Low-Rank Autoregressive Tensor Completion for Multivariate Time Series Forecasting

Chen, Xinyu; Sun, Lijun

doi:10.48550/arxiv.2006.10436

Cited by 4 publications

(6 citation statements)

References 23 publications

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“…We now test our algorithm using four real-world streaming data. For the highway traffic data [44], it records the traffic speed time series over weeks from 11160 sensors and thus can be treated as a dense tensor. Here we choose four weeks data and formulate it as a tensor B ∈ R 11160×288×28 .…”

Section: B Real Data Examplesmentioning

confidence: 99%

Effective Streaming Low-tubal-rank Tensor Approximation via Frequent Directions

Yi¹,

Wang²,

Wang³

et al. 2021

Preprint

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Low-tubal-rank tensor approximation has been proposed to analyze large-scale and multi-dimensional data. However, finding such an accurate approximation is challenging in the streaming setting, due to the limited computational resources. To alleviate this issue, this paper extends a popular matrix sketching technique, namely Frequent Directions, for constructing an efficient and accurate low-tubal-rank tensor approximation from streaming data based on the tensor Singular Value Decomposition (t-SVD). Specifically, the new algorithm allows the tensor data to be observed slice by slice, but only needs to maintain and incrementally update a much smaller sketch which could capture the principal information of the original tensor. The rigorous theoretical analysis shows that the approximation error of the new algorithm can be arbitrarily small when the sketch size grows linearly. Extensive experimental results on both synthetic and real multi-dimensional data further reveal the superiority of the proposed algorithm compared with other sketching algorithms for getting low-tubal-rank approximation, in terms of both efficiency and accuracy.

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Section: B Real Data Examplesmentioning

confidence: 99%

Effective Streaming Low-tubal-rank Tensor Approximation via Frequent Directions

Yi¹,

Wang²,

Wang³

et al. 2021

Preprint

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“…It is not diffificult to see that these two data sets are both large-scale and high-dimensional. In what follows, we create a missing patterns, i.e., random missing (RM), which are same as the work [20]. Then according to the mechanism of RM patterns, we mask certain amount of observations as missing values (i.e., 30%, 70%) in both two data sets, and the remaining partial observations are input data for imputing these masked entries.…”

Section: California Pems Data Setsmentioning

confidence: 99%

“…By using tensor structure to model multivariable time series data, multivariable / multidimensional settings are studied. Signature framework includes: 1) classical time series analysis methods, such as vector autoregressive model [10] , 2) pure low rank matrix factorization / completion, such as low rank matrix factorization [11,12], principal component analysis [13,14] and its variants, and 3) Pure low rank tensor factorization / completion, such as Bayesian tensor factorization [15] and low rank tensor factorization [16,17] , 4) by integrating low rank matrix factorization of time series models, such as time regularized matrix factorization [18] and Bayesian time matrix factorization [19], and 5) low rank tensor completion by integrating time series models (such as LATC) [20]. For this large class of methods, a common goal is to capture temporal dynamics and spatial consistency.…”

Section: Introductionmentioning

confidence: 99%

“…For this large class of methods, a common goal is to capture temporal dynamics and spatial consistency. For example, by integrating the time series model and the pure low rank tensor completion model, the recently developed LATC framework shows superior performance compared with the existing low rank tensor completion model [20] by imposing local consistency and global consistency on the traffic series data [21]. In addition, some nonlinear methods (such as deep learning in [22,23,24]) have been applied to solve the problem of missing traffic data.…”

Section: Introductionmentioning

confidence: 99%

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A Biased Deep Tensor Factorization Network For Tensor Completion

Wu,

2021

Preprint

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Tensor decomposition is a popular technique for tensor completion, However most of the existing methods are based on linear or shallow model, when the data tensor becomes large and the observation data is very small, it is prone to over fitting and the performance decreases significantly. To address this problem, the completion method for a tensor based on a Biased Deep Tensor Factorization Network (BDTFN) is proposed. This method can not only overcome the shortcomings of traditional tensor factorization, but also deal with complex non-linear data. Firstly, the horizontal and lateral tensors corresponding to the observed values of the input tensors are used as inputs and projected to obtain their horizontal (lateral) potential feature tensors. Secondly, the horizontal (lateral) potential feature tensors are respectively constructed into a multilayer perceptron network. Finally, the horizontal and lateral output tensors are fused by constructing a bilinear pooling layer. Tensor forward-propagation is composed of those three step, and its parameters are updated by tensor back-propagation using the multivariable chain rule. In this paper, we consider the large-scale 5-minute traffic speed data set and use it to address the missing data imputation problem for large-scale spatiotemporal traffic data. In addition, we compare the numerical performance of the proposed algorithm with those for state-of-the-art approaches on video recovery and color image recovery. Numerical experimental results illustrate that our approach is not only much more accurate than those state-of-the-art methods, but it also has high speed.

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“…Lastly, almost all of the present studies on response forecasting are based on high-quality data instead of imperfect measurements with missing values. To this end, in light of the recent renaissance in tensor learning [40][41][42], which has already greatly contributed to image processing [43][44][45][46][47][48], recommender systems [49][50][51], and traffic data analysis [52][53][54][55][56][57][58][59][60][61][62]. In the context of SHM, we can naturally consider the data as multivariate time-series matrix and then apply temporal factorization models (e.g., [60]) where the low-rank representation can effectively characterize the complex spatial and temporal dependencies rooted in the data.…”

Section: Introductionmentioning

confidence: 99%

Incremental Bayesian tensor learning for structural monitoring data imputation and response forecasting

Ren¹,

Chen²,

Sun³

et al. 2020

Preprint

Self Cite

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There has been increased interest in missing sensor data imputation, which is ubiquitous in the field of structural health monitoring (SHM) due to discontinuous sensing caused by sensor malfunction. Recent development in Bayesian temporal factorization models for high-dimensional time series analysis has provided an effective tool solve both imputation and prediction problems. However, for large datasets, the default Bayesian temporal factorization model becomes less inefficient since the model has to be fully retrained when new data arrives. A potential solution is to train the model using a short time window covering only most recent data; however, by doing so, we may miss some critical dynamics and long-term dependencies which can only be identified from a longer time window. To address this fundamental issue in temporal factorization models, this paper presents an incremental Bayesian tensor learning scheme to achieve efficient imputation and prediction of structural response in long-term SHM. In particular, a spatiotemporal tensor is first constructed followed by Bayesian tensor factorization that extracts latent features for missing data imputation. To enable structural response forecasting based on long-term and incomplete sensing data, we develop an incremental learning scheme to effectively update the Bayesian temporal factorization model. The performance of the proposed approach is validated on continuous field-sensing data (including strain and temperature records) of a concrete bridge, based on the assumption that strain time histories are highly correlated to temperature recordings. The results indicate that the proposed probabilistic tensor learning framework is accurate and robust even in the presence of large rates of random missing, structured missing and their combination. The effect of rank selection on the imputation and prediction performance is also investigated. The results show that a better estimation accuracy can be achieved with a higher rank for random missing whereas a lower rank for structured missing.

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Low-Rank Autoregressive Tensor Completion for Multivariate Time Series Forecasting

Cited by 4 publications

References 23 publications

Effective Streaming Low-tubal-rank Tensor Approximation via Frequent Directions

Effective Streaming Low-tubal-rank Tensor Approximation via Frequent Directions

A Biased Deep Tensor Factorization Network For Tensor Completion

Incremental Bayesian tensor learning for structural monitoring data imputation and response forecasting

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