Transportation data imputation (transdim).
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[Spatio-temporal forecasting] [Principal component analysis] [Guassian process] [Matrix factorization] [Bayesian matrix and tensor factorization] [Low-rank tensor completion] [Generative Adversarial Nets] [Variational Autoencoder] [Tensor regression] [Poisson matrix factorization] [Graph signal processing] [Graph neural network] [Missing data imputation]
Creating accurate and efficient solutions for the spatio-temporal traffic data imputation and prediction tasks.
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- Random missing: Each sensor lost their observations at completely random. (★★★)
- Non-random missing: Each sensor lost their observations during several days. (★★★★)
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- Forecasting without missing values. (★★★)
- Forecasting with incomplete observations. (★★★★★)
- add a framework indicating overall studies;
Framework: Tensor completion task and its framework including data organization and tensor completion, in which traffic measurements are partially observed.
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define the problems clearly;
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Example: Traffic forecasting using matrix factorization models.
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Real experiment setting: Observations with 0%, 20% and 40% fiber missing rates during first 56 days are treated as stationary inputs. Meanwhile, there are some rolling inputs for forecasting traffic speed during last 5 days (from Monday to Friday) in a rolling manner.
- describe the core challenges intuitively;
- list main contributions of these studies.
- Best algebraic structure for data imputation.
- The context of urban transportation (e.g., biases).
- Data noise avoidance.
- Competitive imputation and prediction performance.
- Capable of various missing data scenarios.
With the development and application of intelligent transportation systems, large quantities of urban traffic data are collected on a continuous basis from various sources, such as loop detectors, cameras, and floating vehicles. These data sets capture the underlying states and dynamics of transportation networks and the whole system and become beneficial to many traffic operation and management applications, including routing, signal control, travel time prediction, and so on. However, the missing data problem is inevitable when collecting traffic data from intelligent transportation systems.
Publicly available at our Zenodo repository!
(a) Time series of actual and estimated speed within two weeks from August 1 to 14.
(b) Time series of actual and estimated speed within two weeks from September 12 to 25.
The imputation performance of BGCP (CP rank r=15 and missing rate α=30%) under the fiber missing scenario with third-order tensor representation, where the estimated result of road segment #1 is selected as an example. In the both two panels, red rectangles represent fiber missing (i.e., speed observations are lost in a whole day).
- Missing data imputation
Urban traffic speed data set (i.e., Guangzhou-data-set(Gdata)) registered traffic speed data from 214 road segments over two months (61 days from August 1 to September 30 in 2016) in Guangzhou, China. We organize the raw data into a time series matrix of (214, 8784). For tensor-based models, we use a third-order tensor (214, 61, 144) as input. Matrix based models are tested with the time series matrix (214, 8784).
We consider two common missing data scenarios (i.e., random missing (RM) and non-random missing (NM)). For RM, we simply remove certain amount of observed entries in the matrix randomly and use these entries as ground truth to evaluate RMSE. For NM, we apply correlated fiber missing experiment by randomly choosing certain amount (e.g., 40%) (location, day) combinations and removing the whole time series in each combination.
| Missingness | BGCP | BPMF | PMF | GAIN |
|---|---|---|---|---|
| 20%, RM | 3.5762 | 4.0403 | 4.0909 | 4.6718 |
| 40%, RM | 3.5969 | 4.1578 | 4.2280 | 5.1776 |
| 20%, NM | 4.4136 | 4.3828 | 4.3575 | 6.5500 |
| 40%, NM | 4.6791 | 4.5586 | 4.4866 | 6.9947 |
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BGCP: Bayesian Gaussian CP decomposition (by Chen et al., 2019). [Imputation example - Jupyter Notebook] [Matlab code is also available!]
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BPMF: Bayesian probabilistic matrix factorization (by Salakhutdinov et al., 2008).
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PMF: Probabilistic matrix factorization (by Salakhutdinov et al., 2007).
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GAIN: Generative Adversarial Imputation Nets (by Yoon et al., 2018).
- The code has been adapted for our implementation.
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TRMF: Temporal regularized matrix factorization. [Matlab code is also available!]
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HaLRTC: High accuracy low rank tensor completion.
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Please consider citing our papers if they help your research.
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贝叶斯泊松分解变分推断笔记, by Yixian Chen (陈一贤).
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变分贝叶斯推断笔记, by Yixian Chen (陈一贤).
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贝叶斯高斯张量分解, by Xinyu Chen (陈新宇).
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贝叶斯矩阵分解, by Xinyu Chen (陈新宇).
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时序矩阵分解 | 时序数据修补与预测, by Jamie Yang (杨津铭).
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如何用贝叶斯概率矩阵分解修复缺失数据？(Jupyter notebook - Python), by Xinyu Chen (陈新宇).
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如何用贝叶斯高斯张量分解修复缺失数据？(Jupyter notebook - Python), by Xinyu Chen (陈新宇).
This work is released under the MIT license.