Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization

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

doi:10.1109/tnnls.2018.2873655

Cited by 60 publications

(14 citation statements)

References 51 publications

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“…TCMs utilize the information from not only the onedimensional EEG signals or simultaneously acquired twodimensional EEG signals, but also EEG signals from other trials which are multi-dimensional. In the analysis of EEG data, TCMs can also incorporate the multiway nature of data, similar to the applications of image processing and social network data [14][15][16][17][18][19]. Solé-Casals et al [7] proposed to reconstruct EEG signals with missing data using TCMs in a brain computer interface (BCI) context.…”

Section: Introductionmentioning

confidence: 99%

On the robustness of EEG tensor completion methods

Duan

Hao

Zhang

et al. 2021

Sci. China Technol. Sci.

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During the acquisition of electroencephalographic (EEG) signals, data may be missing or corrupted by noise and artifacts. To reconstruct the incomplete data, EEG signals are firstly converted into a three-order tensor (multi-dimensional data) of shape time × channel × trial. Then, the missing data can be efficiently recovered by applying a tensor completion method (TCM). However, there is not a unique way to organize channels and trials in a tensor, and different numbers of channels are available depending on the EEG setting used, which may affect the quality of the tensor completion results. The main goal of this paper is to evaluate the robustness of EEG completion methods with several designed parameters such as the ordering of channels and trials, the number of channels, and the amount of missing data. In this work, the results of completing missing data by several TCMs were compared. To emulate different scenarios of missing data, three different patterns of missing data were designed. Firstly, the amount of missing data on completion effects was analyzed, including the time lengths of missing data and the number of channels or trials affected by missing data. Secondly, the numerical stability of the completion methods was analyzed by shuffling the indices along channels or trials in the EEG data tensor. Finally, the way that the number of electrodes of EEG tensors influences completion effects was assessed by changing the number of channels. Among all the applied TCMs, the simultaneous tensor decomposition and completion (STDC) method achieves the best performance in providing stable results when the amount of missing data or the electrode number of EEG tensors is changed. In other words, STDC proves to be an excellent choice of TCM, since permutations of trials or channels have almost no influence on the complete results. The STDC method can efficiently complete the missing EEG signals. The designed simulations can be regarded as a procedure to validate whether or not a completion method is useful enough to complete EEG signals.

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Section: Introductionmentioning

confidence: 99%

On the robustness of EEG tensor completion methods

Duan

Hao

Zhang

et al. 2021

Sci. China Technol. Sci.

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“…Tensor decomposition is a powerful computational technique for extracting valuable information from tensorial data Shi et al 2018;Zhou, Lu, and Cheung 2019;. Taking this advantage, tensor decomposition-based approaches can handle multiple TS simultaneously and achieve good forecasting performance (Dunlavy, Kolda, and Acar 2011;Li et al 2015;Tan et al 2016;Bhanu et al 2018;Faloutsos et al 2018).…”

Section: Introductionmentioning

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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“…Several methods have been proposed for tensor decomposition [37][38][39]. In [37], NMF is applied to variational Bayesian matrix factorization, where each observed entry is assumed to be a beta distribution.…”

Section: Introductionmentioning

confidence: 99%

“…In [37], NMF is applied to variational Bayesian matrix factorization, where each observed entry is assumed to be a beta distribution. Shi et al [38] proposed tensor decomposition with variance maximization for feature extraction. In [39], pairwise similarity information is incorporated into Tucker tensor decomposition.…”

Section: Introductionmentioning

confidence: 99%

Non-parallel dictionary learning for voice conversion using non-negative Tucker decomposition

Takashima

Nakashika

Takiguchi

et al. 2019

J AUDIO SPEECH MUSIC PROC.

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Voice conversion (VC) is a technique of exclusively converting speaker-specific information in the source speech while preserving the associated phonemic information. Non-negative matrix factorization (NMF)-based VC has been widely researched because of the natural-sounding voice it achieves when compared with conventional Gaussian mixture model-based VC. In conventional NMF-VC, models are trained using parallel data which results in the speech data requiring elaborate pre-processing to generate parallel data. NMF-VC also tends to be an extensive model as this method has several parallel exemplars for the dictionary matrix, leading to a high computational cost. In this study, an innovative parallel dictionary-learning method using non-negative Tucker decomposition (NTD) is proposed. The proposed method uses tensor decomposition and decomposes an input observation into a set of mode matrices and one core tensor. The proposed NTD-based dictionary-learning method estimates the dictionary matrix for NMF-VC without using parallel data. The experimental results show that the proposed method outperforms other methods in both parallel and non-parallel settings.

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Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization

Abstract: This is a repository copy of Feature extraction for incomplete data via low-rank tensor decomposition with feature regularization.

Cited by 60 publications

References 51 publications

On the robustness of EEG tensor completion methods

On the robustness of EEG tensor completion methods

Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting

Non-parallel dictionary learning for voice conversion using non-negative Tucker decomposition

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