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Found 21 papers, 3 papers with code
Transforms Based Tensor Robust PCA: Corrupted Low-Rank Tensors Recovery via Convex Optimization
This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum.
Tensor Q-Rank: New Data Dependent Definition of Tensor Rank
Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks.
Exact Recovery of Tensor Robust Principal Component Analysis under Linear Transforms
This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum.
Low-Rank Tensor Completion With a New Tensor Nuclear Norm Induced by Invertible Linear Transforms
This work studies the low-rank tensor completion problem, which aims to exactly recover a low-rank tensor from partially observed entries.
Tensor-Tensor Product Toolbox
The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication.
Exact Low Tubal Rank Tensor Recovery from Gaussian Measurements
Specifically, we show that by solving a TNN minimization problem, the underlying tensor of size $n_1\times n_2\times n_3$ with tubal rank $r$ can be exactly recovered when the given number of Gaussian measurements is $O(r(n_1+n_2-r)n_3)$.
Subspace Clustering by Block Diagonal Representation
Second, we observe that many existing methods approximate the block diagonal representation matrix by using different structure priors, e. g., sparsity and low-rankness, which are indirect.
Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm
Equipped with the new tensor nuclear norm, we then solve the TRPCA problem by solving a convex program and provide the theoretical guarantee for the exact recovery.
Nonconvex Sparse Spectral Clustering by Alternating Direction Method of Multipliers and Its Convergence Analysis
Experimental analysis on several real data sets verifies the effectiveness of our method.
Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization
In this work, we prove that under certain suitable assumptions, we can recover both the low-rank and the sparse components exactly by simply solving a convex program whose objective is a weighted combination of the tensor nuclear norm and the $\ell_1$-norm, i. e., $\min_{{\mathcal{L}},\ {\mathcal{E}}} \ \|{{\mathcal{L}}}\|_*+\lambda\|{{\mathcal{E}}}\|_1, \ \text{s. t.}
Convex Sparse Spectral Clustering: Single-view to Multi-view
Spectral Clustering (SC) is one of the most widely used methods for data clustering.
Fast Proximal Linearized Alternating Direction Method of Multiplier with Parallel Splitting
The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint.
Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm
The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing.
Optimized Projections for Compressed Sensing via Direct Mutual Coherence Minimization
To the best of our knowledge, this is the first work which directly minimizes the mutual coherence of the projected dictionary with a convergence guarantee.
Projection onto the capped simplex
We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof.
Correntropy Induced L2 Graph for Robust Subspace Clustering
In this paper, we study the robust subspace clustering problem, which aims to cluster the given possibly noisy data points into their underlying subspaces.
Correlation Adaptive Subspace Segmentation by Trace Lasso
In this work, we argue that both sparsity and the grouping effect are important for subspace segmentation.
Generalized Singular Value Thresholding
This work studies the Generalized Singular Value Thresholding (GSVT) operator ${\text{Prox}}_{g}^{{\sigma}}(\cdot)$, \begin{equation*} {\text{Prox}}_{g}^{{\sigma}}(B)=\arg\min\limits_{X}\sum_{i=1}^{m}g(\sigma_{i}(X)) + \frac{1}{2}||X-B||_{F}^{2}, \end{equation*} associated with a nonconvex function $g$ defined on the singular values of $X$.
Generalized Nonconvex Nonsmooth Low-Rank Minimization
We observe that all the existing nonconvex penalty functions are concave and monotonically increasing on $[0,\infty)$.
Proximal Iteratively Reweighted Algorithm with Multiple Splitting for Nonconvex Sparsity Optimization
This paper proposes the Proximal Iteratively REweighted (PIRE) algorithm for solving a general problem, which involves a large body of nonconvex sparse and structured sparse related problems.
Smoothed Low Rank and Sparse Matrix Recovery by Iteratively Reweighted Least Squares Minimization
Our convergence proof of IRLS is more general than previous one which depends on the special properties of the Schatten-$p$ norm and $\ell_{2, q}$-norm.
