Low-rank tensor train for tensor robust principal component analysis

Yang, Jing‐Hua; Zhao, Xi-Le; Ji, Teng-Yu; Ma, Tianhui; Huang, Ting‐Zhu

doi:10.1016/j.amc.2019.124783

Cited by 84 publications

(42 citation statements)

References 30 publications

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“…The most significant application of principal component analysis is the implementation of a multivariate record board as a small set of variables with the aim of viewing trends, bounds, groups, and outliers [51]. Principal component analysis is a very flexible device and allows the study of datasets that may include, for example, multicollinearity, misplaced values, and categorical records, in addition to incorrect data [52]. The objective is to detect and express significant data records as a set of primary indices or main components [51,53].…”

Section: Urban Change Detectionmentioning

confidence: 99%

Detection of Urban and Environmental Changes via Remote Sensing

2021

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Rapid climate and environmental change at limited, regional, and general scales have been a major concern for researchers in a number of fields, such as topography, economy, environment, and sustainable development. Changes in land cover and land use have taken into account due to potential impacts on soil depletion, amplified runoff , water balance, and climate change. A detailed understanding of the characteristics of land exploitation and land structure is indispensable for the study of their influences on life and nature. In addition, urban extension is a major form of land extraction and land transformation, as it relates to the rise in population and the availability of financial services. Remote sensing records have been shown to be important for reporting and perceiving urban development and transition, and for providing critical information for future growth. Transformation and shift identification are the tools used to recognise distinctions in a land cover by tracking them at various times. In addition, various change identification and detection approaches are routinely tested with the goal of providing the greatest change detection deductions for a particular appliance. This review would aim to establish a practical plan that combines remote sensing techniques, on the one hand, and modelling approaches, on the other, to track land use, to cover changes, and to predict future trends.

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Section: Urban Change Detectionmentioning

confidence: 99%

Detection of Urban and Environmental Changes via Remote Sensing

2021

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“…However, the spatial resolution is inevitably decreased because of the limited sun irradiance [3]. Thus, we need to utilize some techniques to enhance the spatial quality of the HSIs [4]- [11]. We know that MSIs are obtained with poor spectral resolution but abundant spatial resolution compared with HSIs.…”

Section: Introductionmentioning

confidence: 99%

Hyperspectral Image Superresolution Using Unidirectional Total Variation With Tucker Decomposition

Huang

Deng

et al. 2020

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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The hyperspectral image super-resolution (HSI-SR) problem aims to improve the spatial quality of a low spatial resolution hyperspectral image (LR-HSI) by fusing the LR-HSI combined with the corresponding high spatial resolution multispectral image (HR-MSI). The generated hyperspectral image with high spatial quality, i.e., the target HR-HSI, generally has some fundamental latent properties, e.g., the sparsity and the piecewise smoothness along with the three modes (i.e., width, height, and spectral mode). However, limited works consider both properties in the HSI-SR problem. In this work, a novel unidirectional total variation-based approach is been proposed. On the one hand, we consider the target HR-HSI exhibits both the sparsity and the piecewise smoothness on the three modes, and they can be depicted well by the 1-norm and total variation (TV), respectively. On the other hand, we utilize the classical Tucker decomposition to decompose the target HR-HSI (a 3-mode tensor) as a sparse core tensor multiplied by the dictionary matrices along with the three modes. Especially, we impose the 1-norm on core tensor to characterize the sparsity, and the unidirectional TV on three dictionaries to characterize the piecewise smoothness. The proximal alternating optimization (PAO) scheme and the alternating direction method of multipliers (ADMM) are used to iteratively solve the proposed model. Experiments on three common datasets illustrate the proposed approach has better performance than some current state-of-the-art HSI-SR methods.

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“…Since there exists correlations in the practical datasets such as images and user ratings, the resulting tensor data is often low-rank. The low-rank property has been exploited in problems like low-rank tensor completion [25,26,27,28,29,30] and low-rank tensor recovery [31,32,33,34,35]. Leveraging the low-rank property, a convex relaxation of the Tucker rank can be applied to robust tensor recovery [31,32] and tensor completion [25,26].…”

Section: Introductionmentioning

confidence: 99%

Tensor Recovery from Noisy and Multi-Level Quantized Measurements

Ren

Wang

Xiong

2020

Preprint

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Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements by leveraging the low CANDECOMP/PARAFAC (CP) rank property. We study the recovery of both general low-rank tensors and tensors that have tensor singular value decomposition (TSVD) by solving nonconvex optimization problems. We provide the theoretical upper bounds of the recovery error, which diminish to zero when the sizes of dimensions increase to infinity. We further characterize the fundamental limit of any recovery algorithm and show that our recovery error is nearly order-wise optimal. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee and a TSVD based projected gradient descent algorithm are proposed to solve the nonconvex problems. Our recovery methods can also handle data losses and do not necessarily need the information of the quantization rule. The methods are validated on synthetic data, image datasets, and music recommender datasets.

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Low-rank tensor train for tensor robust principal component analysis

Cited by 84 publications

References 30 publications

Detection of Urban and Environmental Changes via Remote Sensing

Detection of Urban and Environmental Changes via Remote Sensing

Hyperspectral Image Superresolution Using Unidirectional Total Variation With Tucker Decomposition

Tensor Recovery from Noisy and Multi-Level Quantized Measurements

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