# Cross-City Traffic Prediction via Semantic-Fused Hierarchical Graph Transfer
Learning

Kehua Chen, Jindong Han, Siyuan Feng*, and Hai Yang Kehua Chen and Jindong Han
are with Division of Emerging Interdisciplinary Areas (EMIA),
Interdisciplinary Programs Office, The Hong Kong University of Science and
Technology, Hong Kong, China.Siyuan Feng and Hai Yang are with Civil and
Environmental Engineering Department, The Hong Kong University of Science and
TechnologyH. Yang is also with the Intelligent Transportation Thrust, the Hong
Kong University of Science and Technology (Guangzhou), Guangzhou, China* S.
Feng is the corresponding author, E-mail<EMAIL_ADDRESS>
###### Abstract

Accurate traffic prediction benefits urban management and improves
transportation efficiency. Recently, data-driven methods have been widely
applied in traffic prediction and outperformed traditional methods. However,
data-driven methods normally require massive data for training, while data
scarcity is ubiquitous in low-developmental or newly constructed regions. To
tackle this problem, we can extract meta knowledge from data-rich cities to
data-scarce cities via transfer learning. Besides, relations among urban
regions can be organized into various semantic graphs, e.g. proximity and POI
similarity, which is barely considered in previous studies. In this paper, we
propose Semantic-Fused Hierarchical Graph Transfer Learning (SF-HGTL) model to
achieve knowledge transfer across cities with fused semantics. In detail, we
employ hierarchical graph transformation followed by meta-knowledge retrieval
to achieve knowledge transfer in various granularity. In addition, we
introduce meta semantic nodes to reduce the number of parameters as well as
share information across semantics. Afterwards, the parameters of the base
model are generated by fused semantic embeddings to predict traffic status in
terms of task heterogeneity. We implement experiments on five real-world
datasets and verify the effectiveness of our SF-HGTL model by comparing it
with other baselines.

###### Index Terms:

Few-shot learning, Traffic prediction, Graph neural network.

##  I Introduction

As a vital problem in Intelligent Transportation System (ITS), traffic
prediction aims to forecast future transportation status, e.g. traffic flow
[1], traffic speed [2], origin-destination demand [3]. Accurate traffic
prediction benefits urban management and improves transportation efficiency.
Due to the explosion of data volume, various machine learning methods have
been used in traffic prediction and outperformed traditional approaches [4].

Nonetheless, deep learning methods normally require massive data to achieve
satisfactory performance, and limited data size leads to over-fitting
problems. While data scarcity is ubiquitous in cities with low developmental
levels or new districts, it is non-trivial to train a powerful model. In
addition, traffic patterns share common features even though they are in
different cities. For instance, traffic speed in commercial areas decreases
during peak time, and crowd flow from residential areas to commercial areas
tends to surge in the morning. Therefore, if we can extract the traffic
patterns from data-rich cities and adapt the learned patterns to data-scarce
cities, we can still achieve good performance with limited data sizes. Such
knowledge transfer among cities is called cross-city knowledge transfer and
has attracted much attention these years. Generally, there are two paradigms
in cross-city knowledge transfer. The first idea is Divide-Match-Transfer
principle [5, 6]: both source and target cities are first divided into several
regions, and the target regions absorb knowledge from the most similar source
regions after matching. Moreover, the other method utilizes meta learning
methods to extract meta-knowledge from source cities and adapt the knowledge
based on target cities [7, 8]. In traffic prediction, meta-knowledge can be
deemed as various traffic patterns.

In terms of recent research, roads or stations in cities can be treated as
nodes in graphs, and their distance or POI similarity can be regarded as
edges. As such topological structure determines traffic patterns, the
knowledge transfer among graphs is more informative than grid-based transfer.
However, there are still several challenges in cross-city knowledge transfer.
First, most current studies merely achieved knowledge transfer at a solely
local level without the consideration of coarse-scale knowledge. Here we
define “local” as node level in graphs, i.e. region or grid in previous
studies, and define “zone” as a relatively coarse level consisting of more
than one node, and encompasses general characteristics (Fig. 1). For instance,
several subway stations can all belong to one commercial zone from a physical
proximity perspective, and can also belong to one functional category from a
Point of Interest (POI) perspective. The local-level transfer losses such
zonal information. Second, although various semantics have been employed in
traffic predictions since urban data can be normally organized as multiple
semantic graphs, most current knowledge-transfer models do not consider
different semantic information, and we can merely concatenate various semantic
representations for prediction based on current studies. Fig. 2 presents an
example of the construction of various semantic graphs, although each semantic
graph has identical nodes, the nodes could be connected in different ways to
encompass different semantic meanings, e.g. physical proximity and POI
similarity in the example. Third, compared to Divide-Match-Transfer principle,
meta learning methods directly extract meta-knowledge, and hence are more
generalizable. However, previous studies implicitly extract spatial-temporal
patterns along with the model parameters, which does not explicitly integrate
information among patterns, let alone the knowledge fusion of multiple
semantics.

Figure 1: Local- and zone-level transfer. Fig. 1(a) presents the transfer
process among grids or regions. However, grids can be further aggregated into
various zones, the transfer among zones is also meaningful but rarely
considered in previous studies. Figure 2: Example for different semantic
graphs.

To tackle the aforementioned challenges, we propose a novel framework for
spatio-temporal transfer learning named Semantic-Fused Hierarchical Graph
Transfer Learning (SF-HGTL). SF-HGTL takes graphs as inputs and is able to
handle various semantic graphs. Considering the first challenge, we utilize
hierarchical graph transformation for each semantic graph to extract multi-
level information. To extract meta-knowledge for knowledge transfer and tackle
the third challenge, we design several meta-knowledge graphs to extract meta-
knowledge from different levels. Graph structure is more informative compared
to discrete memory vectors. To solve the second challenge as well as reduce
the number of parameters, different semantics share the same meta-knowledge
graphs, and their parameters are adjusted by corresponding meta semantic
nodes. At last, we employ a modulating function to generate task-specific
parameters for the base learner after the fusion of semantics. Note that the
base learner can be any deep learning models, e.g. Recurrent Neural Network
and Graph Neural Network, and we use the base learner to predict traffic
status.

The main contributions of this paper are as follows:

  * •

We design a novel cross-city knowledge transfer framework based on semantic-
fused hierarchical graphs, the framework uses hierarchical graph
transformation to achieve local, zonal and global feature representation, and
we introduce meta-knowledge graphs to benefit information retrieval in the
meta-testing phase.

  * •

We introduce meta semantic nodes that not only adapt meta-knowledge in terms
of various semantics, but also achieve information sharing among semantics
since they utilize same meta-knowledge graphs. Semantic discriminator is
further applied to avoid trivial solutions.

  * •

We implement several experiments based on five real-world datasets to verify
the effectiveness of the proposed framework. The results demonstrate the
superiority of our SF-HGTL model compared to baseline models.

The remainder of the paper is organized as follows. We briefly introduce
related works in Section 2, and propose definitions and problems in Section 3.
Afterwards, the proposed model is revealed in Section 4. Section 5 thoroughly
introduces experiments for evaluation, results and discussions. At last, we
summarize the overall paper in Section 6.

##  II RELATED WORK

This paper is relevant to traffic prediction, transfer learning, and cross-
city knowledge transfer. In this section, we briefly review related works for
the above topics.

###  II-A Traffic Prediction

As a classical problem, researchers have focused on traffic prediction since
several decades ago. Traditional statistical methods include Historical
Average (HA) [9], Autoregressive Integrated Moving Average (ARIMA) [10] and
its variants. Nonetheless, these traditional methods merely capture linear
relations and cannot perfectly depict data patterns. Hence, recent studies
tend to use deep learning methods due to their powerful expressiveness.
Researchers adopted various techniques to tackle traffic prediction problems,
ranging from Recurrent Neural Network (RNN), Convolutional Neural Network
(CNN) to Graph Neural Network (GNN).

Long Short-Term Memory (LSTM) was applied in [11] to predict traffic speed on
a single road, and subsequent studies normally use RNN as a model component
owing to its powerful capacity of capturing non-linear dynamics. Within a
city, traffic status in one region is influenced by proximal regions. To model
such relations, [12] formed traffic speed as various matrices, and then
transformed matrices into image channels. Then CNN was applied to predict
future traffic status. Yet, CNN can only capture Euclidean relations. As an
emerging technique, GNN has been widely used in current models for traffic
prediction. For example, [13] modeled the traffic flow as a diffusion process
on a directed graph and proposed DCRNN to forecast traffic speed. T-GCN [14]
combined Graph Convolutional Network (GCN) and Gated Recurrent Unit (GRU) to
predict traffic status. In addition, [15] came up with ST-MetaNet to capture
traffic spatial and temporal correlations. The authors designed the model
based on deep meta-learning and chose RNN and GNN as meta-learners.

Although deep learning methods achieve accurate traffic prediction, they
typically require massive data. Hence, transfer learning provides an effective
method to alleviate data scarcity.

###  II-B Transfer Learning

Traditional machine learning approaches have achieved great success in various
practical scenarios, such as object detection, and language processing.
However, machine learning normally requires massive labeled data for training,
and the collection of labeled data is time-consuming and expensive.

Transfer learning achieves knowledge transfer from source domains to improve
the learning performance in target domains. Hence, transfer learning is
suitable to handle few-shot problems, i.e. rich data in source domains and
scarce data in target domains. In data-based interpretation [16], the main
objective of transfer learning is to minimize the distribution difference
between source and target domains, such as instance weighting strategy [17]
and feature transformation strategy [18]. In model-based interpretation [16],
the aim is to accurately predict results on the target domain by utilizing
source knowledge. As an emerging method, meta-learning [19] has been used to
achieve transfer learning as an effective method. In meta-learning, a number
of tasks are drawn from task distributions, the model aims to learn a
generalized meta-learner at the meta-training phase, and achieves fast
adaption at the meta-testing phase when new tasks come. As one of the most
famous methods, MAML [20] treats the meta-learner as parameter initialization
by bi-level optimization, we use MAML as the basic framework in this paper.
Besides, [21] raised that the utilization of task discrepancy benefits the
model performance, and various modulating methods have been applied in recent
studies, such as automated relational meta-graph [22], multimodal modulation
network [23], and hierarchical prototype graph [24].

While most previous transfer learning studies focused on image- and text-
related tasks, spatial-temporal transfer learning is at the initial stage and
still without much understanding.

###  II-C Cross-City Knowledge Transfer

To the best of our knowledge, [5] first proposed Divide-Match-Transfer
principle. The authors partitioned the cities into equal-size grids, then
matched target regions with the most correlated source regions. Afterwards,
ConvLSTM was used as the backbone model to learn regional representations for
prediction. At fine-tuning stage, the model tried to minimize the squared
error between regional representations of target regions and matched source
regions.

MetaST [7] designed a memory module to extract long-term patterns from source
cities. The regions in source cities were clustered into several categories as
memory. Then, the attention mechanism was utilized to gather useful
information from the memory during both the meta-training and meta-testing
phases. ST-DANN [6] first mapped source and target data to a common embedding
space, and tried to minimize Maximum Mean Discrepancy (MMD) between two
embeddings. To further capture spatial dependencies, the model introduced a
global attention mechanism. The attention mechanism can also be deemed as a
matching process. [8] designed the model in terms of graph data structure. The
model extracted meta-knowledge through GRU and Graph Attention Network (GAT).
To express the structural information, graph construction loss was introduced.
Last, the node-level meta-knowledge was fed into a parameter generation module
to produce non-shared feature extractor parameters. To alleviate negative
transfer, [25] proposed selective cross-city transfer learning to filter
harmful source knowledge. The authors employed edge-level and node-level
adaption to training the feature network, and designed a weighting network for
loss calculation.

As mentioned in the introduction, there are still challenges and limitations
in current studies, and this paper aims to solve them via semantic-fused
hierarchical graph transfer learning.

##  III DEFINITION AND PROBLEM FORMULATION

In this section, we introduce several definitions used in this paper and
formally illustrate the cross-city knowledge transfer problem.

Definition 1 (Graph): Given a graph
$\mathcal{G}=(\mathcal{V},\mathcal{E},\textbf{X},\textbf{A})$.
$\mathcal{V}=\\{v_{1},v_{2},....,v_{N}\\}$ is the node set, and
$N=|\mathcal{V}|$; $\mathcal{E}=\\{e_{ij}=(v_{i},v_{j})\\}$ is the edge set;
$\textbf{X}\in\mathds{R}^{N\times D}$ is the node feature matrix, and the
feature dimension of each node is $D$; A is the adjacency matrix, each entry
$a_{ij}$ indicates the weight of edge $e_{ij}$.

Definition 2 (Few-Shot Learning): Given a dataset $\mathcal{D}$, where
$\mathcal{D}^{tr}=\\{X^{tr},Y^{tr}\\}$ is the training set that only has a few
samples, and $\mathcal{D}^{ts}$ is the corresponding testing set. The aim of
few-shot learning is to train a model on the training set that minimizes the
prediction error on the test set. Here, we treat traffic prediction problem in
the data-scarce cities as a few-shot learning problem.

In this paper, we follow Model-Agnostic Meta-Learning (MAML) [20] framework to
handle the few-shot learning problem. As Fig. 3 shows, we use a source dataset
$\mathcal{D}_{\mathcal{S}}$ to train the meta learner,
$\mathcal{D}_{\mathcal{S}}$ is organized as various tasks, denoted as
$\\{\mathcal{T}_{i}\\}_{i=1}^{I}$. Each task $\mathcal{T}_{i}$ includes a
support set $\mathcal{S}_{i}$ and a query set $\mathcal{Q}_{i}$. MAML employs
$\mathcal{S}_{i}$ and $\mathcal{Q}_{i}$ to achieve domain adaption via bi-
level optimization. In detail, assuming the initial parameters of the meta
learner as $\theta_{0}$, we first utilize $\mathcal{S}_{i}$ to update model
parameters as $\theta_{i}^{\prime}$. Then $\theta_{i}^{\prime}$ is employed to
calculate loss based on $\mathcal{Q}_{i}$, and the parameters are updated
again to acquire $\theta_{i+1}$, i.e. outer updating. We use $\theta_{i+1}$
for the following training. At the meta-testing stage, the target dataset
$\mathcal{D}_{\mathcal{T}}$ is also formed as tasks, we employ $\theta_{i+1}$
as the initial parameters, fine-tune parameters based on $\mathcal{S}_{k}$ and
test the model performance in $\mathcal{Q}_{k}$.

Figure 3: MAML framework. Various tasks are sampled from datasets and the
updating process is based on bi-level optimization.

Problem Definition 1 (Traffic Prediction): Consider there are $N$
sensors/recorders in a given city, sensor/recorder $n$ measures traffic status
on a specific node (e.g. road link, or subway station) at time $t$, denoted as
$X_{t}^{n}$. Given past $T$ records, the sequential traffic status can be
naturally deemed as node features, then traffic prediction aims to find a
function $g(\cdot)$ that predicts the next $M$ traffic status:

$\displaystyle\begin{bmatrix}X_{1}^{t-T+1}&...&X_{1}^{t}\\\
X_{2}^{t-T+1}&...&X_{2}^{t}\\\ ...&...&...\\\
X_{N}^{t-T+1}&...&X_{N}^{t}\end{bmatrix}\stackrel{{\scriptstyle
g(\cdot)}}{{\longrightarrow}}\begin{bmatrix}X_{1}^{t+1}&...&X_{1}^{t+M}\\\
X_{2}^{t+1}&...&X_{2}^{t+M}\\\ ...&...&...\\\
X_{N}^{t+1}&...&X_{N}^{t+M}\end{bmatrix}$ (1)

The above past $T$ traffic status of $N$ nodes and its corresponding $M$
traffic status are deemed as one sample. Various samples consist of one task
$\mathcal{T}_{i}$.

Figure 4: The proposed model structure. For sample $k$ in support set
$\mathcal{S}_{i}$, the historical traffic status is first fed into GRU to
generate node features. For each semantic, we apply hierarchical graph
transformation and multi-level MK graphs to extract node, region and semantic
information. To reduce parameter amount, meta semantic nodes are introduced to
adjust MK graphs in terms of various semantics. Each sample then generates a
sample embedding, we apply mean pooling to obtain a task embedding. At last,
we retrieve meta-knowledge for task embedding and generate modulated
parameters for meta learner.

Problem Definition 2 (Cross-City Traffic Prediction): Traffic prediction based
on a few training samples can be deemed as a few-shot learning problem, and we
solve it with meta learning. Here we assume only one source and one target
city. Given a source city denoted as
$\mathcal{C}_{\mathcal{S}}=\\{\mathcal{G}_{\mathcal{S}}^{c}\\}_{c=1}^{J}$, a
target city denoted as
$\mathcal{C}_{\mathcal{T}}=\\{\mathcal{G}_{\mathcal{T}}^{c}\\}_{c=1}^{J}$,
where $J$ indicates the number of different semantics and each semantic shares
the same node features $\mathbb{X}$, i.e. past $T$ traffic status. The source
city is data-rich while the target city is data-scarce. We aim to find a
function $f(\cdot)$ that leverages knowledge of the source city to predict
traffic status in the target city as accurately as possible.

##  IV METHODOLOGY

Fig. 4 presents the proposed model architecture. For each sample in task
$\mathcal{T}_{i}$ with multiple semantic graphs, we generate a sample
embedding via a semantic-fusion cell. In detail, we first feed the node
features into a shared GRU, then treat hidden states as the new node features.
Then, hierarchical graph transformation is applied to each semantic graph. At
each transformation layer, the nodes retrieve meta-knowledge (MK) from several
meta-knowledge graphs. To model the relations among various semantics, we
further introduce several meta semantic nodes to adapt the parameters of meta-
knowledge graphs in terms of semantics. Afterwards, each semantic graph is
transformed as a semantic embedding, and we concatenate semantic embeddings as
sample embedding. We treat the average of sample representations as task
embedding. The task embedding then interacts with a task meta-knowledge graph.
By feeding the task embedding into a task modulating function, we acquire the
adapted parameters for the meta learner.

###  IV-A Hierarchical Graph Transformation

Assume there are $k=1,...,K$ samples in support set $\mathcal{S}_{i}$, and
each sample has $c=1,...,J$ semantics. Although various semantics are
available in spatio-temporal prediction problems, the node features are
normally fixed. Here we employ a shared GRU to generate node embeddings based
on historical traffic status:

$\displaystyle\mathbb{h}_{v_{i}}^{(0)}=\text{GRU}(\\{X_{i}^{t-T+1},...,X_{i}^{t}\\})$
(2)

Afterwards, we apply Graph Neural Networks (GNN) to extract non-Euclidean
information. General GNN follows message passing mechanism [26], which
includes two processes: aggregation and updating. At the $l$-th layer, GNN
updates the node embedding $\mathbb{h}_{v_{i}}^{(l)}$ as follows:

$\displaystyle\mathbb{h}_{v_{i}}^{(l)}=\text{UPDATE}(\mathbb{h}_{v_{i}}^{(l-1)},\text{AGG}^{(l)}(\\{(\mathbb{h}_{v_{i}}^{(l-1)},$
(3)
$\displaystyle\mathbb{h}_{v_{j}}^{(l-1)},\mathbb{A})|v_{j}\in\mathcal{N}(v_{i})\\}))$

where $\mathcal{N}(v_{i})$ indicates the neighborhood of node $v_{i}$; UPDATE
can be neural networks; AGG can be mean or max pooling.

However, GNN performs powerfully when focusing on local information since deep
GNN leads to over-smoothing problem [27]. Hence, the hierarchical structure is
able to provide a larger view and conserve node differences. [28] designed a
hierarchical graph representation model to acquire graph embeddings.
Basically, hierarchical graph transformation assigns nodes to clusters at each
layer in order to reduce the node numbers. Denote learned cluster assignment
matrix at layer $l$ as $\mathbb{S}^{(l)}\in\mathds{R}^{n_{l}\times n_{l+1}}$,
the node embeddings at layer $l$ as $\mathbb{Z}^{(l)}$, the new node/cluster
embedding matrix at layer $l+1$ as $\mathbb{X}^{l+1}$, and adjacency matrix at
layer $l$ as $\mathbb{A}^{(l)}$. The main process is first to generate node
embeddings $\mathbb{Z}^{(l)}$ through an embedding GNN, and a cluster
assignment matrix $\mathbb{S}^{(l)}$ through a pooling GNN at layer $l$.
Afterwards, the nodes at layer $l$ are assigned to clusters with new
embeddings $\mathbb{X}^{(l+1)}$ and a new adjacency matrix
$\mathbb{A}^{(l+1)}$ at layer $l+1$:

$\displaystyle\mathbb{Z}^{(l)}=\text{GNN}_{l,\text{embed}}(\mathbb{A}^{(l)},\mathbb{X}^{(l)})$
(4)
$\displaystyle\mathbb{S}^{(l)}=\text{softmax}(\text{GNN}_{l,\text{pool}}(\mathbb{A}^{(l)},\mathbb{X}^{(l)}))$
(5) $\displaystyle\mathbb{X}^{(l+1)}=\mathbb{S}^{{(l)}^{T}}\mathbb{Z}^{(l)}$
(6)
$\displaystyle\mathbb{A}^{(l+1)}=\mathbb{S}^{(l)^{T}}\mathbb{A}^{(l)}\mathbb{S}^{(l)}$
(7)

In short, we denote $l$-th hierarchical graph transformation as
$\text{HGT}(\mathbb{A}^{(l)},\mathbb{X}^{(l)})$. We utilize two-layer
transformations, the nodes after the first transformation demonstrates zonal
information, and the second transformation aggregates the overall graphs as
semantic information. The utilization of hierarchical graph transformation
actually clusters similar nodes together, thus each node at deep levels can be
deemed as a coarse category indicating more general information, e.g. urban
functional zones.

Besides, we add hierarchical link prediction loss to encode nearby nodes
closely, and hierarchical entropy loss to force exclusive assignment:

$\displaystyle\mathcal{L}_{l}=||\mathbb{A}^{(l)},\mathbb{S}^{(l)}\mathbb{S}^{(l)^{T}}||_{F}$
(8)
$\displaystyle\mathcal{L}_{e}=\frac{1}{n_{l}}\sum_{i=1}^{n_{l}}H(\mathbb{S}_{i})$
(9)

where $||\cdot||_{F}$ is the Frobenius norm; $H(\cdot)$ means the entropy
function; and $\mathbb{S}_{i}$ is the $i$-the row of $\mathbb{S}$.

###  IV-B Meta-knowledge Graph Construction

Inspired by [22], we design multiple meta-knowledge graphs to extract
knowledge at different levels, i.e. node MK graph, zone MK graph and semantic
MK graph. Here we take the node MK graph as an example for demonstration.
Specifically, we denote the node MK graph as
$\mathcal{G}_{node}^{mk}(\mathbb{X}_{meta},\mathbb{A}_{M})$ with $N$ nodes.
Both node features $\mathbb{m}_{i}\in\mathbb{X}_{meta}$ and adjacency matrix
$\mathbb{A}_{M}(\mathbb{m}_{i},\mathbb{m}_{j})$ are learned during training:

$\displaystyle\mathbb{A}_{M}(\mathbb{m}_{i},\mathbb{m}_{j})=\sigma(\mathbb{W}|\mathbb{m}_{i}-\mathbb{m}_{j}|/\gamma+\mathbb{b}))$
(10)

where $\mathbb{m}_{i}$ and $\mathbb{m}_{j}$ are node features in the node MK
graph; $\sigma$ is sigmoid function; $\mathbb{W}$ and $\mathbb{b}$ are
learnable parameters; $\gamma$ is a scaling factor.

Afterwards, the node-level graph of each semantic is supposed to retrieve
meta-knowledge from the node MK graph. Here we construct a super-graph
$\mathcal{G}^{S}_{node}$ connecting sample nodes with nodes in
$\mathcal{G}_{node}^{mk}$. For the weights among node $\mathbb{h}_{v_{i}}$ and
meta-node $\mathbb{m}_{i}$, we calculate them via Euclidean distances:

$\displaystyle\mathbb{A}_{C}(\mathbb{h}_{v_{i}},\mathbb{m}_{i})=\frac{\text{exp}(-||(\mathbb{h}_{v_{i}}-\mathbb{m}_{i})/\gamma||_{2}^{2}/2)}{\sum_{n=1}^{N}\text{exp}(-||(\mathbb{h}_{v_{i}}-\mathbb{m}_{n})/\gamma||_{2}^{2}/2)}$
(11)

As Fig. 5 presents, the node features and adjacency matrix of super-graph
$\mathcal{G}^{S}_{\text{node}}$ are
$\mathbb{X}_{S}=\mathbb{X}_{node}\oplus\mathbb{X}_{meta}$, and
$\mathbb{A}_{S}=\mathbb{A}_{node}\oplus\mathbb{A}_{C}\oplus\mathbb{A}_{C}^{T}\oplus\mathbb{A}_{M}$
respectively, where $\oplus$ indicates concatenation operation and $T$ means
matrix transpose.

Figure 5: The construction of super-graphs. For a super-graph, we first
generate $\mathbb{A}_{C}$ based on node features. Afterwards, the node feature
$\mathbb{X}_{s}$ is obtained by concatenating $\mathbb{X}_{node}$ and
$\mathbb{X}_{meta}$, and the adjacency matrix $\mathbb{A}_{S}$ is derived by
$\mathbb{A}_{node},\mathbb{A}_{c},\mathbb{A}^{T}_{c},A_{m}$. The shapes of
$\mathbb{X}_{S}$ and $\mathbb{A}_{S}$ are $(N+K)\times d$ and
$(N+K)\times(N+K)$ respectively.

Then we feed the super-graph into a GNN and integrate node features with meta-
knowledge. In our model, meta-knowledge retrieval is implemented for each
layer of hierarchical graph transformation, i.e.
$\hat{\mathbb{X}}^{(l)}=\text{GNN}^{(l)}(\mathbb{A}_{S},\mathbb{X}_{S}^{(l)})$.
Therefore, we finally acquire a semantic embedding with the combination of
various meta-knowledge:

$\displaystyle\hat{\mathbb{X}}^{(0)}=\text{GNN}^{(0)}(\mathbb{A}_{S}^{(0)},\mathbb{X}_{S}^{(0)})$
(12)
$\displaystyle\mathbb{X}^{(1)},\mathbb{A}^{(1)}=\text{HGT}(\mathbb{A}^{(0)},\hat{\mathbb{X}}^{(0)})$
(13)
$\displaystyle\hat{\mathbb{X}}^{(1)}=\text{GNN}^{(1)}(\mathbb{A}_{S}^{(1)},\mathbb{X}_{S}^{(1)})$
(14)
$\displaystyle\mathbb{X}^{(2)},\mathbb{A}^{(2)}=\text{HGT}(\mathbb{A}^{(1)},\hat{\mathbb{X}}^{(1)})$
(15) $\displaystyle\mathbb{X}_{c}=\text{Mean}(\text{MLP}(\mathbb{X}^{(2)}))$
(16)
$\displaystyle\mathbb{g}_{c}=\text{GNN}^{(2)}(\mathbb{A}_{S}^{(2)},\mathbb{X}_{S}^{(2)})$
(17)

where MLP indicates a fully-connected neural network; $\mathbb{X}_{c}$ means
semantic embeddings before MK retrieval; and $\mathbb{g}_{c}$ indicates
semantic embeddings after MK retrieval; Eq. 12, 14 and 17 represent meta-
knowledge retrieval process, and $\text{Mean}(\cdot)$ is mean pooling.

Subsequently, we acquire graph embeddings $\mathbb{g}_{c}$ for each semantic
graph and fusion semantic graph embeddings to generate a sample embedding,
e.g. concatenation and attention mechanism. Here we simply concatenate
semantic graph embeddings to generate sample $k$’s embedding, we name
hierarchical graph transformation together with semantic fusion process as
semantic fusion cell:

$\displaystyle\mathbb{z}_{k}=\mathbb{g}_{1}\oplus\mathbb{g}_{2}\oplus...\oplus\mathbb{g}_{J}$
(18)

Within a support set $\mathcal{S}_{i}$, we apply mean pooling to sample
embeddings to acquire a task embedding:

$\displaystyle\mathbb{t}_{i}=\text{Mean}(\\{z_{k}\\}_{k=1}^{K})$ (19)

Afterwards, the task embedding further retrieves knowledge from a task MK
graph to achieve task adaptation. The retrieval process is similar to the
aforementioned super-graph construction method. At last, we apply a modulating
function to the initialized parameter $\theta_{0}$ to generate task-specific
parameters:

$\displaystyle\lambda_{i}=\sigma(\mathbb{W}\cdot\mathbb{t}_{i}+\mathbb{b})$
(20) $\displaystyle\theta_{i}=\lambda_{i}\circ\theta_{0}$ (21)

where $\mathbb{W}$ and $\mathbb{b}$ are learnable parameters; $\circ$
indicates element-wise multiplication. $\theta_{i}$ is then used as model
parameters for prediction.

###  IV-C Semantic Adjustment for Meta-knowledge Graph

As introduced above, the proposed model conducts meta-knowledge retrieval for
each semantic, which increases the number of parameters significantly. To
alleviate this problem, we design a semantic adjustment module to achieve
parameter adaption in terms of various semantics.

In detail, various semantic graphs share the same MK graphs, and we introduce
meta semantic nodes $\mathbb{s}_{c}$ to adjust MK graphs according to
different semantics. The utilization of meta semantic nodes can not only
reduce the number of parameters, but also establish connections among
semantics. Similar to Eq. 11, we construct a super-graph based on MK graphs
and meta semantic nodes, then implement GNN to update node features of MK
graphs in terms of meta semantic nodes. Then, MK graphs interact with
hierarchical graphs as mentioned above. Hence, the meaning of Hierarchical in
our SF-HGTL model is twofold: (i) we use hierarchical graph transformation to
aggregate meta-knowledge from node, zone and semantic levels; (ii) we use meta
semantic nodes to hierarchically adjust parameters of MK graphs.

The features of meta semantic nodes are learned during the training phase to
represent different semantics. The current framework merely captures the
discrepancy from various semantic adjacency matrices, the signal information
can vanish after the meta-knowledge retrieval process. Hence, the nodes on MK
graphs rather than meta semantic nodes can represent semantic information,
which leads to the trivial solution.

To solve this problem, we further introduce a semantic discriminator to guide
the learning of meta semantic nodes. Specifically, we treat meta semantic
nodes as prototypes, i.e. forcing different semantic graph embeddings to
approach corresponding meta semantic nodes and keeping away from other
semantics:

$\displaystyle\hat{\mathbb{g}}_{c}=\text{MLP}(\mathbb{g}_{c}),\forall
c=1,...,J$ (22)
$\displaystyle\mathcal{L}_{d}=-\sum_{c=1}^{J}\text{log}\frac{\text{exp}(\mathbb{s}_{c}\cdot\hat{\mathbb{g}}_{c}/\tau)}{\sum_{j=1}^{J}\text{exp}(\mathbb{s}_{c}\cdot\hat{\mathbb{g}}_{j}/\tau)}$
(23)

where $J$ is the number of semantics; $\tau$ is the temperature
hyperparameter. We use an $\text{MLP}(\cdot)$ to increase the expressiveness.

###  IV-D Meta-optimization

As introduced in [20], we split source-city datasets into massive training
tasks $\mathcal{T}_{S}$ in meta-training phase. A task
$\mathcal{T}_{i}\in\mathcal{T}_{S}$ consists of a support set
$\mathcal{S}_{i}$ and a query set $\mathcal{Q}_{i}$, and
$\mathcal{S}_{i}\cap\mathcal{Q}_{i}=\varnothing$. Recall that we use past $T$
steps to predict next $M$ traffic status for one sample, each support set and
query set consist of several samples. Afterwards, batches of tasks are sampled
from $\mathcal{T}_{S}$ to train our model by bi-level optimization. For task
$\mathcal{T}_{i}$, the model first acquires adjusted parameters $\theta_{i}$
as mentioned above, then leverages $\mathcal{S}_{i}$ to inner-update
$\theta_{i}$:

$\displaystyle\theta_{i}\leftarrow\theta_{i}-\alpha\nabla_{\theta}\mathcal{L}_{\mathcal{T}_{i}}(f_{\theta},\mathcal{S}_{i})$
(24)

where $\alpha$ is stepsize; $\mathcal{L}_{\mathcal{T}_{i}}$ is the task-
specific loss function, e.g. Mean Square Error (MSE) and Mean Average Error
(MAE) for our traffic prediction.

Afterwards, the meta-objective is the combination of task loss based on
$\mathcal{Q}_{i}$, hierarchical link prediction loss, hierarchical entropy
loss and semantic loss:

$\displaystyle\Phi\leftarrow\Phi-\beta\nabla_{\Phi}\sum_{i}^{I}(\mathcal{L}_{\mathcal{T}_{i}}(f_{\theta_{i}},\mathcal{Q}_{i})+\mu_{1}\mathcal{L}_{l}+\mu_{2}\mathcal{L}_{e}+\mu_{3}\mathcal{L}_{d})$
(25)

where $\Phi$ is the overall parameters; $\beta$ is the stepsize;
$\mu_{1},\mu_{2},\mu_{3}$ are regularization factors. Algorithm 1 presents the
above training process.

Algorithm 1 SF-HGTL meta-training algorithm

1:Source city dataset $\\{\mathcal{G}_{\mathcal{S}}^{c}\\}_{c=1}^{J}$;
stepsize $\alpha$, $\beta$; temperature hyperparameter $\tau$; and
regularization factors $\mu_{1}$, $\mu_{2}$, and $\mu_{3}$.

2:Initialized model with parameter $\Phi$ for target city.

3:Randomly initialize $\theta_{0}$ and $\Phi$.

4:while not done do

5: Sample a batch of tasks
$\\{\mathcal{T}_{i}\\}_{i=1}^{I}\sim\mathcal{T}_{S}$.

6: for $\mathcal{T}_{i}\in\\{\mathcal{T}_{i}\\}_{i=1}^{I}$ do

7: Obtain $\\{\mathbb{h}_{v_{i}}^{(0)}\\}_{i=1}^{N}$ via Equation (2);

8: Obtain $\mathbb{z}_{k},\forall k=1,...,K$ based on Equation (12)-(18);

9: Compute $\mathcal{L}_{l}$ and $\mathcal{L}_{e}$ via Equation (8)-(9);

10: Compute $\mathcal{L}_{d}$ via Equation (22)-(23);

11: Obtain $\mathbb{t}_{i}$ via Equation (19) and MK retrieval process;

12: Compute $\theta_{i}$ via Equation (20)-(21);

13: Update $\theta_{i}$ with support set $\mathcal{S}_{i}$ via Equation (24).

14: end for

15: Update $\Phi$ via Equation (25).

16:end while

##  V EXPERIMENT

To evaluate the effectiveness of our framework, we implement diverse
experiments with five real-world datasets and compare the model performance
with several baselines. The experiments are related to taxi pickup/dropoff and
metro passenger flow prediction, and our framework can be easily transferred
to other traffic prediction tasks such as traffic speed and flow prediction.
Moreover, an ablation study is conducted to indicate the importance of each
component of our model. At last, we conduct sensitivity analysis to show the
impact of various hyperparameters.

###  V-A Experiment Setup and Datasets

We choose taxi pickup/dropoff and metro passenger flow prediction tasks in
this study. The taxi pickup/dropoff prediction involves three datasets: NY-
Taxi, CHI-Taxi and DC-Taxi [25], we use proximity, road connectivity and POI
graphs in the experiment similar to [25]. The metro passenger flow prediction
involves two datasets: HZMetro and SHMetro [29], we utilize physical,
similarity and correlation graphs in the experiment as introduced in [29]. The
statistics of datasets are listed in Table I.

TABLE I: The description and statistics of four datasets Dataset | NY-Taxi | CHI-Taxi | DC-Taxi | HZMetro | SHMetro |
---|---|---|---|---|---|---
# Nodes | 460 | 476 | 420 | 80 | 288 |
# Physical Edges | 3,886 | 4,018 | 3,538 | 248 | 958 |
Interval | 60 min | 60 min | 60 min | 15 min | 15 min |
Time Span |  | 1/1/2016 - 12/31/2016 |  | 1/1/2019 - 1/25/2019 | 7/1/2016 - 9/30/2016 |
Mean | Pick:32.913, Drop:32.791 | Pick:5.861, Drop:5.950 | Pick:2.732, Drop:2.731 | In:213.930, Out:216.277 | In:223.690, Out:229.271 |
Std | Pick:131.080, Drop:119.994 | Pick:39.043, Drop:34.236 | Pick:16.317, Drop:14.051 | In:358.880, Out:340.822 | In:358.880, Out:340.821 |

NY-Taxi dataset: The dataset is collected based on New York taxis covered
between 74.059° to 73.863° in longitude and 40.645° to 40.848° in latitude.
There are 133 million records in total. The data ranges from January 1st 2016
to December 31st 2016, and the recording interval is 1 hour.

CHI-Taxi dataset: The dataset is collected based on Chicago taxis covered
between 87.740° to 87.576° in longitude and 41.766° to 42.013° in latitude.
There are 24.5 million records in total. The data ranges from January 1st 2016
to December 31st 2016, and the recording interval is 1 hour.

DC-Taxi dataset: The dataset is collected based on Washington taxis covered
between 77.127° to 76.926° in longitude and 38.798° to 38.969° in latitude.
There are 10 million records in total. The data ranges from January 1st 2016
to December 31st 2016, and the recording interval is 1 hour.

HZMetro dataset: The dataset is generated based on transaction records of the
Hangzhou metro system, the system has 2.35 million ridership each day. The
data ranges from January 1st 2019 to January 25th 2019, and the recording
interval is 15 min.

SHMetro dataset: The dataset is generated based on transaction records of the
Shanghai metro system, the system has 811.8 million ridership each day. The
data ranges from July 1st 2016 to September 30th 2016, and the recording
interval is 15 min.

We conduct four experiments to evaluate the model performance, i.e. NY-Taxi to
DC-Taxi, CHI-Taxi to DC Taxi, HZMetro to SHMetro, and SHMetro to HZMetro. For
taxi prediction, we employ the past 6 time steps to predict the next 5 time
steps, including pickup and dropoff volumes. For metro prediction, we use the
past 4 time steps to predict the next 4 time steps, including inflow and
outflow volumes. Min-Max normalization and Z-score normalization are applied
for taxi and metro passenger flow pre-processing respectively.

Evaluation metrics: Since the prediction problem is a regression problem, we
utilize two widely applied methods for evaluation: Mean Average Error (MAE)
and Root Mean Square Error (RMSE).

$\displaystyle\text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}$
(26) $\displaystyle\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}|y_{i}-\hat{y}_{i}|$
(27)

where $\hat{y}_{i}$ and $y_{i}$ are predicted and true values of instance $i$
respectively.

Implementation details: The experiments are conducted on a Linux server with 2
NVIDIA Tesla V100 GPUs. We use TGCN [14] as the base learner to capture both
temporal and spatial relations. The base learner has three TCGN layers with
hidden sizes (16, 32, 32), followed by three MLP layers with hidden sizes
(256, 128, 128). In addition, we choose k-GNN [30] to proceed graph data. The
hidden size of SF-HGTL is 32, the number of centers for MK graphs is 5, the
clustering ratio of hierarchical graph transformation is 0.3, and we let
$\mu_{1}=\mu_{2}=\mu_{3}=0.1$. The learning rates are 1e-3 and 5e-3 for inner
and outer updating respectively, and Adam [31] is employed as the optimizer.
The code is available on github.com/ckjzsa/SF-HGTL.

###  V-B Baselines

We first select several traditional statistical models and state-of-the-art
deep learning methods for comparison:

  * •

ARIMA [32]: Autoregressive Integrated Moving Average is a classic method for
time-series prediction and merely considers linear relations among data.

  * •

GRU [33]: Gated Recurrent Unit is a popular deep learning method to capture
sequential dependency of data.

  * •

TGCN [14]: TGCN employs GCN to capture the spatial features, followed by GRU
to learn temporal dependency.

Above methods merely utilize target data for model learning and do not involve
the knowledge transfer process. Next, we pick several transfer learning models
for comparison:

  * •

Fine-tuned Model: As a natural idea, we first train the base learner through
source cities, and then fine-tune the model based on target cities.

  * •

MAML [20]: As mentioned before, MAML uses bi-level optimization for parameter
initialization, and the base learner is TGCN.

  * •

ST-GFSL [8]: ST-GFSL generates non-shared parameters based on node-level meta-
knowledge. Parameter matching is implemented to retrieve similar features from
source cities.

  * •

CrossTReS [25]: CrossTReS proposed a selective transfer learning framework to
pick beneficial knowledge from the source domain by introducing a weighting
network. Besides, it is suitable to handle multi-graph spatio-temporal
prediction problems.

Note the last two transfer learning methods develop models that focus on
spatial-temporal knowledge transfer on graphs. Moreover, since most methods do
not consider multiple graphs, we parallelly use multiple models with different
semantic graphs followed by concatenation and a prediction head to predict
future traffic status.

###  V-C Experimental Results

Table II and III show the experimental results of taxi pickup/dropoff and
metro passenger flow prediction. The best result is bold, and the second-best
result is underlined. Generally, deep learning methods outperform traditional
methods and transfer-based methods further improve model performance. Although
ST-GFSL model considers spatial-temporal patterns, it does not utilize
semantic information and hence performs worse than CrossTReS and SF-HGTL
models.

For taxi volume prediction, we can find that CrossTReS outperforms SF-HGTL for
short-term prediction, but has worse results for long-term prediction. One
possible reason is that CrossTReS applies selection mechanism to avoid
negative transfer, the re-weighting method works well when the prediction
period is short but suffers more uncertain for long-term prediction. As a
contrast, our SF-HGTL stores meta-knowledge in the MK graphs, and is more
powerful to capture long-term traffic patterns. For metro passenger flow
prediction, CrossTReS has relatively lower RMSE for the transfer from HZMetro
to SHMetro, while our SF-HGTL model has lower MAE. Note that the size of
HZMetro dataset is smaller than that of SHMetro, we can conclude that
CrossTReS captures peak traffic patterns better than SF-HGTL, and SF-HGTL is
better at fitting general traffic patterns when the data size of the source
domain is small. However, when the transfer is from SHMetro to HZMetro, i.e.
source domain has sufficient data, SF-HGTL outperforms other methods almost in
every metric.

TABLE II: The experimental results for taxi pickup/dropoff prediction

Baseline |  NY-Taxi$\xrightarrow{}$ DC-Taxi | CHI-Taxi$\xrightarrow{}$DC-Taxi
---|---|---
RMSE |  MAE |  RMSE |  MAE
1 hour | 3 hour | 5 hour | 1 hour | 3 hour | 5 hour | 1 hour | 3 hour | 5 hour | 1 hour | 3 hour | 5 hour
ARIMA | 6.464 | 12.670 | 15.590 | 1.968 | 3.490 | 4.277 | 6.464 | 12.670 | 15.590 | 1.968 | 3.490 | 4.277
GRU | 5.604 | 9.461 | 11.223 | 1.872 | 2.869 | 3.411 | 5.614 | 9.461 | 11.231 | 1.844 | 2.858 | 3.466
TGCN | 4.960 | 6.993 | 7.860 | 1.841 | 2.624 | 2.938 | 4.862 | 7.093 | 7.696 | 1.841 | 2.517 | 2.723
Fine-tuned | 4.986 | 7.073 | 7.851 | 1.737 | 2.491 | 2.713 | 4.680 | 6.762 | 7.682 | 1.665 | 2.316 | 2.675
MAML | 4.990 | 7.071 | 7.807 | 1.721 | 2.544 | 2.548 | 4.759 | 6.849 | 7.640 | 1.795 | 2.353 | 2.667
ST-GFSL | 4.858 | 7.063 | 7.847 | 1.613 | 2.284 | 2.613 | 4.720 | 6.725 | 7.505 | 1.677 | 2.276 | 2.466
CrossTReS | 4.820 | 6.954 | 7.733 | 1.678 | 2.258 | 2.518 | 4.670 | 6.703 | 7.370 | 1.614 | 2.245 | 2.364
SF-HGTL | 4.966 | 6.618 | 7.271 | 1.626 | 2.041 | 2.390 | 4.707 | 6.667 | 7.302 | 1.658 | 2.068 | 2.266

TABLE III: The experimental results for metro passenger flow prediction

Baseline |  HZMetro$\xrightarrow{}$ SHMetro | SHMetro$\xrightarrow{}$HZMetro
---|---|---
RMSE |  MAE |  RMSE |  MAE
15min | 30min | 60min | 15min | 30min | 60min | 15min | 30min | 60min | 15min | 30min | 60min
ARIMA | 117.034 | 133.054 | 125.461 | 52.351 | 59.130 | 61.755 | 101.400 | 113.407 | 109.088 | 52.416 | 57.517 | 57.835
GRU | 69.921 | 88.188 | 143.522 | 32.146 | 38.309 | 54.856 | 62.723 | 69.639 | 100.848 | 33.177 | 35.978 | 48.669
TGCN | 65.438 | 65.723 | 80.925 | 33.467 | 33.826 | 40.022 | 60.093 | 63.850 | 77.728 | 32.535 | 34.510 | 41.912
Fine-tuned | 64.040 | 64.276 | 77.753 | 32.568 | 32.642 | 38.281 | 60.163 | 62.481 | 73.111 | 31.183 | 32.641 | 38.260
MAML | 63.668 | 64.380 | 77.734 | 32.505 | 32.763 | 38.418 | 58.617 | 61.199 | 72.674 | 31.776 | 33.212 | 39.080
ST-GFSL | 60.512 | 60.971 | 69.347 | 32.200 | 32.302 | 36.690 | 57.580 | 60.326 | 70.837 | 32.879 | 33.614 | 38.179
CrossTReS | 60.242 | 60.793 | 68.608 | 32.188 | 32.309 | 36.401 | 55.983 | 60.807 | 71.886 | 31.677 | 32.264 | 38.587
SF-HGTL | 60.440 | 61.197 | 69.210 | 30.017 | 31.033 | 35.400 | 54.390 | 57.567 | 71.243 | 29.317 | 30.647 | 36.823

###  V-D Ablation Study

We further conduct several experiments to prove the efficacy of each
component: (i) Remove hierarchical graph transformation, denoted as SF-HGTL-
HGT; (ii) Remove meta semantic nodes, denoted as SF-HGTL-MS; (iii) Only keep
task MK graph and remove other MK graphs, denoted as SF-HGTL-MK. We implement
five paralleled experiments based on metro passenger flow prediction
transferring from Hangzhou to Shanghai. Fig. 6 presents the results of five
experiments. The removal of hierarchical graph transformation significantly
decreases the model performance, which means the information of different
granularity is crucial to knowledge transfer. Moreover, the models without
meta semantic nodes and MK graphs also perform worse than our SF-HGTL model,
as these components store meta-knowledge extracted from various tasks.

Figure 6: Ablation study for three model components. The error bar shows the
standard deviation of five experiments.

###  V-E Sensitivity Analysis

In this section, we figure out the influence of several vital hyperparameters,
i.e. hidden dimension, node number in MK graphs, and clustering ratio. Five
experiments are conducted for each hyperparameter based on metro passenger
flow prediction, and we use MAE of three periods to measure the performance.
Fig. 7 presents the results. It can be found that: (i) Hidden size 32 has the
lowest MAE, while hidden size 128 has the highest MAE due to overfitting; (ii)
The number of centers determines the capability of MK graphs, the analysis
shows center number 5 and 15 have the best MAE performance. Note that
increasing centers leads to high computational complexity, so we choose center
number 5 in the study; (iii) As a crucial hyperparameter, the hierarchical
ratio reflects the clustering granularity, a high ratio means few clusters and
vice versa. The results demonstrate that the model performance peaks when the
hierarchical ratio is 0.3.

Figure 7: Sensitivity analysis for three hyperparameters. The error bar shows
the standard deviation of five experiments.

##  VI Conclusion

We propose a novel framework called SF-HGTL to achieve cross-city traffic
prediction. SF-HGTL is based on MAML framework with a modulating function to
dynamically adjust parameters of the base learner in terms of task
heterogeneity. To generate task embeddings, we employ hierarchical graph
transformation on various semantic graphs, and fuse semantic embeddings via
concatenation. In addition, we utilize meta semantic nodes and meta-knowledge
graphs to implement knowledge transfer in different levels. We conduct
experiments on taxi pickup/dropoff volume and metro passenger flow prediction,
and compare the model performance with several state-of-the-art methods. The
results show that our SF-HGTL outperforms other baseline models. Besides, the
ablation study and sensitivity analysis prove the effectiveness of our model.
Nonetheless, the current framework requires complete graphs in both source and
target cities, while the graphs may change with the introduction of new nodes,
e.g. construction of new stations or roads. Hence, how to transfer knowledge
from old nodes to new nodes under dynamic graphs is a non-trivial task. We
leave this for future work.

## Acknowledgment

We would like to acknowledge a grant from RGC Theme-based Research Scheme
(TRS) T41-603/20R, and a research grant (project N_HKUST627/18) from the Hong
Kong Research Grants Council under the NSFC/RGC Joint Research Scheme.

## References

  * [1] Y. Lv, Y. Duan, W. Kang, Z. Li, and F.-Y. Wang, “Traffic flow prediction with big data: a deep learning approach,” _IEEE Transactions on Intelligent Transportation Systems_ , vol. 16, no. 2, pp. 865–873, 2014.
  * [2] M. T. Asif, J. Dauwels, C. Y. Goh, A. Oran, E. Fathi, M. Xu, M. M. Dhanya, N. Mitrovic, and P. Jaillet, “Spatiotemporal patterns in large-scale traffic speed prediction,” _IEEE Transactions on Intelligent Transportation Systems_ , vol. 15, no. 2, pp. 794–804, 2013.
  * [3] D. Zhang, F. Xiao, M. Shen, and S. Zhong, “Dneat: A novel dynamic node-edge attention network for origin-destination demand prediction,” _Transportation Research Part C: Emerging Technologies_ , vol. 122, p. 102851, 2021.
  * [4] D. A. Tedjopurnomo, Z. Bao, B. Zheng, F. Choudhury, and A. K. Qin, “A survey on modern deep neural network for traffic prediction: Trends, methods and challenges,” _IEEE Transactions on Knowledge and Data Engineering_ , 2020\.
  * [5] L. Wang, X. Geng, X. Ma, F. Liu, and Q. Yang, “Cross-city transfer learning for deep spatio-temporal prediction,” _arXiv preprint arXiv:1802.00386_ , 2018.
  * [6] S. Wang, H. Miao, J. Li, and J. Cao, “Spatio-temporal knowledge transfer for urban crowd flow prediction via deep attentive adaptation networks,” _IEEE Transactions on Intelligent Transportation Systems_ , vol. 23, no. 5, pp. 4695–4705, 2021.
  * [7] H. Yao, Y. Liu, Y. Wei, X. Tang, and Z. Li, “Learning from multiple cities: A meta-learning approach for spatial-temporal prediction,” in _The World Wide Web Conference_ , 2019, pp. 2181–2191.
  * [8] B. Lu, X. Gan, W. Zhang, H. Yao, L. Fu, and X. Wang, “Spatio-temporal graph few-shot learning with cross-city knowledge transfer,” _arXiv preprint arXiv:2205.13947_ , 2022.
  * [9] B. L. Smith and M. J. Demetsky, “Traffic flow forecasting: comparison of modeling approaches,” _Journal of transportation engineering_ , vol. 123, no. 4, pp. 261–266, 1997.
  * [10] M. Van Der Voort, M. Dougherty, and S. Watson, “Combining kohonen maps with arima time series models to forecast traffic flow,” _Transportation Research Part C: Emerging Technologies_ , vol. 4, no. 5, pp. 307–318, 1996.
  * [11] X. Ma, Z. Tao, Y. Wang, H. Yu, and Y. Wang, “Long short-term memory neural network for traffic speed prediction using remote microwave sensor data,” _Transportation Research Part C: Emerging Technologies_ , vol. 54, pp. 187–197, 2015.
  * [12] X. Ma, Z. Dai, Z. He, J. Ma, Y. Wang, and Y. Wang, “Learning traffic as images: a deep convolutional neural network for large-scale transportation network speed prediction,” _Sensors_ , vol. 17, no. 4, p. 818, 2017.
  * [13] Y. Li, R. Yu, C. Shahabi, and Y. Liu, “Diffusion convolutional recurrent neural network: Data-driven traffic forecasting,” _arXiv preprint arXiv:1707.01926_ , 2017.
  * [14] L. Zhao, Y. Song, C. Zhang, Y. Liu, P. Wang, T. Lin, M. Deng, and H. Li, “T-gcn: A temporal graph convolutional network for traffic prediction,” _IEEE Transactions on Intelligent Transportation Systems_ , vol. 21, no. 9, pp. 3848–3858, 2019.
  * [15] Z. Pan, Y. Liang, W. Wang, Y. Yu, Y. Zheng, and J. Zhang, “Urban traffic prediction from spatio-temporal data using deep meta learning,” in _Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining_, 2019, pp. 1720–1730.
  * [16] F. Zhuang, Z. Qi, K. Duan, D. Xi, Y. Zhu, H. Zhu, H. Xiong, and Q. He, “A comprehensive survey on transfer learning,” _Proceedings of the IEEE_ , vol. 109, no. 1, pp. 43–76, 2020.
  * [17] J. Huang, A. Gretton, K. Borgwardt, B. Schölkopf, and A. Smola, “Correcting sample selection bias by unlabeled data,” _Advances in neural information processing systems_ , vol. 19, 2006.
  * [18] S. J. Pan, I. W. Tsang, J. T. Kwok, and Q. Yang, “Domain adaptation via transfer component analysis,” _IEEE transactions on neural networks_ , vol. 22, no. 2, pp. 199–210, 2010.
  * [19] J. Vanschoren, “Meta-learning: A survey,” _arXiv preprint arXiv:1810.03548_ , 2018.
  * [20] C. Finn, P. Abbeel, and S. Levine, “Model-agnostic meta-learning for fast adaptation of deep networks,” in _International conference on machine learning_. PMLR, 2017, pp. 1126–1135.
  * [21] A. Achille, M. Lam, R. Tewari, A. Ravichandran, S. Maji, C. C. Fowlkes, S. Soatto, and P. Perona, “Task2vec: Task embedding for meta-learning,” in _Proceedings of the IEEE/CVF international conference on computer vision_ , 2019, pp. 6430–6439.
  * [22] H. Yao, X. Wu, Z. Tao, Y. Li, B. Ding, R. Li, and Z. Li, “Automated relational meta-learning,” _arXiv preprint arXiv:2001.00745_ , 2020.
  * [23] F. Zhao and D. Wang, “Multimodal graph meta contrastive learning,” in _Proceedings of the 30th ACM International Conference on Information & Knowledge Management_, 2021, pp. 3657–3661.
  * [24] Q. Suo, J. Chou, W. Zhong, and A. Zhang, “Tadanet: Task-adaptive network for graph-enriched meta-learning,” in _Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining_, 2020, pp. 1789–1799.
  * [25] Y. Jin, K. Chen, and Q. Yang, “Selective cross-city transfer learning for traffic prediction via source city region re-weighting,” in _Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining_ , 2022, pp. 731–741.
  * [26] W. L. Hamilton, R. Ying, and J. Leskovec, “Representation learning on graphs: Methods and applications,” _arXiv preprint arXiv:1709.05584_ , 2017.
  * [27] D. Chen, Y. Lin, W. Li, P. Li, J. Zhou, and X. Sun, “Measuring and relieving the over-smoothing problem for graph neural networks from the topological view,” in _Proceedings of the AAAI Conference on Artificial Intelligence_ , vol. 34, no. 04, 2020, pp. 3438–3445.
  * [28] Z. Ying, J. You, C. Morris, X. Ren, W. Hamilton, and J. Leskovec, “Hierarchical graph representation learning with differentiable pooling,” _Advances in neural information processing systems_ , vol. 31, 2018.
  * [29] L. Liu, J. Chen, H. Wu, J. Zhen, G. Li, and L. Lin, “Physical-virtual collaboration modeling for intra-and inter-station metro ridership prediction,” _IEEE Transactions on Intelligent Transportation Systems_ , 2020\.
  * [30] C. Morris, M. Ritzert, M. Fey, W. L. Hamilton, J. E. Lenssen, G. Rattan, and M. Grohe, “Weisfeiler and leman go neural: Higher-order graph neural networks,” in _Proceedings of the AAAI Conference on Artificial Intelligence (2019)_ , vol. 33, no. 01, 2019, pp. 4602–4609.
  * [31] D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” _arXiv preprint arXiv:1412.6980_ , 2014.
  * [32] R. J. Hyndman and G. Athanasopoulos, _Forecasting: principles and practice_. OTexts, 2018.
  * [33] K. Cho, B. Van Merriënboer, D. Bahdanau, and Y. Bengio, “On the properties of neural machine translation: Encoder-decoder approaches,” _arXiv preprint arXiv:1409.1259_ , 2014.

|  Kehua Chen received a B.S. degree in civil engineering from Chongqing
University, a dual M.S. degree in Environmental Science from both University
of Chinese Academy of Sciences and University of Copenhagen, and is now a
Ph.D. student with the Division of Emerging Interdisciplinary Areas, Hong Kong
University of Science and Technology. His research interests include spatial-
temporal data mining, urban computing, driver behavior analysis and modeling.
---|---
|  Jindong Han is currently pursuing his Ph.D. degree at the Hong Kong
University of Science and Technology. His research interests include
spatiotemporal data mining, graph representation learning, and urban
computing. He has published several research papers in prestigious conferences
and journals, such as TKDE, AAAI, VLDB, and KDD.
---|---
|  Siyuan Feng received a B.S. degree in civil engineering from Tongji
University, a M.S. degree in Civil Engineering from University of California,
Berkeley, and is now a Ph.D. candidate with the Department of Civil and
Environmental Engineering, Hong Kong University of Science and Technology. His
research interests include economical modelling of multi-modal mobility, deep
learning in spatio-temporal traffic forecasting, reinforcement learning in
multi-model transportation and urban computing.
---|---
|  Hai Yang is currently a Chair Professor at The Hong Kong University of
Science and Technology. He is internationally known as an active scholar in
the field of transportation, with more than 260 papers published in SCI/SSCI
indexed journals and an H-index citation rate of 56. Most of his publications
appeared in leading international journals, such as Transportation Research
and Transportation Science. Prof. Yang is in the Distinguished Journal
Editorial Board of Transportation Research Part B: Methodological, a top
journal in the field of transportation.
---|---