Low rank tensor completion for multiway visual data

Zhang, Long; Liu, Yipeng; Chen, Longxi; Zhu, Ce

doi:10.1016/j.sigpro.2018.09.039

Cited by 137 publications

(57 citation statements)

References 70 publications

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“…Recently, CP decomposition-based channel parameter estimation for mmWave MIMO-OFDM systems is proposed in [41]. Furthermore, developing efficient tensor completion and decomposition methods from incomplete measurements are also desirable [42,43,44,45,46,47]. [51].…”

Section: From Point To Distributed Source Modelsmentioning

confidence: 99%

A survey on 5G massive MIMO localization

Wen

Wymeersch

Peng

et al. 2019

Digital Signal Processing

114

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Section: From Point To Distributed Source Modelsmentioning

confidence: 99%

A survey on 5G massive MIMO localization

Wen

Wymeersch

Peng

et al. 2019

Digital Signal Processing

114

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show abstract

“…However, these methods often require knowing which of the entries or modalities are imperfect beforehand. While there has been some work on using low-rank tensor representations for imperfect data (Chang et al, 2017;Fan et al, 2017;Long et al, 2018;Nimishakavi et al, 2018), our approach is the first to integrate rank minimization with neural networks for multimodal language data, thereby combining the strength of non-linear transformations with the mathematical foundations of tensor structures.…”

Section: Related Workmentioning

confidence: 99%

Learning Representations from Imperfect Time Series Data via Tensor Rank Regularization

Liang¹,

Liu²,

Tsai³

et al. 2019

Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics

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There has been an increased interest in multimodal language processing including multimodal dialog, question answering, sentiment analysis, and speech recognition. However, naturally occurring multimodal data is often imperfect as a result of imperfect modalities, missing entries or noise corruption. To address these concerns, we present a regularization method based on tensor rank minimization. Our method is based on the observation that high-dimensional multimodal time series data often exhibit correlations across time and modalities which leads to low-rank tensor representations. However, the presence of noise or incomplete values breaks these correlations and results in tensor representations of higher rank. We design a model to learn such tensor representations and effectively regularize their rank. Experiments on multimodal language data show that our model achieves good results across various levels of imperfection.

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“…On the other hand, the tensor T-product introduced by Kilmer [21] has been proved to be of great use in many areas, such as image processing [21,29,35,37], computer vision [12], signal processing [7,24,25], low rank tensor recovery and robust tensor PCA [23,24], data completion and denoising [16,25,38]. An approach of linearization is provided by the T-product to transfer tensor multiplication to matrix multiplication by the discrete Fourier transformation and the theories of block circulant matrices [6,19].…”

Section: Introductionmentioning

confidence: 99%