近年來空氣汙染已成為重視的議題。台灣行政院環保署規劃，於2017年至2020年逐步布建1萬200個空氣品質感測器，由物聯網方式蒐集大量且時間解析度密集的空品數據來分析各地區的空氣污染現象。

由於空氣品質感測器本體小且脆弱，容易受到日曬、雨淋或是其他物理因素使得裝置故障而偵測到錯誤的pm2.5數
值，而目前的空氣品質感測器故障偵測方式仰賴現場做檢閱測量。但感測器佈設點過多，以抽檢方式做巡檢是沒有效率的巡檢方式。

我們建構一個基於深度時空圖模型的異常偵測框架，模型包含圖卷積和時間卷積兩個方法，時間卷積處理過往空氣品質感測器偵測到的pm2.5時序資料，找出時間上的相關性，同時於每個時間點，對感測器與其周圍感測器點建立成一個無向聯通圖，由圖卷積的方式，找出空間特徵，最後模型預測當下的pm2.5數值，並與空氣品質感測器偵測到的數值計算R2-score分數，並對所有空氣品質感測器站點的R2-score做低到高排序，R2-score越低代表感測器越有可能出現異常。經過實驗，在有限巡檢個數之下，我們模型找到有問題個數的比率跟過往異常偵測的方法和隨機挑選都來的高，優先檢查本模型認定的故障感測器可降低巡檢所需的人力與時間成本。

Air pollution is an essential issue in Taiwan. From 2017 to 2020, the Environmental Protection Administration of Executive Yuan in Taiwan has gradually deployed 10,200 air quality sensors, which have collected a large amount of air quality data with high time resolution. However, because the air quality sensors are small and fragile, environmental factors, such as sun, rain, and other physical characteristics, may influence or even damage these sensors. As a result, the monitored PM2.5 values from these malfunctioning sensors are inaccurate. The current strategy to identify the failure sensors requires on-site inspection. However, since the number of sensors is huge and sensors are located all over Taiwan, it is inefficient to discover the malfunctioning sensors by scheduled inspection or random sampling.

We propose an anomaly detection framework to identify the malfunctioning sensors based on a deep spatial-temporal graph model consisting of graph convolution and time convolution.

The time convolution discovers the temporal relationship among the monitored PM2.5 values of a sensor. At each time point, an undirected connected graph is established between each sensor and its surrounding sensors. The graph convolution utilizes these graphs to learn the spatial characteristics. We leverage this deep spatial-temporal graph model to predict the current PM2.5 value of a target sensor. We calculate the R2-score between the predicted PM2.5 values and the monitored PM2.5 values for each sensor and rank these sensors by their corresponding R2-scores in ascending order. We claim a sensor has malfunctioned if the R2-score is low (i.e., the predicted and the monitored PM2.5 values are very different). Experimental results show that our model identifies more problematic sensors with fewer trials. Consequently, examining the sensors with the order outputted by our model can save labor and time costs.

[1] Z. Wu, S. Pan, G. Long, J. Jiang, and C. Zhang, “Graph wavenet for deep spatialtemporal graph modeling,” arXiv preprint arXiv:1906.00121, 2019.
[2] B. Yu, H. Yin, and Z. Zhu, “Spatio-temporal graph convolutional networks: A deep
learning framework for traffic forecasting,” arXiv preprint arXiv:1709.04875, 2017.
[3] 行 政 院 交 通 環 境 資 源 處, “空 污 感 測 物 聯 網 應 用 於 環 保 稽 查 推 動
成果.” https://www.ey.gov.tw/Page/448DE008087A1971/4d1b964c-9294-4505-
8814-6d14d57ae05d.
[4] 行政院環保署, “空氣品質感測器架構圖.” https://img.ltn.com.tw/Upload/
news/600/2017/07/03/118.jpg.
[5] S. Glantz and B. Slinker, Primer of Applied Regression & Analysis of Variance, ed.
McGraw-Hill, Inc., New York, 2001.
[6] L.-J. Chen, Y.-H. Ho, H.-H. Hsieh, S.-T. Huang, H.-C. Lee, and S. Mahajan, “Adf:
An anomaly detection framework for large-scale pm2. 5 sensing systems,” IEEE
Internet of Things Journal, vol. 5, no. 2, pp. 559–570, 2017.
[7] Z. Qi, T. Wang, G. Song, W. Hu, X. Li, and Z. Zhang, “Deep air learning: Interpolation, prediction, and feature analysis of fine-grained air quality,” IEEE Transactions
on Knowledge and Data Engineering, vol. 30, no. 12, pp. 2285–2297, 2018.
[8] S. Hochreiter and J. Schmidhuber, “Long short-term memory,” Neural computation,
vol. 9, no. 8, pp. 1735–1780, 1997.
[9] Y.-S. Chang, H.-T. Chiao, S. Abimannan, Y.-P. Huang, Y.-T. Tsai, and K.-M. Lin,
“An lstm-based aggregated model for air pollution forecasting,” Atmospheric Pollution Research, vol. 11, no. 8, pp. 1451–1463, 2020.
[10] Y. Li, R. Yu, C. Shahabi, and Y. Liu, “Diffusion convolutional recurrent neural
network: Data-driven traffic forecasting,” arXiv preprint arXiv:1707.01926, 2017.
[11] J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated
recurrent neural networks on sequence modeling,” arXiv preprint arXiv:1412.3555,
2014.
[12] A. v. d. Oord, S. Dieleman, H. Zen, K. Simonyan, O. Vinyals, A. Graves, N. Kalchbrenner, A. Senior, and K. Kavukcuoglu, “Wavenet: A generative model for raw
audio,” arXiv preprint arXiv:1609.03499, 2016.
[13] F. Yu and V. Koltun, “Multi-scale context aggregation by dilated convolutions,”
arXiv preprint arXiv:1511.07122, 2015.
[14] M. Deza and E. Deza, “Encyclopedia of distances,” 2014.
[15] D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega, and P. Vandergheynst, “The
emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains,” IEEE Signal Processing Magazine,
vol. 30, no. 3, pp. 83–98, 2013.
[16] W. N. Anderson Jr and T. D. Morley, “Eigenvalues of the laplacian of a graph,”
Linear and multilinear algebra, vol. 18, no. 2, pp. 141–145, 1985.
[17] M. Defferrard, X. Bresson, and P. Vandergheynst, “Convolutional neural networks
on graphs with fast localized spectral filtering,” arXiv preprint arXiv:1606.09375,
2016.
[18] A. Micheli, “Neural network for graphs: A contextual constructive approach,” IEEE
Transactions on Neural Networks, vol. 20, no. 3, pp. 498–511, 2009.
[19] J. Atwood and D. Towsley, “Diffusion-convolutional neural networks,” in Advances
in neural information processing systems, pp. 1993–2001, 2016.
[20] Y. N. Dauphin, A. Fan, M. Auli, and D. Grangier, “Language modeling with gated
convolutional networks,” in International conference on machine learning, pp. 933–
941, PMLR, 2017.
[21] 行政院環境保護署, “認識空污感測物聯網.” https://airtw.epa.gov.tw/CHT/
Encyclopedia/AirSensor/AirSensor_2.aspx.
[22] J. A. Hanley and B. J. McNeil, “A method of comparing the areas under receiver
operating characteristic curves derived from the same cases.,” Radiology, vol. 148,
no. 3, pp. 839–843, 1983.
[23] K. H. Zou, A. J. O’Malley, and L. Mauri, “Receiver-operating characteristic analysis
for evaluating diagnostic tests and predictive models,” Circulation, vol. 115, no. 5,
pp. 654–657, 2007.
[24] T. K. Ho, “The random subspace method for constructing decision forests,” IEEE
transactions on pattern analysis and machine intelligence, vol. 20, no. 8, pp. 832–844,
1998.
[25] T. Ho, “A data complexity analysis of comparative advantages of decision forest
constructors,” Pattern Anal. Appl., vol. 5, pp. 102–112, 06 2002.
[26] R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the
Royal Statistical Society: Series B (Methodological), vol. 58, no. 1, pp. 267–288,
1996.
[27] L. Breiman, “Better subset regression using the nonnegative garrote,” Technometrics,
vol. 37, pp. 373–384, 1995.
[28] D. E. Hilt and D. W. Seegrist, Ridge, a computer program for calculating ridge regression estimates, vol. 236. Department of Agriculture, Forest Service, Northeastern
Forest Experiment …, 1977.
[29] M. H. Gruber, Improving efficiency by shrinkage: the James-Stein and ridge regression estimators. Routledge, 2017.
[30] A. E. Hoerl and R. W. Kennard, “Ridge regression: Biased estimation for nonorthogonal problems,” Technometrics, vol. 12, no. 1, pp. 55–67, 1970.
[31] Y. Chauvin and D. E. Rumelhart, Backpropagation: theory, architectures, and applications. Psychology press, 1995.
[32] D. E. Rumelhart, G. E. Hinton, and R. J. Williams, “Learning representations by
back-propagating errors,” nature, vol. 323, no. 6088, pp. 533–536, 1986.
[33] S. Bai, J. Z. Kolter, and V. Koltun, “An empirical evaluation of generic convolutional
and recurrent networks for sequence modeling,” arXiv preprint arXiv:1803.01271,2018.