On identifiability of higher order block term tensor decompositions of rank Lr⊗ rank-1

Yang, Ming; Li, Wen; Xiao, Mingqing

doi:10.1080/03081087.2018.1502251

Cited by 7 publications

(4 citation statements)

References 15 publications

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“…Thus, instead of operating on original data or performing some data cleaning that precedes the analysis, we assume the data to be decomposed into two parts: the clean data D and the corruptions E. Then, the graph learning is performed on clean data. Following the RPCA idea that the clean data is low-rank and corruptions are sparse [56,60,61], we jointly learn the clean data and the graph. Finally, our proposed Robust Graph Construction (RGC) model can be formulated as:…”

Section: Formulationmentioning

confidence: 99%

Robust Graph Learning From Noisy Data

Kang

Pan

Hoi

et al. 2020

IEEE Trans. Cybern.

241

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Learning graphs from data automatically has shown encouraging performance on clustering and semisupervised learning tasks. However, real data are often corrupted, which may cause the learned graph to be inexact or unreliable. In this paper, we propose a novel robust graph learning scheme to learn reliable graphs from real-world noisy data by adaptively removing noise and errors in the raw data. We show that our proposed model can also be viewed as a robust version of manifold regularized robust PCA, where the quality of the graph plays a critical role. The proposed model is able to boost the performance of data clustering, semisupervised classification, and data recovery significantly, primarily due to two key factors: 1) enhanced low-rank recovery by exploiting the graph smoothness assumption, 2) improved graph construction by exploiting clean data recovered by robust PCA. Thus, it boosts the clustering, semi-supervised classification, and data recovery performance overall. Extensive experiments on image/document clustering, object recognition, image shadow removal, and video background subtraction reveal that our model outperforms the previous state-of-the-art methods.

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Section: Formulationmentioning

confidence: 99%

Robust Graph Learning From Noisy Data

Kang

Pan

Hoi

et al. 2020

IEEE Trans. Cybern.

241

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“…An array of numbers arranged on a regular grid with a variable number of axes is described as a tensor. As the dimensionality reaches beyond 3D, conventional data representations such as vector-based and matrix-based become insufficient, and highly dimensional data sets are usually formulated as tensors [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Tensor Robust Principal Component Analysis via Non-Convex Low Rank Approximation

et al. 2019

Self Cite

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Tensor Robust Principal Component Analysis (TRPCA) plays a critical role in handling high multi-dimensional data sets, aiming to recover the low-rank and sparse components both accurately and efficiently. In this paper, different from current approach, we developed a new t-Gamma tensor quasi-norm as a non-convex regularization to approximate the low-rank component. Compared to various convex regularization, this new configuration not only can better capture the tensor rank but also provides a simplified approach. An optimization process is conducted via tensor singular decomposition and an efficient augmented Lagrange multiplier algorithm is established. Extensive experimental results demonstrate that our new approach outperforms current state-of-the-art algorithms in terms of accuracy and efficiency.

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“…(x) − F(x)| > |F(x ) − F(x)| (20)From the definition of subgradient, we have∇f (x) ∈ ∂f (x ). (21)Thus, |∂F(x )| ≥ C|F(x )−F(x)| θ .By Lemma 2, the explicit estimation of the Lojasiewicz exponent of F(x) is given by Eq (17)…”

mentioning

confidence: 97%

Low-Rank Tensor Thresholding Ridge Regression

Guo¹,

Zhang²,

Xu³

et al. 2019

IEEE Access

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In the area of subspace clustering, methods combining self-representation and spectral clustering are predominant in recent years. For dealing with tensor data, most existing methods vectorize them into vectors and lose most of the spatial information. For removing noise of the data, most existing methods focus on the input space and lack consideration of the projection space. Aiming at preserving the spatial information of tensor data, we incorporate tensor mode-d product with low-rank matrices for selfrepresentation. At the same time, we remove noise of the data in both the input space and the projection space, and obtain a robust affinity matrix for spectral clustering. Extensive experiments on several popular subspace clustering datasets show that the proposed method outperforms both traditional subspace clustering methods and recent state-of-the-art deep learning methods.INDEX TERMS Tensor, low-rank, subspace clustering.

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On identifiability of higher order block term tensor decompositions of rank L_r⊗ rank-1

Cited by 7 publications

References 15 publications

Robust Graph Learning From Noisy Data

Robust Graph Learning From Noisy Data

Tensor Robust Principal Component Analysis via Non-Convex Low Rank Approximation

Low-Rank Tensor Thresholding Ridge Regression

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