Source-linked AI summary
PCNN: Deep Convolutional Networks for Short-term Traffic Congestion Prediction
Meng Chen, Xiaohui Yu, Yang Liu
TL;DR
Short-term traffic congestion prediction must account for repeated temporal patterns and multiscale variation while producing congestion levels useful to road users. PCNN folds periodic time series into a two-dimensional matrix and applies convolutions to learn local and multiscale patterns. Experiments on real urban traffic data show that PCNN outperforms the evaluated baselines.
Problem
Existing traffic forecasting often targets flow or travel time, while this paper addresses directly forecasting short-term congestion levels for urban road segments.
Method
PCNN folds periodic congestion time series into a two-dimensional input matrix and applies convolutional operations to model local temporal dependencies and multiscale traffic patterns.
Results
21.1%: PCNN's MRE rate drops compared with LSTM using one-dimensional input for overall prediction.
Takeaways & Limitations
Folding periodic traffic data into two-dimensional inputs is effective, and PCNN provides a decision-support tool for traffic operators' alternative traffic-management strategies.
Abstract
from arXiv · showhide
Traffic problems have seriously affected people's life quality and urban development, and forecasting the short-term traffic congestion is of great importance to both individuals and governments. However, understanding and modeling the traffic conditions can be extremely difficult, and our observations from real traffic data reveal that (1) similar traffic congestion patterns exist in the neighboring time slots and on consecutive workdays; (2) the levels of traffic congestion have clear multiscale properties. To capture these characteristics, we propose a novel method named PCNN based on deep Convolutional Neural Network, modeling Periodic traffic data for short-term traffic congestion prediction. PCNN has two pivotal procedures: time series folding and multi-grained learning. It first temporally folds the time series and constructs a two-dimensional matrix as the network input, such that both the real-time traffic conditions and past traffic patterns are well considered; then with a series of convolutions over the input matrix, it is able to model the local temporal dependency and multiscale traffic patterns. In particular, the global trend of congestion can be addressed at the macroscale; whereas more details and variations of the congestion can be captured at the microscale. Experimental results on a real-world urban traffic dataset confirm that folding time series data into a two-dimensional matrix is effective and PCNN outperforms the baselines significantly for the task of short-term congestion prediction.
I. INTRODUCTION
Traffic congestion prediction targets short-term congestion levels because these are directly meaningful to road users, yet traffic exhibits local coherence, periodicity, and multiscale variation. PCNN folds periodic time series into a two-dimensional matrix and applies convolutions to learn temporal and multigrained patterns, outperforming the evaluated baselines.
- Motivation: Short-term congestion levels are forecast directly because road users often need to know how jammed a road segment will be soon.Congestion level is defined from average travel time relative to ideal-condition baseline travel time.
- Challenges: Traffic congestion varies with neighboring time slots, repeats across consecutive workdays, and combines local fluctuations with global trends.These properties make both immediate and periodic historical conditions relevant to prediction.
- PCNN approach: PCNN folds periodic congestion data into a two-dimensional matrix containing recent conditions and analogous historical patterns.The input uses a 24-hour period and combines values around the current slot from previous days with immediately preceding values.
- PCNN approach: Convolutions over the folded matrix model local temporal dependencies and multi-grained features for future congestion prediction.The learned features are passed to an output layer, and the objective is optimized with SGD.
- Experiments: On real vehicle passage records from Jinan, PCNN produces smaller forecast errors than regressive, pattern-recognition, and neural-network baselines.Applying two-dimensional inputs also improves the evaluated methods over their original one-dimensional inputs.
II. RELATED WORK
Short-term traffic forecasting research includes regressive models, pattern-recognition methods, and neural networks. Existing approaches model temporal dependence, nonstationarity, or time-varying traffic characteristics in different ways.
- Overview: Traffic congestion prediction extends short-term traffic forecasting, a pivotal intelligent transportation systems application.The related work is organized into regressive models, pattern-recognition methods, and neural networks.
- Regressive models: ARIMA models and variants are commonly used because traffic data tend to be closely related to previous values.They perform reasonably under normal conditions but less satisfactorily when external changes occur.
- Pattern recognition methods: Pattern-recognition methods include SVM and K-nearest neighbors for short-term traffic forecasting.Prior work uses wavelet-chaos analysis with SVM and addresses nonstationary or time-varying traffic characteristics.
C. Neural networks
The paper situates PCNN within neural-network traffic forecasting and introduces it to model periodicity, local coherence, and multiscale temporal features. PCNN combines time-series folding with convolution-based multi-grained learning for short-term congestion prediction.
- Motivation: PCNN targets short-term traffic congestion prediction, a problem previous work less often addressed directly than traffic flow or travel time forecasting.
- Problem definition: The paper defines congestion level from segment travel time relative to a baseline and predicts the next time slot's congestion level from observed history.
- Architecture: A convolutional stack learns local temporal dependencies and multi-grained features from the folded matrix.The paper motivates convolutions as suitable for local structural information and multiscale features.
- Architecture: PCNN is trained as a deep convolutional network whose architecture contains convolutional and fully connected components.
- Architecture: The method uses time-series folding to convert historical congestion data into an image-like two-dimensional input matrix.The architecture includes time-series folding as one of its two major components.
B. Time series folding
Time-series folding arranges recent observations and preceding-day histories into a two-dimensional matrix, after which stacked convolutions model dependencies at multiple temporal ranges.
- Time series folding: The folding design uses preceding d days because the data show local coherence and periodicity but no stronger similarity for the same weekday across previous weeks.
- Multi-grained learning: Multiple convolutional layers extend the modeled temporal range because a single kernel captures only near dependencies.
- Multi-grained learning: Each of the first L−1 layers uses 64 filter maps with 2×2 kernels and stride 1, sharing weights across locations.
- Multi-grained learning: The convolutions extract neighboring-day and neighboring-slot dependencies, then transmit multi-grained features to the output layer for congestion prediction.
D. Loss function
PCNN trains by minimizing regularized squared prediction error, with the formulation supporting both one-step and multi-step congestion forecasts.
- Loss function: The objective function uses squared error between predicted and observed congestion levels.
- Loss function: The loss formulation includes the full parameter set Θ and a regularization coefficient λ.
- Loss function: For u-step-ahead prediction, PCNN uses preceding-day values around the target slot together with recent observations before producing the forecast.
E. Algorithm and optimization
The training procedure constructs folded instances from historical congestion data and optimizes PCNN with mini-batch backpropagation. Experiments use workday vehicle-passage records from Jinan and examine data characteristics and input-size effects.
- Algorithm and optimization: Training instances pair each folded input matrix X_m,n with its target congestion level c_m,n.
- Algorithm and optimization: PCNN updates parameters on randomly selected mini-batches by minimizing the objective until stopping criteria are met.
- Experimental setting: The dataset contains six weeks of vehicle-passage records from 614 road segments in Jinan, China.
- Experimental setting: Experiments retain 30 workdays and records from 6:00 to 24:00, using five-minute time slots initially.
- Dataset characteristics: Congested traffic occurs in about 36% of time slots and concentrates around morning and evening peaks.
2) Hyperparameters:
PCNN is evaluated with MAE, RMSE, and MRE, using predicted and observed congestion levels over test days and time slots.
- PCNN is evaluated using mean absolute error (MAE), root-mean-square error (RMSE), and mean relative error (MRE).
- The metrics compare predicted congestion levels with observed values across test days and daily time slots.
B. Performance of PCNN
PCNN performs best with a 10×12 input matrix formed using six neighboring time slots and nine preceding days, while five convolutional layers balance accuracy and training cost.
- Identifying a suitable size of the input matrix: t = 6 performs best, indicating that using traffic conditions within half an hour around the current slot is suitable in this case.
- Identifying a suitable size of the input matrix: d = 9 obtains the best performance, and the default configuration uses t = 6, d = 9, and 10 training epochs.
- Identifying a suitable size of the input matrix: The resulting default input matrix has size 10×12.
- Identifying the number of convolutional layers: Five convolutional layers are selected because shallow networks capture insufficient multigrained features, whereas very deep networks produce larger errors and require more training time.
3) Accuracy of forecast by different traffic conditions and time of day:
Forecast errors vary with traffic conditions and time of day, with peak-hour complexity producing larger errors and a small fraction of extreme relative errors.
- MAE and RMSE improve consistently as traffic changes from normal to congested, while MRE shows a consistent reduction in percentage deviation.
- Mean errors can exceed or approximately equal the third quartile, indicating the presence of a few extremely large forecast errors.
- The mean MRE is around 20%, supporting the authors’ characterization of PCNN forecasts as reliable and accurate.
C. Comparisons with state-of-the-art methods
PCNN is compared with conventional, pattern-recognition, and neural-network baselines using one- and two-dimensional inputs. Folding periodic data into matrices improves several baselines, and PCNN achieves the strongest reported comparisons across conditions and time granularities.
- Baseline comparisons: The comparison includes HA, LR, ARIMA, SARIMA, K-NN, MLP, and LSTM baselines for short-term congestion prediction.
- Input representation: Two-dimensional inputs reduce MRE by 2.8% for LR and 5.4% for MLP compared with their one-dimensional versions.
- Overall comparison: PCNN reduces MRE by 21.1% relative to LSTM with one-dimensional input and by 15.2% relative to MLP(2).
- Overall comparison: The reported explanation is that the matrix combines current and historically similar conditions, while convolutions capture local temporal dependencies and multiscale features.
- Time granularity: Prediction errors decline as time slots increase from 10 to 60 minutes, and PCNN outperforms MLP and LSTM across these granularities.
VI. CONCLUSION
PCNN folds traffic time series into a two-dimensional matrix and uses multiple convolutions to model local temporal dependencies and multiscale traffic patterns. On a real traffic dataset, it significantly outperforms state-of-the-art baselines.
- PCNN folds time series data into a two-dimensional matrix for short-term traffic congestion prediction.This representation is designed for urban traffic congestion data.
- Multiple convolutional operations model local temporal dependency and multiscale traffic patterns.The approach uses a convolution-based deep neural network as its predictive model.
- PCNN significantly outperforms state-of-the-art baselines on a real traffic dataset.The evaluation uses real traffic data and compares PCNN with existing forecasting methods.