Matrix completion under interval uncertainty

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and apply an alternating projection method to solve it. To the best of our knowledge, we are the first to propose a method that solves RPCA problem without considering any objective function, convex relaxation, or surrogate convex constraints. We demonstrate through extensive numerical experiments on a variety of applications, including shadow removal, background estimation, face detection, and galaxy evolution, that our approach matches and often significantly outperforms current state-of-the-art in various ways.

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“…One can also think of the matrix completion (MC) problem as a special case of (7) [12,40,30,10,29,13,33,14]. For MC problems, S = 0.…”

Section: Robust Matrix Completionmentioning

confidence: 99%

A Nonconvex Projection Method for Robust PCA

Dutta

Hanzely

Richtárik

2019

AAAI

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“…An alternative strategy is to pose regression learning as the problem of completing a low rank matrix [9]. Further, Marecek et al [39] recently proposed a matrix completion algorithm under interval uncertainty, to impute the missing entries of a data matrix in the presence of equality and inequality constraints. In this paper, we exploit matrix completion algorithms for the problem of object counting from binary user feedback.…”

Section: Proposed Frameworkmentioning

confidence: 99%

“…(2). The MACO algorithm proposed by Marecek et al [39] uses alternating parallel co-ordinate descent to complete a matrix in the presence of equality, lower bound and upper bound constraints. Let X be the m Â n matrix to be reconstructed.…”

Section: Rq2: Counting With Binary User Feedbackmentioning

confidence: 99%

“…The problem in Eq. (3) is NP-hard, even with U ¼ L ¼ [39]. A popular heuristic enforces low rank in a synthetic way by writing X as a product of two matrices, X ¼ AB, where A 2 < mÂr and B 2 < rÂn Hence, X is of rank at most r. The alternating parallel co-ordinate descent algorithm to solve the above optimization is outlined in Algorithm 1 (please refer to [39] for more detailed derivations).…”

Section: Rq2: Counting With Binary User Feedbackmentioning

confidence: 99%

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Enriching the Fan Experience in a Smart Stadium Using Internet of Things Technologies

Panchanathan

Chakraborty

McDaniel

et al. 2017

Int. J. Semantic Computing

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Rapid urbanization has brought about an influx of people to cities, tipping the scale between urban and rural living. Population predictions estimate that 64% of the global population will reside in cities by 2050. To meet the growing resource needs, improve management, reduce complexities, and eliminate unnecessary costs while enhancing the quality of life of citizens, cities are increasingly exploring open innovation frameworks and smart city initiatives that target priority areas including transportation, sustainability, and security. The size and heterogeneity of urban centers impede progress of technological innovations for smart cities. We propose a Smart Stadium as a living laboratory to balance both size and heterogeneity so that smart city solutions and Internet of Things (IoT) technologies may be deployed and tested within an environment small enough to practically trial but large and diverse enough to evaluate scalability and efficacy. The Smart Stadium for Smart Living initiative brings together multiple institutions and partners including Arizona State University (ASU), Dublin City University (DCU), Intel Corporation, and Gaelic Athletic Association (GAA), to turn ASU’s Sun Devil Stadium and Ireland’s Croke Park Stadium into twinned smart stadia to investigate IoT and smart city technologies and applications.

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“…The first challenge has been recently addressed [8] by considering a variant of the problem with explicit uncertainty set around each "supposedly known" value. Formally, let X be an m × n matrix to be reconstructed.…”

Section: Introductionmentioning

confidence: 99%