no code implementations • ICCV 2021 • Canyi Lu
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.
no code implementations • 26 Oct 2019 • Hao Kong, Canyi Lu, Zhouchen Lin
Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks.
no code implementations • 16 Jul 2019 • Canyi Lu, Pan Zhou
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.
no code implementations • CVPR 2019 • Canyi Lu, Xi Peng, Yunchao Wei
This work studies the low-rank tensor completion problem, which aims to exactly recover a low-rank tensor from partially observed entries.
1 code implementation • 17 Jun 2018 • Canyi Lu
The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication.
1 code implementation • 7 Jun 2018 • Canyi Lu, Jiashi Feng, Zhouchen Lin, Shuicheng Yan
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 $O(r(n_1+n_2-r)n_3)$.
no code implementations • 23 May 2018 • Canyi Lu, Jiashi Feng, Zhouchen Lin, Tao Mei, Shuicheng Yan
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.
1 code implementation • 10 Apr 2018 • Canyi Lu, Jiashi Feng, Yudong Chen, Wei Liu, Zhouchen Lin, Shuicheng Yan
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.
no code implementations • 8 Dec 2017 • Canyi Lu, Jiashi Feng, Zhouchen Lin, Shuicheng Yan
Experimental analysis on several real data sets verifies the effectiveness of our method.
no code implementations • CVPR 2016 • Canyi Lu, Jiashi Feng, Yudong Chen, Wei Liu, Zhouchen Lin, Shuicheng Yan
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.}
no code implementations • 21 Nov 2015 • Canyi Lu, Shuicheng Yan, Zhouchen Lin
Spectral Clustering (SC) is one of the most widely used methods for data clustering.
no code implementations • 14 Nov 2015 • Canyi Lu, Huan Li, Zhouchen Lin, Shuicheng Yan
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.
no code implementations • 23 Oct 2015 • Canyi Lu, Jinhui Tang, Shuicheng Yan, Zhouchen Lin
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.
no code implementations • 13 Aug 2015 • Canyi Lu, Huan Li, Zhouchen Lin
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.
no code implementations • 3 Mar 2015 • Weiran Wang, Canyi Lu
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.
no code implementations • 18 Jan 2015 • Canyi Lu, Jinhui Tang, Min Lin, Liang Lin, Shuicheng Yan, Zhouchen Lin
In this paper, we study the robust subspace clustering problem, which aims to cluster the given possibly noisy data points into their underlying subspaces.
no code implementations • 18 Jan 2015 • Canyi Lu, Jiashi Feng, Zhouchen Lin, Shuicheng Yan
In this work, we argue that both sparsity and the grouping effect are important for subspace segmentation.
no code implementations • 6 Dec 2014 • Canyi Lu, Changbo Zhu, Chunyan Xu, Shuicheng Yan, Zhouchen Lin
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 $X$.
no code implementations • CVPR 2014 • Canyi Lu, Jinhui Tang, Shuicheng Yan, Zhouchen Lin
We observe that all the existing nonconvex penalty functions are concave and monotonically increasing on $[0,\infty)$.
no code implementations • 28 Apr 2014 • Canyi Lu, Yunchao Wei, Zhouchen Lin, Shuicheng Yan
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.
no code implementations • 29 Jan 2014 • Canyi Lu, Zhouchen Lin, Shuicheng Yan
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.