Abstract
With the booming of the Internet of Things, tremendous amount of sensors have been installed in different geographic locations, generating massive sensory data with both time-stamps and geo-tags. Such type of data usually have shown complex spatio-temporal correlation and are easily missing in practice due to communication failure or data corruption. In this paper, we aim to tackle the challenge – how to accurately and efficiently recover the missing values for corrupted spatio-temporal sensory data. Specifically, we first formulate such sensor data as a high-dimensional tensor that can naturally preserve sensors’ both geographical and time information, thus we call spatio-temporal Tensor. Then we model the sensor data recovery as a low-rank robust tensor completion problem by exploiting its latent low-rank structure and sparse noise property. To solve this optimization problem, we design a highly efficient optimization method that combines the alternating direction method of multipliers and accelerated proximal gradient to minimize the tensor’s convex surrogate and noise’s \(\ell _1\)-norm. In addition to testing our method by a synthetic dataset, we also use passive RFID (radio-frequency identification) sensors to build a real-world sensor-array testbed, which generates overall 115,200 sensor readings for model evaluation. The experimental results demonstrate the accuracy and robustness of our approach.
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Notes
- 1.
The rank of a matrix is often linked to the order, complexity, or dimensionality of the underlying system, which tends to be much smaller than the data size.
- 2.
We assume the additive noises are sufficiently sparse relative to the data tensor \(\mathcal {O}\).
- 3.
- 4.
Available in www.sandia.gov/~tgkolda/TensorToolbox/index-2.6.html.
- 5.
Available in http://sun.stanford.edu/~rmunk/PROPACK/.
- 6.
Available in au.mathworks.com/help/curvefit/smoothing-data.html.
- 7.
Available in www.cis.pku.edu.cn/faculty/vision/zlin/RPCA+MC_codes.zip.
- 8.
Available in www.cs.rochester.edu/u/jliu/code/TensorCompletion.zip.
- 9.
Available in https://github.com/ryotat/tensor.
- 10.
In each iteration, all the tensor completion based methods require to calculate 3 times SVD that is most time-consuming computation task so we use iteration number as evaluation metric for computation time.
- 11.
We collect over all one hour’s RSS readings, the sampling rate is 2 Hz. During the data collection, a participant is doing various activities between the RFID sensor-array and reader, including walking, sitting, standing, lying down as well as falling down etc. By doing so, the collected RSSI reading will reveal different patterns.
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Ruan, W., Xu, P., Sheng, Q.Z., Falkner, N.J.G., Li, X., Zhang, W.E. (2017). Recovering Missing Values from Corrupted Spatio-Temporal Sensory Data via Robust Low-Rank Tensor Completion. In: Candan, S., Chen, L., Pedersen, T., Chang, L., Hua, W. (eds) Database Systems for Advanced Applications. DASFAA 2017. Lecture Notes in Computer Science(), vol 10177. Springer, Cham. https://doi.org/10.1007/978-3-319-55753-3_38
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