Multivariate and Propagation Graph Attention Network forSpatial-Temporal Prediction with Outdoor Cellular Traffic

Chung-Yi Lin1,2, Hung-Ting Su1, Shen-Lung Tung2, Winston H. Hsu11National Taiwan University, 2Chunghwa Telecom Laboratories

ABSTRACTSpatial-temporal prediction is a critical problem for intelligent trans-portation, which is helpful for tasks such as traffic control and ac-cident prevention. Previous studies rely on large-scale traffic datacollected from sensors. However, it is unlikely to deploy sensorsin all regions due to the device and maintenance costs. This paperaddresses the problem via outdoor cellular traffic distilled fromover two billion records per day in a telecom company, becauseoutdoor cellular traffic induced by user mobility is highly relatedto transportation traffic. We study road intersections in urban andaim to predict future outdoor cellular traffic of all intersectionsgiven historic outdoor cellular traffic. Furthermore, We proposea new model for multivariate spatial-temporal prediction, mainlyconsisting of two extending graph attention networks (GAT). FirstGAT is used to explore correlations among multivariate cellulartraffic. Another GAT leverages the attention mechanism into graphpropagation to increase the efficiency of capturing spatial depen-dency. Experiments show that the proposed model significantlyoutperforms the state-of-the-art methods on our dataset.

CCS CONCEPTS• Information systems→ Data mining.

KEYWORDSmultivariate spatial-temporal prediction, graph attention network,outdoor cellular trafficACM Reference Format:Chung-Yi Lin1,2, Hung-Ting Su1, Shen-Lung Tung2, Winston H. Hsu1.2021. Multivariate and Propagation Graph Attention Network for Spatial-Temporal Prediction with Outdoor Cellular Traffic. In Proceedings of the 30thACM International Conference on Information and Knowledge Management(CIKM ’21), November 1–5, 2021, Virtual Event, QLD, Australia. ACM, NewYork, NY, USA, 5 pages. https://doi.org/10.1145/3459637.3482152

1 INTRODUCTIONRecently, spatial-temporal prediction becomes one of the funda-mental techniques in building intelligent transportation. Based onlarge-scale data (e.g., traffic speed, volume) collected from sensors,previous studies [7, 16] achieve successful performance. However,it is unlikely to deploy sensors in all regions (e.g., road intersections,

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rural areas) due to the device and maintenance costs, which givesrise to the task of data collection for spatial-temporal prediction.

We seek an alternative approach to evaluate the traffic statewithout sensors. With billions of mobile devices entering the in-ternet, massive records of cellular traffic [1] are collected at celltowers. Many studies have been made for its application, such ascellular vehicle probes for traffic state estimation [3, 9], and cellulartraffic prediction modeling [1, 11, 12]. Nevertheless, existing stud-ies rarely consider transportation traffic induced by user mobility.According to the analyses from over billions of records, outdoorcellular traffic is found to be induced by user mobility. Therefore,we leverage outdoor cellular traffic representing the traffic state forspatial-temporal forecasting.

In this paper, we propose a new spatial-temporal dataset1 viaoutdoor cellular traffic distilled from over a billion records per dayin a telecom company, which is extremely valuable for surveillingtraffic states in regions without sensors. For instance, accumulatedoutdoor cellular traffic in a unit time step exceeds the threshold,the region might occur certain events (e.g., traffic congestion orparade). We study the road intersections of a major city forming aroad network and collect corresponding outdoor cellular traffic intime steps. This paper aims to predict the future outdoor cellulartraffic of all intersections given historic outdoor cellular traffic as anew spatial-temporal task.

Spatial-temporal prediction with a road network has been widelystudied. Recent researches [7, 8, 13, 14] have achieved great suc-cess in prediction by conducting propagating information on thegraph data within graph neural networks (GNN). However, thedataset of previous studies is the traffic speed detected from sen-sors, which is usually less varied between time steps. While in ourdataset, the quantity of outdoor cellular traffic can drastically vari-ous in different times, especially the peak (e.g., 18:00) is 200 timesgreater than the least active times (e.g., 03:00) in the same road in-tersection, such significant difference is more challenging than thatprior dataset. Therefore, We argue that expanding the uni-historicdata into multivariate consisting of various temporal-periodic datais critical to capturing more hidden correlations in the complextemporal pattern, which has not been explored in previous meth-ods. As more complicated temporal features fed into the predictivemodel, we notice that the propagation process of GNN does notconsider the dynamic attention between nodes during updatingnode information, which might reduce the capacity of modeling.

To address the challenges, we propose a new framework forspatial-temporal prediction, namely MPGAT (Multivariate andPropagation Graph Attention Network), mainly consisting of twoextending graph attention networks (GAT) [10] modules. (1) Multi-variate GAT (M-GAT) explores the correlations amongmultivariateinput, which can be effectively adapted to multivariate time series.

1the dataset is accessible on Github: https://github.com/cylin-cmlab/CIKM21-MPGAT

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(2) Propagation GAT (P-GAT) incorporates the propagation strat-egy into GAT to captures the spatial dependency between regions,benefited from the attention mechanism and spatial closeness ofthe graph. We evaluate the proposed framework on our dataset.Experimental results with statistic analysis show that MPGAT out-performs significantly several state-of-the-art models.

2 DATASET DESCRIPTIONDataCollection: The data was collected from a large-scale cellular-geographic system in a telecom company, which receives over twobillion records from mobile devices in one day. Each record con-tains International Mobile Station Equipment Identification (IMEI,a unique number of a mobile phone), International Mobile Sub-scriber Identity (IMSI, a unique number of a subscriber), the cre-ation time, the GPS location, and the location type (categorized bythe telecom company, e.g., outdoor and indoor). As privacy consid-erations, we use IMEI to represent each mobile subscriber due toIMSI being able to identify the mobile subscriber particularly, andIMEI is anonymized by hashing.Spatial-temporal Dataset: To explicitly discover the spatial de-pendency, we study six road intersections (e.g., around the trainstation and college) as a road network, as shown in Figure 1. Then,we individually aggregated the quantity of outdoor IMEI located atintersections in the unit time step (i.e., 5-minutes) as age spatial-temporal dataset. Specifically, the aggregated IMEI quantity overtime steps demonstrates strong temporal correlations, and geo-graphically connected intersections contain spatial dependence.

Figure 1: The dataset of outdoor cellular traffic is collectedaround the six road intersections(left fig.), and the IMEIquantities for every time step are shown in the right fig.

3 PRELIMINARIESIntersection Network: Each road intersection is geographicallyconnected to adjacent neighbors, creating an intersection network.Thus, we define the network as a directed graph 𝐺𝑖𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛 =(𝑉 ,𝐸), where𝑉 is a set of 𝑁 intersections of the network, 𝐸 is the setof edges representing the connectivity between the intersections.Multivariate Input: According to our dataset, IMEI quantity hasa drastic change in different time steps, therefore we expand IMEIquantity of unit time step as different temporal-periodic series to

capture more temporal patterns, forming a multivariate input:(1)The IMEI quantity adjacent to predictions:

𝑋𝑞 = {𝑥𝑞,𝑡0−𝑇𝑖𝑛+1, ..., 𝑥𝑞,𝑡0 }∈𝑅𝑁×𝑇𝑖𝑛 denotes historical IMEI quan-tity with 𝑇𝑖𝑛 time steps adjacent to the predictions, revealing theshort-term factor, where 𝑥𝑞,𝑡0 is the IMEI quantity of 𝑁 intersec-tions at time step 𝑡0.(2)The moving average of IMEI quantity adjacent to predictions:

𝑋𝑚𝑎𝑇𝑚= {𝑥𝑚𝑎𝑇𝑚 ,𝑡0−𝑇𝑖𝑛+1, ..., 𝑥𝑚𝑎𝑇𝑚 ,𝑡0 }∈𝑅𝑁×𝑇𝑖𝑛 is a set of mov-

ing average (MA) of IMEI quantity over 𝑇𝑖𝑛 time steps, where eachvalue of 𝑋𝑚𝑎𝑇𝑚

is calculated by accumulating the IMEI quantityover 𝑇𝑚 time steps and then dividing the sum by 𝑇𝑚 . Moving aver-age is commonly used with time-series data to smooth out short-term fluctuations and highlight longer-term trends [15]. The fea-tures of 𝑋𝑚𝑎5 and 𝑋𝑚𝑎20 are adopted in this paper.(3)The daily intervals adjacent to prediction: [2]

Suppose the sampling frequency is p time steps per day, 𝑋𝑑 =

{𝑥𝑑,𝑡0−𝑇𝑖𝑛×𝑝 , 𝑥𝑑,𝑡0−𝑇𝑖𝑛−1×𝑝 , ..., 𝑥𝑑,𝑡0 }∈𝑅𝑁×𝑇𝑖𝑛 denotes a set of daily-interval data, consisting of IMEI quantity at 𝑡0 time step in differentdays closed to predictions. For example, there are 𝑝(=288) time stepsin one day by 5-minute time step. We consider the daily-intervalquantity as one of the features to capture the sequence regularpattern.Problem: Given 𝑋 = {𝑋1, ..., 𝑋𝐹 }∈𝑅𝐹×𝑁×𝑇𝑖𝑛 to denote the mul-tivariate input of all the intersections over observed time steps,predict future IMEI quantity set 𝑌 = {𝑌 1, ..., 𝑌𝑁 }∈𝑅𝑁×𝑇𝑜𝑢𝑡 overthe coming time steps, where 𝐹 is the number of features in mul-tivariate input, 𝑁 is the number of intersections in 𝐺𝑖𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛 ,𝑇𝑖𝑛 and 𝑇𝑜𝑢𝑡 is the length of time steps, and 𝑌𝑘 is the future IMEIquantity of intersection 𝑘 .

4 METHODOLOGYFigure 2 illustrates the framework of our proposed Multivariate andPropagation Graph Attention Network (MPGAT). The multivari-ate input 𝑋 , such as 𝑋 = {𝑋𝑞, 𝑋𝑚𝑎5 , 𝑋𝑚𝑎20 , 𝑋𝑑 }, is fed to M-GATto capture correlations between multivariate input 𝑋 . Then, thedistilled outputs from M-GAT are forwarded to the connected TCNlayer. For capturing the spatial-temporal dependency, TCN is in-terleaved with P-GAT as a spatial-temporal block, where P-GAT isto model the spatial dependency between intersections. By stack-ing multiple spatial-temporal blocks, the capacity of modeling thespatial-temporal dependencies increases [14]. To avoid gradientvanishing, Residual Layers [4] is appended from the top of each in-terleaved layer to its end, and the Skipped Layers are concatenatedafter each TCN to an output layer.

4.1 Multivariate Graph Attention (M-GAT)As we aforementioned, the IMEI quantity series has been expandedinto multivariate input. Due to the strong feature-extraction ca-pability of GAT, M-GAT contains multiple GAT layers to capturethe associations between multivariate input. Inspired by [5], M-GAT treats each component of multivariate input as one node in acomplete graph and contains two stacked GAT layers.

We consider a single layer of M-GAT as an example. For intersec-tion 𝑘 , the set of multivariate input𝑋𝑘 = {𝑋 𝑘

1 , ..., 𝑋 𝑘𝐹

} ∈ 𝑅𝐹×𝑇𝑖𝑛 isfirst projected as a set of latent representations𝑌𝑘 = {𝐻 𝑘

1 , ..., 𝐻 𝑘𝐹

}

Figure 2: The framework ofMPGAT, whereM-GAT explorescorrelations amongmultivariate input, and P-GAT capturesspatial dependency with multiple directions separately.

∈ 𝑅𝐹×𝑇𝑖𝑛×𝐷′by a convolution layer before M-GAT, where𝑇𝑖𝑛 is the

length of historical time steps, and 𝐷′is the dimension of latent

representation. Afterward, 𝑌𝑘 is fed to M-GAT, forming a completegraph with 𝐹 nodes. The attention score between nodes representsthe importance from node 𝑗 to node 𝑖 , where 𝑖 , 𝑗 ∈ {1, 2, . . . , 𝐹 }, andcan be computed as follows:

𝑎 𝑘𝑖 𝑗 =

𝑒𝑥𝑝 (𝐿𝑒𝑎𝑘𝑦𝑅𝑒𝐿𝑈 (𝑤𝑇𝑐 (𝐻 𝑘

𝑖∥ 𝐻 𝑘

𝑗)))∑𝐹

𝑗=1 𝑒𝑥𝑝 (𝐿𝑒𝑎𝑘𝑦𝑅𝑒𝐿𝑈 (𝑤𝑇𝑐 (𝐻 𝑘

𝑖∥ 𝐻 𝑘

𝑗)))

(1)

, where ∥ is the concatenation operation, 𝑤𝑇𝑐 ∈𝑅2𝐷

′is the weight

vector with transposition, and the attention score is normalized bya SoftMax function with LeakyReLU.

With the normalized attention scores, the output of one M-GATlayer for node 𝑖 is given by:

�̂� 𝑘𝑖 = 𝜎 (

𝐹∑︁𝑗=1

(𝑎 𝑘𝑖 𝑗 𝐻

𝑘𝑗 )) (2)

, where 𝜎 denotes a non-linear activation function. �̂� 𝑘𝑖

is the ag-gregated latent representation for feature 𝑖 of intersection 𝑘 , whichcontains the implicit influence from others. For 𝑁 intersections,the output set is presented as �̂� = {�̂�1, ..., �̂�𝐹 } ∈ 𝑅𝐹×𝑁×𝑇𝑖𝑛×𝐷

′. To

reduce the model complexity, we only distill the latent representa-tions of IMEI quantity outputted at the last layer of M-GAT, denotesas �̂�𝑞 ∈ 𝑅𝑁×𝑇𝑖𝑛×𝐷

′, and feeding �̂�𝑞 into the next layer of MPGAT.

4.2 Propagation Graph Attention (P-GAT)P-GAT consists of two directions Attention Propagation and oneGlobal learning to capture the spatial dependency between inter-sections. To our best knowledge, we are the first work to apply theattention mechanism on graph propagation.Attention Propagation: The advantage of the propagation pro-cess [13] is that it aggregated node information through the graph

Figure 3: Multivariate input 𝑋𝑘 of each intersection 𝑘 is pro-jected into latent representations 𝐻𝑘 , and M-GAT capturescorrelations among multivariate with graph attention.

structure recursively and preserves a proportion of nodes’ statesduring the process, eliminating the smoothing problem with dif-fusion method in [7]. With the benefit of propagating the statesthrough graph structure, we generalize the attention mechanisminto the propagation process, as shown in Figure 4. Considering𝑁 nodes with the set of initial representations 𝑉𝑖𝑛 = {𝑉1, . . . ,𝑉𝑁 }from the previous layer, the propagation and output is defined as:

𝑉 ` = (1 − 𝛽)𝑉𝑖𝑛 + 𝛽 (𝐴𝑚𝑎𝑠𝑘 𝑉`−1) (3)

𝑉 = Δ(∥𝑈`=0𝑉` ) (4)

, where 𝑉 0 = 𝑉𝑖𝑛 , 𝐴𝑚𝑎𝑠𝑘 is the masked attention matrix for uni-direction, ` represents the propagation steps, 𝛽 is a hyperparameterbetween 0 and 1 to control the ratio of node’s propagation, Δ is amultilayer perceptron layer (MLP) to transform the channel dimen-sion of concatenation results, and 𝑉 is the final output of 𝑁 nodes.In practice, we employ the CNN as MLP, and set𝑈 is 2.

In case of the directed graph 𝐺𝐼𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛 , P-GAT models twodirections, the forward and the backward propagations with ownmasked attentionmatrix. Consider each intersection of𝐺𝐼𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛

as one node, the attention score 𝑎𝑖 𝑗 in uni-direction𝐴𝑚𝑎𝑠𝑘 betweennodes 𝑖 and 𝑗 , where 𝑖 , 𝑗 ∈ {1, 2, . . . , 𝑁 }, is computed as:

𝑒𝑖 𝑗 = 𝑤𝑇𝑝 (𝑉𝑖 ∥ 𝑉𝑗 ) (5)

𝑎𝑖 𝑗 =𝑒𝑥𝑝 (𝐿𝑒𝑎𝑘𝑦𝑅𝑒𝐿𝑈 (𝑒𝑖 𝑗 ))∑𝑁𝑖

𝑗=1 𝑒𝑥𝑝 (𝐿𝑒𝑎𝑘𝑦𝑅𝑒𝐿𝑈 (𝑒𝑖 𝑗 ))(6)

, where 𝑉𝑖 is the latent representation of node 𝑖 from the previouslayer,𝑤𝑇

𝑝 ∈ 𝑅2𝐷′′is a weight vector with transposition, 𝐷

′′is the

dimension of 𝑉𝑖 , and 𝑁𝑖 denotes the adjacent neighbors of node 𝑖 .The attention coefficient 𝑒𝑖 𝑗 in Equation 5 is masked according tothe adjacency matrices in the corresponding direction, where 𝑒𝑖 𝑗is masked with a large negative value (e.g., -9e15) if node 𝑖 and 𝑗

are not adjacent; otherwise, the coefficient 𝑒𝑖 𝑗 would be preserved.In this way, the attention score 𝑎𝑖 𝑗 between adjacent nodes wouldincrease after SoftMax normalization, while the non-adjacent isset to zero. The matrix 𝐴𝑚𝑎𝑠𝑘 can be represented as [𝑎𝑖 𝑗 ], whichimplies the relationship between adjacent nodes but excludes thenon-adjacent.Global Learning: To discover hidden correlations among nodes,we employ another attention module to enhance the learning ca-pacity. Similar to M-GAT, Global Learning treats each intersection

Table 1: The average performance of MAPE comparison on outdoor cellular traffic dataset

Models Mean ±std. Dev. h1 Mean ±std. Dev. h Mean ±std. Dev. h Mean ±std. Dev. h

5min 15min 30min 60min

GWNET(’19)[14] 0.1576±0.0027 -1/1 0.1781±0.0034 0/1 0.1934±0.0028 0/1 0.2194±0.0037 0/1MTGNN(’20)[13] 0.1629±0.0032 1/1 0.1811±0.0027 1/1 0.1951±0.0031 0/1 0.2198±0.0033 0/1STAWNET(’21)[8] 0.1611±0.0026 1/1 0.1823±0.0037 1/1 0.1947±0.0029 0/1 0.2180±0.0026 -1/1MPGAT-1 0.1582±0.0024 0.1778±0.0019 0.1940±0.0025 0.2213±0.0029MPGAT 0.1511±0.0013 0.1720±0.0012 0.1876±0.0016 0.2149±0.0026

h1 means whether the result of MPGAT-1/MPGAT is significant according to Wilcoxon rank-sum test compared to the baseline method.

Figure 4: The function of attention propagation in P-GAT.

as a node and builds a complete graph to capture the hidden rela-tionships of spatial dependency. We use Equation 6 to construct anattention matrix, where 𝑒𝑖 𝑗 is not masked, 𝑁𝑖 denotes all the nodesof𝐺𝐼𝑛𝑡𝑒𝑟𝑠𝑒𝑐𝑡𝑖𝑜𝑛 . All nodes would learn globally the attention scoretoward others and updates the node information directly throughthe global attention.Output: P-GAT explores the bi-directional correlation with direc-tional modeling and captures the implicit associations adaptivelywith global modeling for spatial dependency learning. Finally, P-GAT fuses two propagation modeling and global modeling outputsas an input fed to the next layer.

5 EXPERIMENTSDataset: This paper verifies the proposed MPGAT and the com-pared models with the outdoor cellular traffic dataset, which con-tains the IMEI quantity in 5-minutes time steps of six road intersec-tions ranging from Jan.1, 2020, to Jun.30, 2020. The dataset is splitwith 70% for training, 10% for validation, and 20% for testing.Comparison Methods: Our dataset is a spatial-temporal datasetwith a road network, similar tasks such as traffic speed have gener-ally been addressed better by graph-based models [16]. Due to thepage limitation, we focus on the latest graph-based models as base-lines in our evaluation: GWENT [14], MTGNN [13], STAWNET [8].To verify the effectiveness of the correlation among multivariate,we build two models, MPGAT-1 and MPGAT, where MPGAT-1 isremoving M-GAT and use univariate IMEI quantity as input.Experimental Settings: Our experiments are conducted with aNVIDIA DGX-1. In practice, the length of historical input 𝑇𝑖𝑛 is12 for all models including ours and baselines. MPGAT uses eightspatial-temporal blocks to cover the input sequence, where eachblock has a TCN interleaved with a P-GAT. We adapt the Adamoptimizer with a learning rate of 0.001 to train our model. The eval-uation metrics we choose mean absolute percentage error (MAPE).

Main Results: We implement our model and compare it with thebaselines for 5 min,15 min, 30 min, and 60 min predictions on ourdataset. We run 30 testing times and report the average values, asshown in Table 1. To determine whether MPGAT-1 and the MPGAToutperform in statistical significance with the compared models,we conducted the Wilcoxon rank-sum test inspired by [6], where h= 1 is the proposed model significantly outperformed the comparedmodel, h = -1 is the compared model significantly outperformedthe proposed model, and h = 0 is not significantly different. Forexample, h = -1/1 means that MPGAT-1 is worse, but MPGAT isbetter than the compared model.

According to Table 1, as the prediction time increases, MAPEof the same method rises for all, showing that the longer the pre-diction time, the more challenging the prediction task. Second,with the statistical analysis, MPGAT significantly achieves the bestperformance in the dataset. Third, MPGAT-1 is slightly underper-formed than GWNET while outperforming others in the short-termprediction. It is more beneficial to practical applications on short-term factors, e.g., transportation agencies can immediately optimizetraffic congestion.

Figure 5 shows the changes in the prediction performance ofvarious methods as the prediction steps increase. We observe thatMPGAT consistently outperforms MPGAT-1 and baseline models,indicating it is critical to explore the correlation amongmultivariate,especially that our dataset has a drastic change between neighbor-ing time steps. Moreover, we notice that the MAPE value of thesame method conducted on our dataset is two times larger thanthe traffic speed dataset [7], which indicates that spatial-temporalprediction with cellular traffic data is more challenging. We are op-timistic that our proposed task and dataset would pave a new pathfor spatial-temporal prediction and urban computing applications.

6 CONCLUSIONIn this paper, we propose a new spatial-temporal dataset via out-door cellular traffic and a model MPGAT for multivariate spatial-temporal prediction. Experimental results show that the proposedMPGAT significantly outperforms other models on the dataset. Inthe future, we intend to expand the dataset more robust to cover theentering city and use transfer learning to employ on other cities.

ACKNOWLEDGMENTSThis work was supported in part by the Ministry of Science andTechnology, Taiwan, under Grant MOST 110-2634-F-002-026. We

Figure 5:MAPEof comparedmethods in different predictiontimes shows MPGAT achieves better results in all cases.

benefit from NVIDIA DGX-1 AI Supercomputer and are grateful tothe National Center for High-performance Computing.

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