Robust Matrix Completion Based on Factorization and Truncated-Quadratic Loss Function

Wang, Zhi-Yong; Li, Xiao Peng; So, Hing Cheung

doi:10.1109/tcsvt.2022.3214583

Cited by 12 publications

(5 citation statements)

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“…As the Huber [20], truncated-quadratic [3] and hybrid ordinary-Welsch (HOW) [19] functions can yield SIRs using the LF transform, we generalize this class of functions and devise a framework to produce an SIR with closed-from proximity operator. Then, the generated SIR is considered as a nonconvex rank surrogate for LRMC.…”

Section: Framework To Generate Sir and Its Application To Lrmcmentioning

confidence: 99%

“…L OW-RANK matrix completion (LRMC) aims to find the missing entries of an incomplete matrix using the lowrank property [1]- [3]. The observed data in many real-life applications such as image inpainting [4], [5], hyperspectral image restoration [6], [7] and collaborative filtering [8], [9], may be incomplete. Thus LRMC is widely used as an efficient tool to deal with the above issues because their main information lies in a low-dimensional subspace [10].…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

“…Motivated by the results in [3], [19]- [21], we devise a framework to generate SIRs with closed-form proximity operators. Note that the loss functions considered in [3], [19] are a special case of our framework. Besides, it is analyzed that the subproblems associated with our SIRs are convex with closed-form solutions and our SIRs can yield a less bias solution than the ℓ 1 -norm.…”

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confidence: 99%

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Adaptive Rank-One Matrix Completion Using Sum of Outer Products

Wang

et al. 2023

IEEE Trans. Circuits Syst. Video Technol.

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This paper presents a novel loss function referred to as hybrid ordinary-Welsch (HOW) and a new sparsity-inducing regularizer associated with HOW. We theoretically show that the regularizer is quasiconvex and that the corresponding Moreau envelope is convex. Moreover, the closed-form solution to its Moreau envelope, namely, the proximity operator, is derived. Compared with nonconvex regularizers like the ℓp-norm with 0 < p < 1 that requires iterations to find the corresponding proximity operator, the developed regularizer has a closed-form proximity operator. We apply our regularizer to the robust matrix completion problem, and develop an efficient algorithm based on the alternating direction method of multipliers. The convergence of the suggested method is analyzed and we prove that any generated accumulation point is a stationary point. Finally, experimental results based on synthetic and real-world datasets demonstrate that our algorithm is superior to the stateof-the-art methods in terms of restoration performance.

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Section: Framework To Generate Sir and Its Application To Lrmcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Adaptive Rank-One Matrix Completion Using Sum of Outer Products

Wang

et al. 2023

IEEE Trans. Circuits Syst. Video Technol.

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“…Matrix completion (MC) [1], [2] refers to recovering the missing entries of a partially-observed matrix. It has numerous applications in signal processing and machine learning, such as hyperspectral imaging [3] and image inpainting [4]. MC can be formulated as a constrained rank minimization problem [5], but it is NP-hard since the rank is discrete.…”

Section: Introductionmentioning

confidence: 99%

Robust Recommendation via Social Network Enhanced Matrix Completion

Wang¹,

Shen²,

Jiang³

2023

STAT SINICA

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Robust product recommendation is crucial for internet platforms to boost their businesses. One challenge though is that the user-product rating matrix often has many missing entries. Social network information generates new insights about user behaviors. To fully utilize the social network information, we develop a novel approach, namely MCNet, which combines the random dot product graph model and the low-rank matrix completion to recover the missing entries in the user-product rating matrix from the internet platform. Our algorithm improves the accuracy and the efficiency of recovering the incomplete matrices. We study the asymptotic properties of the estimator. Furthermore, we perform extensive simulations and show that MCNet outperforms the existing approaches, especially when data have small signals. Moreover, MCNet yields robust estimation under misspecified models. We apply MCNet and the competitors to predict the missing entries in the user-product rating matrices on the Yelp and Douban movie platforms. MCNet generally gives the smallest testing errors among all the comparative methods.

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