are corrupted in random locations.  ... 
arXiv:1911.05774v2 fatcat:eojp5fxderaejjx3j55b72rtqq

Special issue: Optimization models and algorithms for data science

Panos Parpas, Daniel Ralph, Wolfram Wiesemann
2017 Mathematical programming  
In the first paper (Max-Norm Optimization for Robust Matrix Recovery), Ethan X.  ...  The matrix completion problem aims to reconstruct an unknown matrix given information from a small number of noise-contaminated entries.  ...  In the first paper (Max-Norm Optimization for Robust Matrix Recovery), Ethan X.  ... 
doi:10.1007/s10107-017-1217-5 fatcat:nhc36v3vujdslf6cmaakqndg4q

Sparsity Based Approaches for Distribution Grid State Estimation - A Comparative Study

Shweta Dahale, Hazhar Sufi Karimi, Kexing Lai, Balasubramaniam Natarajan
2020 IEEE Access  
Among the sparsity-based approaches, compressive sensing methods tend to outperform matrix completion and tensor completion methods in terms of error performance.  ...  Specifically, the performance and complexity of spatial methods (1-D compressive sensing and matrix completion) and spatio-temporal methods (2-D compressive sensing and tensor completion) are compared  ...  A matrix completion formulation that is robust to bad data is presented in [14] .  ... 
doi:10.1109/access.2020.3035378 fatcat:lzoryb3vonb4nedewy2zzos5ki

Robust Kernel Approximation for Classification [chapter]

Fanghui Liu, Xiaolin Huang, Cheng Peng, Jie Yang, Nikola Kasabov
2017 Lecture Notes in Computer Science  
Keywords: robust kernel approximation, indefinite kernel learning, support vector machine Corresponding author. 1 The kernel matrix K associated to a positive definite kernel K is PSD.  ...  The derived optimization problem including the kernel learning and the dual SVM classification can be solved by an alternate iterative algorithm.  ...  The results on these data sets demonstrate that the proposed method is robust to noises and outliers, and it tackles the highly indefinite kernel better than the nearly PSD one.  ... 
doi:10.1007/978-3-319-70087-8_31 fatcat:wpzdv73fbjeiplgtju5wcxp43u

Automatic Robust Linear Receiver for Multi-Access Space-Time Block Coded MIMO Systems

Jun Yang, Xiaochuan Ma, Chaohuan Hou, Yicong Liu, Zheng Yao
2009 IEEE Signal Processing Letters  
Index Terms-Multi-access MIMO communications, orthogonal space-time block codes, robust linear receiver.  ...  In this letter, we develop a fully automatic robust linear receiver technique for joint space-time decoding and interference rejection in multi-access MIMO systems that use orthogonal space-time block  ...  The user parameter (which is nearly optimal) is used for the worst-case-based method.  ... 
doi:10.1109/lsp.2009.2022791 fatcat:4i2obmlsg5dapj34evexi5jsum

Generation of optimal linear parametric models for LFT-based robust stability analysis and control design

Harald Pfifer, Simon Hecker
2008 2008 47th IEEE Conference on Decision and Control  
It is optimally suited for LFT-based robust stability analysis and control design.  ...  The effectiveness of the proposed method is demonstrated by a robust stability analysis for a nonlinear generic missile model.  ...  Both algorithms yield similar results but the SVD-based one has performed faster and numerically more robust in case of rank deficient and nearly rank deficient problems in several test cases. III.  ... 
doi:10.1109/cdc.2008.4738780 dblp:conf/cdc/PfiferH08 fatcat:mtyllnd4f5cfljpcd6mdpadyti

Matrix Completion and Related Problems via Strong Duality [article]

Maria-Florina Balcan and Yingyu Liang and David P. Woodruff and Hongyang Zhang
2018 arXiv   pre-print
Our framework shows that exact recoverability and strong duality hold with nearly-optimal sample complexity guarantees for matrix completion and robust PCA.  ...  We apply our framework to two prototypical matrix factorization problems: matrix completion and robust Principal Component Analysis (PCA).  ...  Two prototypical examples are matrix completion and robust Principal Component Analysis (PCA).  ... 
arXiv:1704.08683v5 fatcat:jekealzx3fcarhoqqet2zaewvi

Robust linear receivers for space-time block coded multiaccess MIMO systems with imperfect channel state information

Yue Rong, S. Shahbazpanahi, A.B. Gershman
2005 IEEE Transactions on Signal Processing  
The proposed receivers are based on worstcase performance optimization.  ...  Index Terms-Imperfect channel state information, multiaccess MIMO communications, orthogonal space-time block codes, robust linear receivers. .  ...  The parameter is taken (which is nearly optimal for this example).  ... 
doi:10.1109/tsp.2005.851199 fatcat:jzziuywfyrhj3jm6h4rfymd7pm

Neighbor Joining Algorithms for Inferring Phylogenies via LCA Distances

Ilan Gronau, Shlomo Moran
2007 Journal of Computational Biology  
One notion of robustness is defined by the ability to reconstruct the correct topology given nearly additive input.  ...  The topology of T is uniquely determined by any dissimilarity matrix D which is nearly additive with respect to it.  ...  OPTIMAL ROBUSTNESS OF DLCA In this section we discuss the robustness of DLCA.  ... 
doi:10.1089/cmb.2006.0115 pmid:17381342 fatcat:zplzpphu4vbgzp7lqy32ow4fgq

A Robust Compressive Quantum State Tomography Algorithm Using ADMM [article]

Kezhi Li, Shuang Cong
2014 arXiv   pre-print
The proposed algorithm is much faster, robust to outlier noises (even very large for some entries) and can solve the reconstruction problem distributively.  ...  It is proved that the estimation then can be converted to a convex optimization problem with quantum mechanics constraints.  ...  Alternating Direction Method of Multipliers (ADMM) ADMM is an optimization method with good robustness and can support decomposition.  ... 
arXiv:1401.6533v1 fatcat:7l3owt5dm5gd3h2n7ojhyz5564

Robust transmit eigen beamforming based on imperfect channel state information

A. Abdel-Samad, T.N. Davidson, A.B. Gershman
2006 IEEE Transactions on Signal Processing  
A major drawback of most existing transmit beamforming techniques is that they require nearly perfect knowledge of the channel at the transmitter, which is typically not available in practice.  ...  The proposed design combines beamforming along the eigenvectors of the (deterministic) autocorrelation of the channel matrix perceived by the transmitter and power loading across those beams.  ...  Fig. 5 . 5 SNR of conventional, robust, and omnidirectional beamformers versus the norm of error matrix.  ... 
doi:10.1109/tsp.2006.872537 fatcat:actat66n4jetfolinnpe7dsl44
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