Vehicle trajectory modelling with consideration of distant neighbouring dependencies for destination prediction

Figures & data

Figure 1. Workflow of the DND model.

Figure 2. Dependencies strength between neighbouring nodes. If someone needs to go from A to X, he must first go through B or C. From the perspective of graph theory, the cost from A to X is 2 degrees and the cost from B to X is 1 degree. It reflects that the dependencies strength between B and X is stronger than A and X.

Figure 3. Distant dependencies influence the destination distribution.

Figure 4. Framework of the DND model.

Figure 5. An example of destination prediction under six different completion scenarios of a full trajectory. Control points with a probability greater than 0.5% are labelled. As the completion increase, the predicted destination of the prefixes is gradually approaching the real destination. (a) Trajectory completion: 0%. (b) Trajectory completion: 8%. (c) Trajectory completion: 43%. (d) Trajectory completion: 68%. (e) Trajectory completion: 82%. (f) Trajectory completion: 98%.

Table 1. Models for performance comparison.

Abbreviation	Source	Year	Data	Description
TCONV-LE	Lv et al.	2018	points to images	A convolutional neural network based model, which converts data into images to keep the spatial relationship between trajectory data. It is currently one of the best performing models on the ECML-PKDD dataset.
DPNLP	Fan et al.	2018	points to embeddings	A deep learning based model combines convolutional neural network and recurrent neural network. It extracts spatial features by obtaining the relationship between locations in traffic network.
LSTM-TNP	-	-	points of trajectory nodes	An LSTM neural network reads trajectory nodes one by one. It uses longitude and latitude as the inputting features for each trajectory node.
MLP	de Brébisson et al.	2015	points	A multi-layer perceptron model won the ECML/PKDD challenge. It only uses the latitudes and longitudes of the first and last 5 points in the trajectory.
RNN	de Brébisson et al.	2015	points	A recurrent neural network, reads GPS points one by one and updates a fixed-length internal state with the same transition matrix at each time step.
Bi-RNN	de Brébisson et al.	2015	points	A bidirectional recurrent neural network, which regards a trajectory as a sequence of GPS points. This model uses a sliding window of 5 successive GPS points as a transition state of RNN.

Table 2. Performance comparison, both the units of $ME$ and $EV$ are kilometres.

Metrics	DND	TCONV-LE	DPNLP	LSTM-TNP	MLP	RNN	Bi-RNN	DT
$ME$	1.08	1.25	1.20	1.38	1.38	1.54	1.48	1.99
$EV$	1.77	1.87	1.83	2.09	2.29	2.31	2.46	4.25
$AC{C}_1$	64.12%	58.07%	60.02%	52.94%	55.02%	47.35%	52.07%	40.07%
$AC{C}_2$	85.31%	84.74%	83.58%	79.97%	79.05%	75.17%	76.88%	64.51%
$AC{C}_3$	93.43%	91.86%	92.27%	90.73%	89.53%	87.28%	88.13%	78.39%

Figure 6. Error bar of final destination prediction according to trajectory completion.

Figure 7. Error bar of final destination prediction according to trajectory length.

Figure 8. Scatter plot of mean Euclidean distance vs TNV similarity rank.

Figure 9. Scatter plot of mean degrees vs TNV similarity rank.

Figure 10. Geographic distribution of TSV clusters in Porto.

Figure 11. Start point distribution, destination distribution and road selection patterns of different TSV clustering results.

Lv, J., et al., 2018. T-CONV: a convolutional neural network for multi-scale taxi trajectory prediction. In: 2018 IEEE international conference on big data and smart computing (bigcomp), 15-18 January 2018 Shanghai. 82–89.

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Fan, X., et al., 2018. A deep learning approach for next location prediction. In: 2018 IEEE 22nd international conference on Computer Supported Cooperative Work in Design ((CSCWD)), 9-11 May 2018 Nanjing. IEEE, 69–74.

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de Brébisson, A., et al., 2015. Artificial neural networks applied to taxi destination prediction. arXiv Preprint arXiv. 1508.00021.

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