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- Yangyang Xu, Wotao Yin
- SIAM J. Imaging Sciences
- 2013

This paper considers regularized block multi-convex optimization, where the feasible set and objective function are generally non-convex but convex in each block of variables. We review some of its interesting examples and propose a generalized block coordinate descent method. (Using proximal updates, we further allow non-convexity over some blocks.) Under… (More)

- Yangyang Xu, Wotao Yin, Zaiwen Wen, Yin Zhang
- ArXiv
- 2011

This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to find nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M. This problem is closely related to the two existing problems: nonnegative matrix factorization and low-rank matrix completion,… (More)

- Ming-Jun Lai, Yangyang Xu, Wotao Yin
- SIAM J. Numerical Analysis
- 2013

In this paper, we first study q minimization and its associated iterative reweighted algorithm for recovering sparse vectors. Unlike most existing work, we focus on unconstrained q minimization, for which we show a few advantages on noisy measurements and/or approximately sparse vectors. Inspired by the results in [Daubechies et al., Comm. Pure Appl. Math.,… (More)

- Yangyang Xu, Ruru Hao, Wotao Yin, Zhixun Su
- ArXiv
- 2013

Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data reconstruction, and so on. We propose a new model to recover a low-rank tensor by simultaneously performing low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An alternating… (More)

- Yangyang Xu, Wotao Yin
- SIAM Journal on Optimization
- 2015

The stochastic gradient (SG) method can minimize an objective function composed of a large number of differentiable functions or solve a stochastic optimization problem, very quickly to a moderate accuracy. The block coordinate descent/update (BCD) method, on the other hand, handles problems with multiple blocks of variables by updating them one at a time;… (More)

- Yangyang Xu, Wotao Yin
- ArXiv
- 2013

Various algorithms have been proposed for dictionary learning. Among those for image processing, many use image patches to form dictionaries. This paper focuses on whole-image recovery from corrupted linear measurements. We address the open issue with representing an image by overlapping patches: the overlapping leads to an excessive number of dictionary… (More)

- Guiying Guo, Yangyang Xu, Mancheng Gong, Yan Cao, Ruihua An
- Tumor Biology
- 2013

This study was conducted to analyze the expression of the ubiquitin-specific protease Usp28 and assess its clinical significance in human bladder cancer. mRNA and protein expression levels of Usp28 were determined by real-time polymerase chain reaction (PCR) and Western blot in 24 paired bladder cancers and the adjacent non-cancerous tissues. In addition,… (More)

- Yangyang Xu
- Math. Program. Comput.
- 2015

Multi-way data arises in many applications such as electroencephalography classification, face recognition, text mining and hyperspectral data analysis. Tensor decomposition has been commonly used to find the hidden factors and elicit the intrinsic structures of the multi-way data. This paper considers sparse nonnegative Tucker decomposition (NTD), which is… (More)

- Qing Ling, Yangyang Xu, Wotao Yin, Zaiwen Wen
- 2012 IEEE International Conference on Acoustics…
- 2012

This paper introduces algorithms for the decentralized low-rank matrix completion problem. Assume a low-rank matrix W = [W<sub>1</sub>,W<sub>2</sub>, ...,W<sub>L</sub>]. In a network, each agent ℓ observes some entries of W<sub>ℓ</sub>. In order to recover the unobserved entries of W via decentralized computation, we factorize the unknown… (More)

- Zhimin Peng, Yangyang Xu, Ming Yan, Wotao Yin
- SIAM J. Scientific Computing
- 2016

Finding a fixed point to a nonexpansive operator, i.e., x * = T x * , abstracts many problems in numerical linear algebra, optimization, and other areas of scientific computing. To solve fixed-point problems, we propose ARock, an algorithmic framework in which multiple agents (machines, processors, or cores) update x in an asynchronous parallel fashion.… (More)