Low-Rank High-Order Tensor Completion With Applications in Visual Data

Qin, Wenjin; Wang, Hailin; Zhang, Feng; Wang, Jianjun; Luo, Xin; Huang, Tingwen

doi:10.1109/tip.2022.3155949

Cited by 77 publications

(23 citation statements)

References 70 publications

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“…While tcam proves to constitute a useful tool for the analysis of longitudinal experimental designs, it relies on fully sampled cohorts, i.e., where all participants provide the same number of samples corresponding to similar time points. Even though missing data imputation is a classic use-case for low-rank approximations in general [ 6 , 9 ] and the recent progress made in the applications of tsvdm to incomplete data [ 26 ], the accuracy and reliability of reconstructed data generally depend on assumptions regarding the generative process of the data, the frequency of observed values or their distribution across subjects, features and timepoints. Maintaining tcam ’s universality to all kinds of ’omics data necessitates a detachment of the factorization from imputation and normalization of the data.…”

Section: Discussionmentioning

confidence: 99%

Dimensionality reduction of longitudinal ’omics data using modern tensor factorizations

et al. 2022

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Longitudinal ’omics analytical methods are extensively used in the field of evolving precision medicine, by enabling ‘big data’ recording and high-resolution interpretation of complex datasets, driven by individual variations in response to perturbations such as disease pathogenesis, medical treatment or changes in lifestyle. However, inherent technical limitations in biomedical studies often result in the generation of feature-rich and sample-limited datasets. Analyzing such data using conventional modalities often proves to be challenging since the repeated, high-dimensional measurements overload the outlook with inconsequential variations that must be filtered from the data in order to find the true, biologically relevant signal. Tensor methods for the analysis and meaningful representation of multi-way data may prove useful to the biological research community by their advertised ability to tackle this challenge. In this study, we present tcam—a new unsupervised tensor factorization method for the analysis of multi-way data. Building on top of cutting-edge developments in the field of tensor-tensor algebra, we characterize the unique mathematical properties of our method, namely, 1) preservation of geometric and statistical traits of the data, which enables uncovering information beyond the inter-individual variation that often takes-over the focus, especially in human studies. 2) Natural and straightforward out-of-sample extension, making tcam amenable for integration in machine learning workflows. A series of re-analyses of real-world, human experimental datasets showcase these theoretical properties, while providing empirical confirmation of tcam’s utility in the analysis of longitudinal ’omics data.

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Section: Discussionmentioning

confidence: 99%

Dimensionality reduction of longitudinal ’omics data using modern tensor factorizations

et al. 2022

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“…The key issue of removing noise from corrupted visual data is to fully utilize the structure priors of the underlying data. Low-rank prior [18][19][20][21] and nonlocal prior [22][23][24][25] are two commonly-used structure priors for visual data recovery. In this section, we briefly review some works on these two priors.…”

Section: Related Workmentioning

confidence: 99%

Color Image Denoising via Tensor Robust PCA with Nonconvex and Nonlocal Regularization

Geng

Guo

Zhang

2021

ACM Multimedia Asia

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Tensor robust principal component analysis (TRPCA) is a promising way for low-rank tensor recovery, which minimizes the convex surrogate of tensor rank by shrinking each tensor singular values equally. However, for real-world visual data, large singular values represent more signifiant information than small singular values. In this paper, we propose a nonconvex TRPCA (N-TRPCA) model based on the tensor adjustable logarithmic norm. Unlike TRPCA, our N-TRPCA can adaptively shrink small singular values more and shrink large singular values less. In addition, TRPCA assumes that the whole data tensor is of low rank. This assumption is hardly satisfied in practice for natural visual data, restricting the capability of TRPCA to recover the edges and texture details from noisy images and videos. To this end, we integrate nonlocal self-similarity into N-TRPCA, and further develop a nonconvex and nonlocal TRPCA (NN-TRPCA) model. Specifically, similar nonlocal patches are grouped as a tensor and then each group tensor is recovered by our N-TRPCA. Since the patches in one group are highly correlated, all group tensors have strong low-rank property, leading to an improvement of recovery performance. Experimental results demonstrate that the proposed NN-TRPCA outperforms some existing TRPCA methods in visual data recovery. The demo code is available at https://github.com/qguo2010/NN-TRPCA.

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“…Using the low-rank property, missing entries in the observations can be potentially inferred by the partially sampled data. The MC technique has been studied for image processing [22], remote sensing [24], and wireless sensor networks [25]. It also has been used in bioinformatics, such as in the recognition of long non-coding RNA (lncRNA) disease associations [26], and in microRNA target prediction [27].…”

Section: Introductionmentioning

confidence: 99%

“…Low-rank matrix completion (MC) is a promising method to estimate missing entries for incomplete or inexact observed data [21], where the low-rank property of data measurements is believed to exist in many real-world applications. This is due to the characteristics of intrinsic low dimensional space or an underlying trend of massive measured data [22], [23]. Using the low-rank property, missing entries in the observations can be potentially inferred by the partially sampled data.…”

Section: Introductionmentioning

confidence: 99%

Refined Matrix Completion for Spectrum Estimation of Heart Rate Variability

Zhu

Tan

et al. 2022

Preprint

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Heart rate variability (HRV) is the reflection of physiological effects modulating heart rhythm. In particular, spectral HRV metrics provide valuable information to investigate activities of the cardiac autonomic nervous system. However, uncertainties and artifacts from measurements can reduce signal quality and therefore affect the evaluation of HRV measures. In this paper, we propose a new method for HRV spectrum estimation with measurement uncertainties using matrix completion (MC). We show that missing values of HRV spectrum can be efficiently estimated using the MC method by leveraging the low rank property of the spectrum matrix. In addition, we proposed a refined matrix completion (RMC) method to improve the estimation accuracy and computational efficiency by introducing model information for the HRV spectrum. Experimental studies on five public benchmark datasets show the effectiveness and robustness of the developed RMC method for estimating missing entries for HRV spectrum with different masking ratios. Furthermore, our developed RMC method is compared with five deep learning models and the traditional MC method; the results of this comparison study demonstrate that our developed RMC method obtains the least estimation error with the minimal computation cost, indicating the advantages of our developed method for HRV spectrum estimation.

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Low-Rank High-Order Tensor Completion With Applications in Visual Data

Cited by 77 publications

References 70 publications

Dimensionality reduction of longitudinal ’omics data using modern tensor factorizations

Dimensionality reduction of longitudinal ’omics data using modern tensor factorizations

Color Image Denoising via Tensor Robust PCA with Nonconvex and Nonlocal Regularization

Refined Matrix Completion for Spectrum Estimation of Heart Rate Variability

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