Learn More
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)
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)
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)
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)
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)
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)
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)
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 &#x2113; observes some entries of W<sub>&#x2113;</sub>. In order to recover the unobserved entries of W via decentralized computation, we factorize the unknown(More)
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)