Tensor Rank Estimation and Completion via CP-based Nuclear Norm

Shi, Qiquan; Lu, Haiping; Cheung, Yiu-ming

doi:10.1145/3132847.3132945

Cited by 24 publications

(27 citation statements)

References 34 publications

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“…We employ the ALSs method for optimisation. In fact, the HOSVD algorithm can solve problem (5) under typical conditions, and its pseudocode is shown in Algorithm 1 (see Fig. 1), where m represents the maximum number of iterations and ε is the threshold.…”

Section: Orthogonal Random Projection Methods For Tensor Completionmentioning

confidence: 99%

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Orthogonal random projection for tensor completion

Feng

Zhou

2020

IET Computer Vision

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The low‐rank tensor completion problem, which aims to recover the missing data from partially observable data. However, most of the existing tensor completion algorithms based on Tucker decomposition cannot avoid using singular value decomposition (SVD) operation to calculate the Tucker factors, so they are not suitable for the completion of large‐scale data. To solve this problem, they propose a new faster tensor completion algorithm, which uses the method of random projection to project the unfolding matrix of each mode of the tensor into the low‐dimensional subspace, and then obtain the Tucker factors by the orthogonal decomposition. Their method can effectively avoid the high computational cost of SVD operation. The results of the synthetic data experiments and real data experiments verify the effectiveness and feasibility of their method.

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Section: Orthogonal Random Projection Methods For Tensor Completionmentioning

confidence: 99%

“…The number of dimensions of a tensor is the order and each dimension is a mode of it [5]. Scalars are denoted by lowercase letters, e.g.…”

Section: Notationsmentioning

confidence: 99%

Orthogonal random projection for tensor completion

Feng

Zhou

2020

IET Computer Vision

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“…Other representative schemes are pattern based sub-Nyquist sampling [8]. To apply the subspace-based parameter estimation algorithm, the following joint tensor completion and CANDECOMP/PARAFAC (CP) decomposition problem is formulated [3,18]. In the CP decomposition model [9], tensor is decomposed into a sum of rank-one tensors, implying that each component corresponds to one path.…”

Section: Proposed Methods 31 Tensor Completionmentioning

confidence: 99%

Tensor completion-based 5G positioning with partial channel measurements

Wen

Svensson

2020

Proceedings of the Twenty-First International Symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Netw

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5G mmWave communication systems have promising properties for high precision user localization and environment mapping. Such information is of high value for emerging applications such as connected automated driving (CAD), and it has also potential to be explored to substantially improve efficiency and reliability of mmWave communications itself. However, the acquisition of such information cannot come with too large overhead in the system. Existing studies have so far relied on complete channel measurements, implying a prohibitive channel training overhead. In this paper, we exploit the possibility of 5G positioning using partial channel measurements. We utilize a tensor completion technique to recover the complete channel information from low rank channel measurements. Simulation results demonstrate the trade-off between user positioning accuracy and channel training overhead, and show that sub-meter precision with negligible performance loss is feasible at sample ratio reductions of at least 30%, and meter level precision is achievable with sample ratio reduction of 50%. CCS CONCEPTS • Communication hardware, interfaces and storage → Signal processing systems.

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“…In short, we do not need to carefully tune the parameters for BHT-ARIMA while we usually can obtain better results by setting smaller values such as { τ = 2 − 4, R M = τ and small (p = 1 − 5, d = 1, q = 1)}. Moreover, the Tuckerrank can be estimated automatically (Yokota, Lee, and Cichocki 2016;Shi, Lu, and Cheung 2017). Effect of applying MDT on all modes / temporal mode As discussed in Remark 1 about why we apply MDT only along the temporal mode, we here verify it by testing on the Smoke video.…”

Section: Analysis Of Parameters and Convergencementioning

confidence: 99%

Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting

Shi

Yin

Cai

et al. 2020

AAAI

Self Cite

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This work proposes a novel approach for multiple time series forecasting. At first, multi-way delay embedding transform (MDT) is employed to represent time series as low-rank block Hankel tensors (BHT). Then, the higher-order tensors are projected to compressed core tensors by applying Tucker decomposition. At the same time, the generalized tensor Autoregressive Integrated Moving Average (ARIMA) is explicitly used on consecutive core tensors to predict future samples. In this manner, the proposed approach tactically incorporates the unique advantages of MDT tensorization (to exploit mutual correlations) and tensor ARIMA coupled with low-rank Tucker decomposition into a unified framework. This framework exploits the low-rank structure of block Hankel tensors in the embedded space and captures the intrinsic correlations among multiple TS, which thus can improve the forecasting results, especially for multiple short time series. Experiments conducted on three public datasets and two industrial datasets verify that the proposed BHT-ARIMA effectively improves forecasting accuracy and reduces computational cost compared with the state-of-the-art methods.

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Tensor Rank Estimation and Completion via CP-based Nuclear Norm

Abstract: This is a repository copy of Tensor Rank Estimation and Completion via CP-based Nuclear Norm.

Cited by 24 publications

References 34 publications

Orthogonal random projection for tensor completion

Orthogonal random projection for tensor completion

Tensor completion-based 5G positioning with partial channel measurements

Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting

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