# Heterogeneous Graph Neural Networks with Post-hoc Explanations for Multi-
modal and Explainable Land Use Inference

Xuehao Zhai  Junqi Jiang  Adam Dejl  Antonio Rago  Fangce Guo  Francesca Toni
Aruna Sivakumar

###### Abstract

Urban land use inference is a critically important task that aids in city
planning and policy-making. Recently, the increased use of sensor and location
technologies has facilitated the collection of multi-modal mobility data,
offering valuable insights into daily activity patterns. Many studies have
adopted advanced data-driven techniques to explore the potential of these
multi-modal mobility data in land use inference. However, existing studies
often process samples independently, ignoring the spatial correlations among
neighbouring objects and heterogeneity among different services. Furthermore,
the inherently low interpretability of complex deep learning methods poses a
significant barrier in urban planning, where transparency and extrapolability
are crucial for making long-term policy decisions. To overcome these
challenges, we introduce an explainable framework for inferring land use that
synergises heterogeneous graph neural networks (HGNs) with Explainable AI
techniques, enhancing both accuracy and explainability. The empirical
experiments demonstrate that the proposed HGNs significantly outperform
baseline graph neural networks for all six land-use indicators, especially in
terms of ‘office’ and ‘sustenance’. As explanations, we consider feature
attribution and counterfactual explanations. The analysis of feature
attribution explanations shows that the symmetrical nature of the ‘residence’
and ‘work’ categories predicted by the framework aligns well with the
commuter’s ‘work’ and ‘recreation’ activities in London. The analysis of the
counterfactual explanations reveals that variations in node features and types
are primarily responsible for the differences observed between the predicted
land use distribution and the ideal mixed state. These analyses demonstrate
that the proposed HGNs can suitably support urban stakeholders in their urban
planning and policy-making. The source code will be available at
https://github.com/xuehao0806/GNN-land-use.

###### keywords:

Urban information fusion , Heterogeneous Graph Neural Networks , Explainable
AI

††journal: Elsevier

[label1]organization=Imperial College London, Department of Civil and
Environmental Engineering, addressline=Exhibition Rd, South Kensington,
city=London, postcode=SW7 2AZ, country=UK [label2]organization=Imperial
College London, Department of Computing, addressline=South Kensington Campus,
city=London, postcode=SW7 2AZ, country=UK

##  1 Introduction

Land use is a term used by urban planners to describe the function of human-
made spaces in which people live, work, and recreate on a day-to-day basis.
Typically, city planners are responsible for determining land use plans,
shaping a city’s layout by dictating what types of buildings can be located in
a given space. However, due to the complex and dynamic nature of the urban
environment, the actual function — both activity pattern and intensity — may
deviate from the intentions of land use planning [1, 2, 3]. For instance, an
area initially planned as a commercial zone might gradually transition into a
mixed-use area because of population growth and changes in housing demands. As
the cities dynamically evolve, this deviation between land use planning and
actual usage may widen, leading to inefficient use of resources, community
dissatisfaction and social inequality [4, 5]. To support sustainable urban
planning and related policies, stakeholders need accurate and effective tools
to detect the spatial distribution of human activities.

Urban land use inference has been a challenging task for decades. Early
studies primarily used simple statistical methods (e.g., linear regressions)
[6, 7] and simulation-based methods (e.g., Cellular Automata) [8, 9] with
survey data to explore urban growth patterns and dynamics with rule-based
interactions. However, these traditional methods rely on over-simplified
assumptions, struggling to accurately reflect complex real-world scenarios,
especially for large metropolitan areas. In recent years, the advent of the
era of big data has provided a new paradigm for this problem. Emergent sensor
and location technologies have facilitated the collection of human activity-
based data, such as mobile phone and mobility records. These passive data
sources offer alternative ways for monitoring people’s daily activities,
facilitating the description of the urban space function. Furthermore,
advanced AI models have shown significant promise in handling multi-modal and
non-linear data in urban systems [10, 11]. These opportunities provide a
strong foundation for quantitatively detecting urban land use. In the past
decade, 23% (38 out of 165) of ML-based research papers in urban spatial
studies focused on inferring land use and urban form [12], which shows that
this problem has gradually become one of the main branches of AI applications
in the field of urban studies.

Despite these recent advances, inferring land use in an accurate, explainable
and thus trustworthy manner remains difficult in practice. The challenges in
existing research can be summarised from three perspectives: data selection,
methodology and post-hoc analysis.

A primary challenge lies in determining what type of activity-based data is
efficient and how to fuse multi-modal data reasonably. Many activity-based
datasets [1, 13] have been used in urban land use inference. However, inherent
bias exists in many types of data when used for the representation of human
activity. For instance, the number of mobile calls or messages occurring in an
area could be affected by factors such as user occupation types and user
communication preferences, potentially skewing observed usage intensity.
Similar problems exist with social media data, which is strongly related to
the user’s age. Moreover, data involves user privacy, which is highly
restricted for commercial use in many countries, making these types of data
unavailable to many practical projects. Mobility data, on the other hand,
offers low-cost, real-time, and objective insights into people’s daily
movements. Meanwhile, travel demand has been systemically proven to be closely
related to land use patterns [14, 15]. For example, a higher volume of bus
passengers recorded during weekday peak hours suggests that the land use
surrounding this station is work-related or residential. While mobility data
can provide insights into daily human movements and associated land use
patterns, a few questions remain about a) which modes of transportation data
are most indicative of land use; b) how to aggregate this data across time and
space effectively; and c) how to integrate data from various transportation
modes to form a comprehensive analysis.

Another challenge lies in determining how to address the spatial dependency
inherent in urban activities and the heterogeneity among different mobility
services. Urban activities tend to cluster, exhibiting continuity along road
networks and potential disruptions by physical barriers like rivers, railways
and highways [16]. Moreover, different types of mobility data contribute to
different degrees of understanding surrounding land uses. Large transit hubs
primarily facilitate transfers and are closely tied to adjacent transport
services, whereas smaller nodes are crucial for serving ‘first or last mile’
travel and are strongly linked to local residential and work activities [3].
Most deep learning models process samples independently, overlooking the
spatial dependency between samples and their surrounding objects. Although
recent studies [17, 18] try to solve this problem by employing homogeneous
graph networks, these methods often fail to encapsulate the multi-level nodes
(e.g., bike stops, bus stations) and edges (e.g., road networks, tube
networks) in complex urban areas.

A third challenge lies in the fact that establishing explainability is also
essential in policy and land use studies in order to build trust among
government planners and policymakers. Effective land use models must be
accurate, reliable, accountable for anomalies, and capable of extrapolation
[19]. However, the black-box nature of deep learning models often hampers
their trustworthiness in real-world applications. Therefore, a (black-box)
model’s credibility with planners needs to be established by systematically
proving these properties through post-hoc analysis, thus reinforcing their
utility in practical urban planning contexts.

Motivated by these challenges, this paper makes contributions in three key
aspects: integrating mobility data, fusing multiple sources of mobility data
from different travel modes using heterogeneous graph neural networks, and
enhancing model explainability by using post-hoc explainable AI methods.
Specifically, we make the following contributions:

  * 1.

We build a heterogeneous graph to integrate mobility data from multiple travel
modes, including bus, tube (ie London underground) and sharing-bike, as well
as topology network data, as shown in Figure 1. These rich information sources
enable deep learning models to learn spatial representations that capture the
heterogeneity of objects within the urban transport system.

  * 2.

We pioneer the application of Heterogeneous Graph Networks (HGNs) for data
fusion and land use inference tasks, addressing the spatial dependency of land
use features and the heterogeneity among different types of nodes and edges
(Figure 2). Our findings indicate that the proposed method markedly enhances
predictive performance over traditional neural networks and homogeneous graph
neural networks.

  * 3.

We pioneer the usage of feature attribution explanations in land use inference
to empower explainability, addressing stakeholders’ concerns as to how
mobility distribution in a day could affect land use predictions. We show that
our model’s behaviours can be verified against the stakeholders’ expectations
by highlighting the importance of different parts in the temporal patterns of
human activity in London (UK).

  * 4.

We also define a new counterfactual explanation notion specifically suitable
for explaining HGNs in land use inference tasks. We demonstrate through
example analysis that our counterfactual explanations can be used to reveal
changes required for the input to achieve the ideal mixed land use prediction.
Through experiments, we also use such explanations to investigate the
contributions of different elements in the input data to the differences
between the model’s predictions and the ideal mixed land use states.

The remainder of this paper is organised as follows: Section 2 presents a
literature review of relevant research on land use analysis, graph deep
learning, and explainable AI; Section 3 describes the data collection and pre-
processing steps; Section 4 outlines the methodology for Heterogeneous Graph
Modelling framework and post-hoc explanations methods; Section 5 reports the
results and performance metrics; Section 6 discusses the implications of our
findings, limitations, and recommendations for future research.

##  2 Literature Review

This section will begin by reviewing the related work in land use inference.
We then overview work on multi-modal data fusion and explainable AI.

###  2.1 Land use inference

In the literature on land use, early research used simple statistical
approaches (e.g., linear regressions) or simulation-based models (e.g.,
cellular automata) to understand urban growth patterns. Due to the development
of sensor and location technologies, land use modelling has evolved from
relying on survey data to incorporating activity-based big data (e.g., social
media data, mobile data and transport data), enhancing understanding of urban
dynamics in a fine-grained manner. In line with this change, there has been a
significant shift from traditional model-driven to advanced data-driven
methods. For example, Toole et al [1] applied call frequency data and
correlation analysis to infer land use types in Boston, USA. The latest trend
in urban land use inference incorporates big data and machine learning
techniques to provide highly accurate insights and dynamic forecasts of land
use. Hu et al [17] employed vehicle GPS and trajectory data, using Graph
Convolutional Neural Networks, to categorise road network patterns in Beijing
into commercial, public, and traffic types. Similarly, Sun et al [20] applied
mobile phone data and deep convolutional autoencoders to deduce various land
use types—residential, commercial, business, and industrial—in Wuhan, China. A
specific summary of activity data-based research in this domain is given in
Table LABEL:table1 below, where the first three studies use mobile data, and
the subsequent ones use mobility data.

Table 1: Summary of papers on data-driven land use inference Paper |  Scenario |  Data |  Method |  Land use types
---|---|---|---|---
[1] |  Boston, USA |  Mobile phone data |  Random forests |  Residential, commercial, industrial, parks
[21] |  Harbin, China |  Call frequencies |  Correlation analysis |  Work, residential
[20] |  Wuhan, China |  Mobile phone calls |  Deep Convolutional Autoencoder |  Residential, commercial, business, industrial, mixed
[2] |  Beijing, China |  GPS Trajectory |  Topic-based model |  Education, residential, entertainment, mixed, tourist interest
[3] |  San Francisco, USA |  Shared cycling ridership |  Neural network |  Residential, work, consumption, transport
[22] |  Hangzhou, China |  Public bike ridership, Taxi GPS |  Latent semantic classification |  Residential, business, industrial, administration
[17] |  Beijing, China |  Vehicle GPS and vehicle trajectory |  Graph Convolutional Neural Network |  Commercial, public, traffic
[23] |  Beijing, China |  Taxi trajectory and bus ridership |  Latent clustering; Noise reduction |  Residential, commercial, mixed
[24] |  Chengdu, China |  Online Car-Hailing; POI |  Ensemble empirical modal decomposition |  Business, office, residential, tourist interest
[18] |  Seoul, Korea |  Taxi ridership |  Statistical methods |  Residential, industrial, commercial, green
[25] |  Shanghai, China |  Metro ridership |  Spatiotemporal similarity |  Residential, employment, transport, mixed
[26] |  Calgary, Canada |  GTFS and APC data |  Statistical methods |  Residential, commercial, recreational, industrial, institutional
[27] |  Shenzhen, China |  Surround buildings and activities data |  Transformer |  Residential, commercial, recreational, industrial, institutional

A recent review paper found that 23% (38 out of 165) of AI-based research
papers in urban spatial studies focused on inferring land use and urban form
[12], which showed that inferring land use has become one of the main branches
of AI application in the field of city planning domain. However, this field is
still in its early developmental stages, and in practice faces numerous
challenges in maintaining accuracy and trustworthiness.

One major gap lies in fusing multi-modal data to overcome the potential bias
and incompleteness of each data source. Given Table LABEL:table1, two forms of
mobility data typically used are: trajectory data and ridership data (inbound
and outbound flow at the station level). Trajectory data reflects usage
intensity at a road level but fails to accurately represent the land use
function of surrounding space. For example, a highway from a suburban area to
a city centre might predominantly serve daily commuters, but this does not
necessarily mean there are significant residential or work facilities along
this highway. On the other hand, ridership data, which measures the flow of
passengers into and out of stations, provides a more intuitive reflection of
travel related to human activities. However, a single type of transit facility
is typically not able to cover the entire urban space. Data fusion can be an
effective way to address the lack of spatial coverage and potential biases.
Yet, only a few studies [23] have performed data fusion (e.g., ensemble
methods at the output level) to merge different datasets, which limits the
exploration of intrinsic spatial heterogeneity and complementary relationships
within the mobility system.

Another gap exists in the methods for improving the explainability of land use
inference models. The successful application of AI in critical domains largely
depends on whether the model is explainable and trustworthy. However,
explainability often represents a trade-off with accuracy [28] and
trustworthiness has been shown to be a complex phenomenon which is affected by
explainability in many ways [29, 30, 31, 32, 33]. Indeed, the black-box nature
of complex data-driven models often hampers their adoption in real-world
applications, particularly in urban planning and policy-making where
transparency and accountability are highly valued [34]. Besides, stakeholders
anticipate that the model can go beyond the prediction of the outcome; they
also expect it to be able to respond to hypothetical or “what-if” scenarios,
like “what efforts can be made to achieve sustainable land use planning”.
However, few land use inference studies have provided explainable modelling or
post-hoc explanations for their proposed models.

###  2.2 Multi-modal data fusion

The need for fusion of multi-modal data for better accuracy and robustness is
not unique to land use inference but also exists in many efforts for the
development of smart and sustainable cities, such as traffic prediction [35,
36], energy management [37, 38], and healthcare [39]. In urban studies,
commonly used fusion strategies can be divided into the following categories:
fuzzy logic-based [11, 40], Bayesian-based [41, 42], ensemble-based [43, 44],
and graph-based [11, 45, 46]. For the mobility data discussed in this paper,
graph-based methods like GraphSages [47] and Graph Attention Networks [48] are
particularly effective due to the strong ability to process spatial dependency
among the facilities in a large-scale graph form. For example, Hu et al [17]
introduced a Graph Convolutional Network (GCN) to understand the social
function of road segments, showing significant accuracy compared with
traditional machine learning.

To better characterise the spatial heterogeneity and hierarchy inside the
mobility system, we propose a novel hetero-graph deep learning framework for
mobility data fusion. As an extended version of Graph Neural Networks (GNNs) –
Heterogeneous Graph Networks (HGNs) are designed to handle graph structures
with multiple types of nodes and edges. Existing studies have proven that HGNs
are highly effective in fusing multi-modal data and representing complex graph
structures in various domains, such as recommendation systems [49], biomedical
structures [50], and social networks [51]. In scenarios like urban systems,
HGNs have been applied to critical problems like traffic prediction, and
signal control with significant performance improvement [36, 52]. However, no
research has been undertaken so far on techniques related to the use of HGNs
in land use inference. This paper proposes a novel framework using an
attention-based heterogeneous graph neural network model to effectively
represent the complex interactions within multi-modal mobility systems.

###  2.3 Explainability

Recent works on graph-based explanation have provided new tools for
understanding the function of elements in heterogeneous mobility graphs. Given
the requirement of this paper, two types of analytic XAI methods are
considered: feature attribution analysis and counterfactual analysis.

  * 1.

Feature attribution methods quantify the approximate importance of individual
input features on a particular model prediction through an attribution value.
These techniques, such as Integrated Gradients [53] and SHapley Additive
exPlanations (SHAP) [54], clarify the roles of input features in the
prediction of the outcome and have been successfully used in understanding
graph elements (nodes and edges) in many critical domains, such as molecular
science [55, 56] and Internet of Things [57].

  * 2.

Counterfactual explanations demonstrate which changes are needed in the
factual input to achieve a different output prediction [58]. These methods
have been used in domains like molecular science [59] and recommendation
systems [60] to understand how potential changes in the graph might result in
desired outcomes.

Although these XAI methods have been used to explain GNNs in many critical
domains, no studies have applied them to the land use inference problem.
Facing this gap, this paper pioneers the use of the integrated-gradient method
to analyse how mobility distribution influences the inferred land use types.
Additionally, we introduce a new counterfactual explanation notion designed
specifically for heterogeneous graph structures, aimed at identifying
necessary minimum input modifications to achieve the ideal mixed land use
state.

##  3 Preliminaries

This section introduces the research problem and the basic concepts for
building heterogeneous graph models. The notation used throughout this paper
is shown in Table 2.

Table 2: Notation and Descriptions. The table is divided into three sections: the first section includes general operations; the second section includes components of the graph; and the third section includes elements related to the learning problem.  Notation |  Description
---|---
$\oplus$ |  A concatenation operation
$\lvert*\rvert$ |  The cardinality of a set
$\mathcal{G}$ |  A graph
$\mathcal{V}$ |  A set of nodes
$\mathcal{E}$ |  A set of edges
$\mathcal{A}$ |  A set of node types
$\mathcal{R}$ |  A set of edge types
$v_{i}\in\mathcal{V}$ |  A single node with subscript $i$ (also referred to simply as $i$)
$e_{ij}\in\mathcal{E}$ |  An edge representing a pair of nodes $(v_{i},v_{j})$ iff $v_{i}$ and $v_{j}$ are connected
$\phi$ |  A node-to-type mapping
$\psi$ |  An edge-to-type mapping
$\mathcal{F}$ |  A set of features of each node
$\mathcal{T}$ |  A set of land use targets
$x_{i,j}$ |  The $j$-th feature for node $i$
$h^{(0)}_{i}$ |  The initial node representation after the feature transformation
$h^{(l)}_{s}$ |  The updated representation of target node $s$ at layer $l$
$\Theta$ |  The set of parameters for training
$W_{\phi(i)}^{\text{P}}$ |  The initial projection matrix for node type $\phi(i)$
$W_{\tau,\phi(s)}^{\text{MH}}$ |  The multi-head matrix for source node type in head $\tau$
$W_{\psi(e)}^{\text{MP}}$ |  The message passing matrix for edge type $\psi(e)$
$W_{\tau}^{\text{Q}},W_{\tau}^{\text{K}},W_{\tau}^{\text{A}}$ |  The query, key and attention matrices for head $\tau$
$W^{\text{AG}}_{\phi(t)}$ |  The aggregation matrix for target node type $\phi(t)$
$m^{(l)}(s,e,t)$ |  The message representation from $v_{s}$ to $v_{t}$ through edge $e$ at layer $l$
$\alpha^{(l)}(s,e,t)$ |  The attention weights from $v_{s}$ to $v_{t}$ through edge $e$ at layer $l$
$\xi$ |  The scaling factor in the attention mechanism
$\theta$ |  The number of heads in the multi-head mechanism

We begin by defining heterogeneous graphs.

######  Definition 1.

Graph: A graph $\mathcal{G}$ is represented as
$(\mathcal{V},\mathcal{E})$,where $\mathcal{V}$ is a set of nodes (or
vertices), i.e., $\mathcal{V}=\\{v_{1},\ldots,v_{|\mathcal{V}|}\\}$, and
$\mathcal{E}$ denotes a set of edges connecting nodes, i.e.,
$\mathcal{E}=\\{e_{1},\ldots,e_{|\mathcal{E}|}\\}$. Each edge
$e\in\mathcal{E}$ is a pair of nodes $(v_{i},v_{j})$ iff $v_{i}$ and $v_{j}$
are connected.

In a heterogeneous graph nodes and/or edges belong to different types, as
follows:

######  Definition 2.

Heterogeneous graph: Let $\mathcal{A}$ denote a set of node types and
$\mathcal{R}$ denote a set of edge types, such that
$|\mathcal{A}|+|\mathcal{R}|>2$. Then a heterogeneous graph $\mathcal{G}$ is
$(\mathcal{V},\mathcal{E})$ such that there exists a function
$\phi:\mathcal{V}\rightarrow\mathcal{A}$ that maps each node with its
corresponding node type and a function
$\psi:\mathcal{E}\rightarrow\mathcal{R}$ that maps each edge with its
corresponding edge type.

######  Definition 3.

Meta relation: The meta relation for an edge $e=(v_{s},v_{t})$ linked from
source node $v_{s}$ to target node $v_{t}$ is denoted as
$\langle\phi(s),\psi(e),\phi(t)\rangle$.

Urban mobility systems can be conceptualised as heterogeneous graph structures
with multiple types of service facilities in the form of nodes (e.g., tube and
bus stations) and spatial connections among them in the form of edges (e.g.,
transit routes). Specifically, we consider two categories of edges: edges in
the road network and edges in the transit networks. When travellers transfer
between different types of stations, they usually need to walk. Therefore, as
shown in Figure 1, we regard the connections across various types of nodes as
the shortest path on the road network (①, ②, ③). For edges between nodes of
the same type, there may be shortest routes in a road network (④) or
connecting paths in a specific network, such as a tube network or a bus
network (⑤ and ⑥).

Given the complexities in the data, this paper aims to build an explainable
heterogeneous graph-based framework for the land use inference problem. To
begin with, the research is framed as a multi-task regression problem. This
setting stems from practical considerations: compared with merely categorising
land use types, it is more useful for stakeholders to obtain the intensities
of different land use because of the need to analyse diversity [3].

Mathematically, we build a multivariate mapping function $\mathcal{M}$ that
regresses land use intensity based on daily mobility distribution and urban
heterogeneous graph structure, shown as follows:

$Y=\mathcal{M}_{\Theta}\left(\mathcal{G};X\right)$ (1)

where the parameters set for training are $\Theta$, the nodes feature
$X\in\mathbb{R}^{|\mathcal{V}|\times|\mathcal{F}|}$ ($\mathcal{F}$ is the set
of features of each node111Concretely, we denote nodes features as the daily
passenger inbound data of each station (15-minute interval ridership from 6:00
to 22:00, forming 64 input features).) represents the mobility inbound or
outbound variables at different time intervals, such as ‘15-min passengers
inflow in a typical day’222A ‘typical day’ refers to the mean values of data
collected over multiple statistical periods (weeks, months) under normal, non-
exceptional conditions [3]. for all nodes in $\mathcal{G}$.
$Y\in\mathbb{R}^{|\mathcal{V}|\times|\mathcal{T}|}$ ($\mathcal{T}$ is the set
of targets333Concretely, we use, as $\mathcal{T}$, the land use indicators in
this task (e.g., office and residence).) denotes the multi-regression targets.
The goal of land use inference is to find an optimised set of $\Theta^{*}$ to
minimise the loss between the estimated land use indicators and land use
labels:

$\Theta^{*}=\underset{\Theta}{\arg\min}\frac{1}{n}\sum_{i=1}^{n}\operatorname{loss}(\mathcal{F}_{\Theta}\left(\mathcal{G};X\right),\hat{Y})$
(2)

where $\hat{Y}\in\mathbb{R}^{|\mathcal{V}|\times|\mathcal{T}|}$ refers to the
land use ground-truth labels and $n$ refers to the number of samples in the
training dataset.

Figure 1: This figure depicts a heterogeneous mobility network featuring meta-
relations that highlight various connection types. The left panel displays a
central London area with nodes coloured by different types of mobility
services, representing tube stations (blue), bus stops (green), and bike
stations (orange). The middle panel presents a legend for road routes (solid
black lines), tube routes (dashed blue lines), and bus routes (dashed green
lines), accompanied by daily ridership graphs for each mode of transport. The
right panel outlines meta-relations with nodes and their connections,
illustrating the complexity of information in a multi-modal mobility network.

##  4 Methodology

Figure 2 illustrates the framework of this methodology, divided into three
main parts: a) Graph Building and Sampling: synthesising traffic data into
typical daily patterns, collecting edge information from a hierarchical urban
mobility network, and sampling heterogeneous subgraphs; b) Graph Neural
Network Modelling: processing these subgraphs through a HGN with layer-wise
and residual connections, embedding the output into a feature vector, and
using a fully connected linear layer to predict land use targets; c)
Explanation Techniques: using feature attribution explanations to determine
the contribution of input features to the predictions and counterfactual
explanations to explore the impact of changes in the graph structure on
prediction outcomes.

Figure 2: Overview of our framework for land use inference based on multi-
mobility systems.

###  4.1 Heterogeneous Attention Embedding

Given the rich mobility information and road topology information, our primary
focus is on effectively embedding structural data and node-level mobility
features within urban mobility networks. Inspired by the recent progress of
HGNs in social network analysis [61], we propose a Heterogeneous Graph Encoder
based on HGNs. The HGN module aims to learn node representations through
predetermined meta-relations. To model the influence of various node types, we
utilise a multi-head attention mechanism.

Firstly, we define a node feature transformation function that aligns features
$x_{i}$ of nodes $v_{i}$ to a unified feature space, based on their node types
$\phi(i)$. This is formulated as:

$h^{(0)}_{i}=W_{\phi(i)}^{\text{P}}\cdot x_{i},$ (3)

where $W^{\text{P}}$ is a type-specific linear projection matrix. Through
this, we derive the initial node representation $h^{(0)}_{i}$ for node $i$.

Subsequently, we implement a multi-head mechanism to compute the message
representation $m^{(l)}(s,e,t)$ at layer $l\geq 0$ from source nodes $v_{s}$
to target nodes $v_{t}$. This process accommodates the types of nodes
$\phi(s),\phi(t)$ and edges $\psi{(e)}$ in the heterogeneous graph, as
expressed:

$m^{(l)}(s,e,t)=\underset{\tau\in[1,\theta]}{\oplus}\left(\left(W_{\tau,\phi(s)}^{\text{MH}}h_{s}^{(l-1)}\right)W_{\psi(e)}^{\text{MP}}\right)$
(4)

Here, $\oplus$ represents the concatenation operation, and $\theta$ the total
number of heads, while $W_{\tau,\phi(s)}^{\text{MH}}$ and
$W_{\psi(e)}^{\text{MP}}$ are matrices designated for processing based on node
and edge types.

Next, we apply a multi-head attention framework to derive attention weights
$\alpha^{(l)}(s,e,t)$, facilitating the interaction between source $v_{s}$ and
target $v_{t}$ nodes via edges $\psi(e)$, described as follows:

$\text{head}^{(l)}_{\tau}(s,e,t)=\left(\left(W_{\tau}^{\text{Q}}h^{(l-1)}_{s}\right)^{T}W_{\tau}^{\text{A}}\left(W_{\tau}^{\text{K}}h^{(l-1)}_{t}\right)^{T}\right)\frac{1}{\sqrt{\xi}},$
(5)

$\alpha^{(l)}(s,e,t)=\text{Softmax}\left(\underset{\tau\in[1,\theta]}{\oplus}\text{head}^{(l)}_{\tau}(s,e,t)\right),$
(6)

where $W_{\tau}^{\text{Q}},W_{\tau}^{\text{K}}$, and $W_{\tau}^{\text{A}}$ are
the linear projection matrices per head $\tau$, tailored according to node and
edge types, and $\xi$ is an adaptive scaling factor for the attention
mechanism.

Finally, the information is aggregated from the neighbours of the target node
with attention weights to update the representation of the target node,
expressed as:

$h^{(l)}_{t}=W^{\text{AG}}_{\phi(t)}\left(\sum_{v_{s}\in\mathcal{N}(v_{t})}\left(\alpha^{(l)}(s,e,t)\cdot
m^{(l)}(s,e,t)\right)\right)+h^{(l-1)}_{t},$ (7)

with $W^{\text{AG}}$ as the aggregation-specific linear matrix considering the
type of the target node. Here, $\mathcal{N}(v_{t})$ denotes the set of
neighbour nodes of the target node $v_{t}$.

###  4.2 Explainable AI methods for post-hoc explanations

This section discusses the XAI methods to enhance explainability for land use
inference: feature attribution analysis and counterfactual analysis. Two main
reasons drive this need: stakeholders, particularly in urban planning and
development, need to understand the importance (to decision-making) of
specific elements in predictive models, especially for intricate input-outcome
relationships. This justifies the use of feature attribution explanations.
Additionally, these stakeholders seek to identify minimal changes that can be
made to achieve desired outcomes, such as a community with balanced land use.
This is our reason for choosing to also include counterfactual explanations.
Details of these two methods are shown follow.

####  4.2.1 Feature attribution methods

The first class of techniques we use to explain the predictions of our model
are _feature attribution methods_. These techniques quantify the approximate
importance of the individual input features on a particular model prediction
through linear _feature attribution scores_. Such scores can provide
invaluable insights regarding the reasoning of deep learning models and
uncover possible issues or biases [62, 63].

In the context of explaining an HGN model $\mathcal{M}$ applied to a
heterogeneous graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, we can formalise
the feature attribution scores as follows. Given a target node in the graph
$v_{i}\in\mathcal{V}$ and a target output $y_{i,j}$, our goal is to compute
the attribution scores $S\in\mathbb{R}^{|\mathcal{V}|\times|\mathcal{F}|}$
estimating the importance of every node and feature combination for the model
output $y_{i,j}$. Intuitively, the element $S_{k,l}$ of the attribution score
matrix provides an estimate of how much the $l$-th feature of the $k$-th node,
$x_{k,l}$, affected the $j$-th output at the $i$-th node, $y_{i,j}$. To get a
more holistic view of the importance of the different features, we will also
consider the aggregated attribution scores $a\in\mathbb{R}^{|\mathcal{F}|}$
where $a_{k}=\sum^{|\mathcal{V}|}_{i=0}S_{i,k}$. Each element of the
aggregated attribution scores vector estimates how much a particular input
feature affected the target output when considering its combined effect from
all the nodes in the graph.

In our work, we use two different feature attribution methods for explaining
our HGN model — Gradient $\cdot$ Input [64] and Integrated Gradients [65].
Gradient $\cdot$ Input is a simple gradient-based attribution method defined
as follows, in our setting:

######  Definition 4.

Gradient $\cdot$ Input Explanation. Given an explained model $\mathcal{M}$, an
input graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, a target node
$v_{i}\in\mathcal{V}$ and a target output $y_{i,j}$, the Gradient $\cdot$
Input feature attributions scores are defined as:

$\displaystyle S^{G\cdot I}_{k,l}=x_{k,l}\cdot\frac{\partial y_{i,j}}{\partial
x_{k,l}}=x_{k,l}\cdot\frac{\partial\mathcal{M}(\mathcal{G})_{i,j}}{\partial
x_{k,l}}$

The advantage of Gradient $\cdot$ Input is its computational efficiency, its
conceptual simplicity as well as its good ability to faithfully capture the
behaviour of the model in the small region around the considered input [66].
However, the attributions produced by Gradient $\cdot$ Input may also be
unreliable, particularly if the function of the considered model is highly
irregular (resulting in a problem known as shattered gradients [67]) or
saturates for the given input (e.g., due to the predicted output already being
sufficiently high). These limitations are largely addressed by Integrated
Gradients explanations, which are defined as follows, in our setting:

######  Definition 5.

Integrated Gradients Explanation. Given an explained model $\mathcal{M}$, an
input heterogeneous graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, a target
node $v_{i}\in\mathcal{V}$, a target output $y_{i,j}$ and a reference graph
$\overline{\mathcal{G}}=(\overline{\mathcal{V}},\overline{\mathcal{E}})$, the
Integrated Gradients feature attributions scores are defined as:

$\displaystyle
S^{IG}_{k,l}=(x_{k,l}-\overline{x_{k,l}})\cdot\int^{1}_{\alpha=0}\frac{\partial\mathcal{M}(\overline{\mathcal{G}}+\alpha\cdot(\mathcal{G}-\overline{\mathcal{G}})_{i,j}}{\partial
x_{k,l}}d\alpha$

In contrast with Gradient $\cdot$ Input, which only considers the gradient at
the explained input instance, Integrated Gradients are based on an aggregate
gradient on the path from some suitable reference to the currently considered
input. This helps to naturally smooth out any local irregularities in the
gradient and to capture the influence of the input features even if their
effect already saturated close to the currently considered input [65]. In our
experiments, we will consider the neutral reference graph
$\overline{\mathcal{G}}$ with the same structure as the input graph
$\mathcal{G}$, but all the features on the nodes and edges set to zero. Using
zero feature values has been advocated as a reasonable default choice for the
reference input [65]. We must also note that Integrated Gradients in the pure
form defined above are typically intractable for complex deep learning models.
Thus, in practice, the integrated gradient scores are computed, in our
setting, via the following approximation:

######  Definition 6.

Approximate Integrated Gradients Explanation. Given an explained model
$\mathcal{M}$, an input heterogeneous graph
$\mathcal{G}=(\mathcal{V},\mathcal{E})$, a target node $v_{i}\in\mathcal{V}$,
a target output $y_{i,j}$, a reference graph
$\overline{\mathcal{G}}=(\overline{\mathcal{V}},\overline{\mathcal{E}})$ and a
number of steps $n$, the approximate Integrated Gradients feature attributions
scores are defined as:

$\displaystyle
S^{IG-A}_{k,l}=(x_{k,l}-\overline{x_{k,l}})\cdot\sum^{n}_{k=0}\frac{1}{n}\cdot\frac{\partial\mathcal{M}(\overline{\mathcal{G}}+\frac{k}{n}\cdot(\mathcal{G}-\overline{\mathcal{G}})_{i,j}}{\partial
x_{k,l}}$

Throughout this paper, when considering Integrated gradient explanations, we
will use the above approximation with $n=50$ as the number of steps.

In addition to the above gradient-based methods, we also initially considered
perturbation approaches based on Shapley Values [54]. However, given the large
size of the considered input graph, we found these to be highly
computationally inefficient, taking several hours to compute the explanation
for a single output. We also note that there are several bespoke methods
specifically focused on explaining GNN models, such as GNN-Explainer [68].
Unfortunately, the available implementations for these methods were not
compatible with the library for HGNs that we used, which is why we opted to
use the above methods instead. Extending GNN-Explainer and other GNN-specific
explainability methods to our heterogeneous model poses an interesting line of
future work, but is outside the scope of this paper.

####  4.2.2 Counterfactual Explanations

In contrast to attributing model output predictions to parts of input
features, Counterfactual Explanations (CEs) reveal the minimal changes needed
from the factual input to achieve a different and more desirable output
prediction [58]. In this section, we define CEs suitable for the land use
inference task with heterogeneous graphs. For graph data, CEs often take the
form of subgraphs or modified graph inputs [69] due to the connectivity
between the nodes, which is especially the case in land use inference since
our interest is always on an area [70]. We start by defining the subgraph
consisting of a target node and its neighbouring nodes.

######  Definition 7.

1-hop complete subgraph. Given an input heterogeneous graph
$\mathcal{G}=(\mathcal{V},\mathcal{E})$ and a target node
$v_{i}\in\mathcal{V}$, the _1-hop complete subgraph_ of $v_{i}$ is defined as
$\mathcal{G}_{i}=(\mathcal{V}_{i},\mathcal{E}_{i})$, where
$\mathcal{V}_{i}=\\{v_{j}\text{ }|\text{ }e_{i,j}\in\mathcal{E}\vee
e_{j,i}\in\mathcal{E}\\}\cup\\{v_{i}\\}$ and $\mathcal{E}_{i}=\\{e_{j,k}\text{
}|\text{ }v_{j},v_{k}\in\mathcal{V}_{i},\text{ }e_{j,k}\in\mathcal{E}\\}$.

Another concept central to CEs for graph data is the dissimilarity measure
between two subgraphs, which allows comparisons of candidate CEs.
Specifically, suppose we have two candidate subgraph CEs; that which is more
similar to the input is considered the better candidate, because it would
require less effort to change from the input [58]. Given the multi-modal
nature of our data, we design a dissimilarity measure covering the differences
in node features, node types, edge types, and (sub)graph structure as follows:

######  Definition 8.

Local subgraph dissimilarity. Given an input heterogeneous graph
$\mathcal{G}=(\mathcal{V},\mathcal{E})$, two 1-hop complete subgraphs
$\mathcal{G}_{i}=(\mathcal{V}_{i},\mathcal{E}_{i})$ and
$\mathcal{G}_{j}=(\mathcal{V}_{j},\mathcal{E}_{j})$ for nodes
$v_{i},v_{j}\in\mathcal{V}$, respectively, the _local subgraph dissimilarity_
between $\mathcal{G}_{i}$ and $\mathcal{G}_{j}$ is:

$d(\mathcal{G}_{i},\mathcal{G}_{j})=d_{\mathcal{V}}(\mathcal{G}_{i},\mathcal{G}_{j})+d_{\mathcal{A}}(\mathcal{G}_{i},\mathcal{G}_{j})+d_{\mathcal{R}}(\mathcal{G}_{i},\mathcal{G}_{j})+d_{\mathcal{G}}(\mathcal{G}_{i},\mathcal{G}_{j})$

where:

$\displaystyle d_{\mathcal{V}}(\mathcal{G}_{i},\mathcal{G}_{j})$
$\displaystyle=\frac{1}{\lvert\mathcal{V}_{j}\rvert}\sum_{v_{k}\in\mathcal{V}_{j}}\frac{1}{2}(\textit{L2\\_dist}(x_{i},x_{k})+\textit{cosine\\_dist}(x_{i},x_{k}))$

is the _node feature dissimilarity_ , L2_dist and cosine_dist are L2
(Euclidean) distance and cosine distance respectively,

$\displaystyle d_{\mathcal{A}}(\mathcal{G}_{i},\mathcal{G}_{j})$
$\displaystyle=1-\frac{\sum_{k=1}^{\lvert\mathcal{A}\rvert}min(\overline{\phi(\mathcal{V}_{i})}_{k}),\overline{\phi(\mathcal{V}_{j})}_{k})}{\sum_{k=1}^{\lvert\mathcal{A}\rvert}max(\overline{\phi(\mathcal{V}_{i})}_{k}),\overline{\phi(\mathcal{V}_{j})}_{k})}$

is the _node type dissimilarity_ , $\phi$ maps nodes to its corresponding
type, $\phi(\mathcal{V}_{i})$ is the node types of subgraph nodes
$\mathcal{V}_{i}$,
$\overline{\phi(\mathcal{V}_{i})}\in\mathbb{R}^{\lvert\mathcal{A}\rvert}$
represents the counts of each node type in $\mathcal{A}$,

$\displaystyle d_{\mathcal{R}}(\mathcal{G}_{i},\mathcal{G}_{j})$
$\displaystyle=abs(\frac{1}{\lvert\mathcal{E}_{i}\rvert}\sum_{e_{k,l}\in\mathcal{E}_{i}}\psi({e_{k,l}})-\frac{1}{\lvert\mathcal{E}_{j}\rvert}\sum_{e_{m,n}\in\mathcal{E}_{j}}\psi({e_{m,n}}))$

is the _edge type dissimilarity_ , $\psi$ maps edges to its corresponding
type,

$\displaystyle d_{\mathcal{G}}(\mathcal{G}_{i},\mathcal{G}_{j})$
$\displaystyle=|\lvert\mathcal{E}_{i}\rvert-\lvert\mathcal{E}_{j}\rvert|$

is the _graph structure dissimilarity_ , $abs(*)$ takes the absolute value of
a real number.

This score combines four sources of dissimilarities. Firstly,
$d_{\mathcal{V}}$ denotes the node features differences where L2 captures the
magnitude differences, while cosine distance captures the traffic pattern
differences. $d_{\mathcal{A}}$ calculates the node type differences between
the nodes in the two subgraphs using the multiset Jaccard distance [71].
$d_{\mathcal{R}}$ calculates the absolute differences between the average road
types, obtained by the edge types in both subgraphs. Finally,
$d_{\mathcal{G}}$ represents the graph structure differences expressed as the
absolute difference between the numbers of edges, which is often considered as
sparsity in graph CEs [69]. We now use Local subgraph dissimilarity as a core
heuristic444Note that our dissimilarity notion is not a distance, e.g., it
does not satisfy symmetry, as $d(\mathcal{G}_{i},\mathcal{G}_{j})\neq
d(\mathcal{G}_{j},\mathcal{G}_{i})$. to guide the search for CEs:

######  Definition 9.

Counterfactual Explanation. Given an explained model $\mathcal{M}$, an input
heterogeneous graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$, a target node
$v_{i}\in\mathcal{V}$ with predicted output $y_{i}$, a desirable prediction
result $y^{\prime}\neq y_{i}$, the _counterfactual explanation_ for $v_{i}$’s
prediction is $\mathcal{G}_{j}=(\mathcal{V}_{j},\mathcal{E}_{j})$, the 1-hop
complete subgraph for node $v_{j}$, which is:

$\underset{v_{j}\in\mathcal{V}|y_{j}=y^{\prime}}{\textit{argmin}}\quad
d(\mathcal{G}_{i},\mathcal{G}_{j})$

Our definition finds a 1-hop complete subgraph from the given heterogeneous
graph data as the CE for a given target node. It is the closest (measured by
local subgraph dissimilarity) subgraph to the 1-hop complete subgraph of the
target node, among all the subgraphs of nodes which are predicted with a pre-
specified desirable prediction by our explained model. Our method has the same
spirit as the nearest-neighbour CEs method for tabular data, which finds the
closest point in the training dataset as the CE for an input point [72]. Such
CEs taken from the dataset have the advantage of lying within the data
manifold, therefore they are realistic data and not algorithmic artefacts
[73]. Additionally, they are more robust to perturbations that could occur in
the inference pipeline [74].

Practically, the CEs can be computed as the following. First, initialise the
1-hop complete subgraph for the target node. Then, filter out the nodes
predicted with the desirable label. In an iterative procedure, for each of
these nodes, take their 1-hop complete subgraph, and compute the local
subgraph dissimilarity between the subgraph and the input node’s subgraph. The
subgraph with the lowest dissimilarity is returned as the CE. As will be seen
in Section 5.4.5, we specify a mixed prediction and use CEs to investigate
what changes are needed to achieve a community with balanced land use [75,
76].

##  5 Empirical Experiments

###  5.1 Dataset description

Since no open-source database currently offers well-processed graph datasets
concerning urban mobility data and transport facilities, the first step of our
case study is to construct a heterogeneous graph dataset of multi-modal urban
mobility information. As shown in Figure 3, London (inner and central) is
chosen as the study area due to the high complexity and diversity of its land
use. In addition, its dense mobility network allows for fine-grained regional
analysis to cover most of the study area.

Figure 3: The heterogeneous input is based on three data sources: a) locations
of the tube, bus, and cycling stations, marked in blue, green, and orange
respectively; b) connectivity among tube stations in the tube network; c) road
network at different levels, which is used to build neighbourhood connections.

The constructed dataset comprises four parts: node features, edge features,
labels and zoning as described below.

  * 1.

Nodes features. For any mobility station, we use its ridership distribution on
a ‘typical weekday’(as averaged over the weekdays in 2017) as the input nodes
feature. This ridership information is provided by the Transport of London
(TfL) open data (tfl.gov.uk/info-for/open-data-users/our-open-data).
Specifically, three types of mobility services are selected – tube (186
stations), bus (3167 stations) and bike sharing (883 stations) – as shown in
Figure 3(a). The daily passenger inbound data of each station is processed
into 15-minute interval ridership from 6:00 to 22:00 (64 input features).

  * 2.

Edge features. The edges are of two types: tube network edges, derived from
connectivity data among tube stations, as shown in Figure 3(b), and road
network edges, based on a comprehensive road network, shown in Figure 3(c).
There are specifically five types of road edge categories involved: Primary,
secondary, tertiary, residential, and unclassified (a detailed introduction of
this information can be found at
https://wiki.openstreetmap.org/wiki/Key:highway). These types of edge-level
geography information are collected from the Open Street Map and encoded into
one-hot vectors to represent the edge-level information. We do not use
connectivity in the bus network because the available data does not
distinguish the direction of routes among the bus stops. Although including
this information would complete the heterogeneous map, it is beyond the scope
of this research.

  * 3.

Labels. In the land use inference problem, there is no established paradigm
for labelling. We adhere to the recommended practices of the most cited
foundational studies [1] – using the density of POIs to characterise the
intensity of specific land use characteristics in a region. To ensure
comprehensiveness and objectivity, we selected six POI categories from the OSM
database: office, sustenance, transport, retail, leisure and residence. Due to
the restriction of OSM’s API on the quantity of data collected, it is
difficult to obtain complete POI data for the London area. Consequently, we
chose a few major tags to represent each land use category, as detailed in
Table 3 (the specific introduction of the used tags can be found at
https://wiki.openstreetmap.org/). The spatial distributions of these labels
are displayed in Figure 9 in A.

  * 4.

Catchment area. We establish a criterion that assigns each node a catchment
area—a circular region centred on the node with a predetermined radius. Each
node is labelled by the land use indicators within this catchment area. This
process considers two types of label tags:

    * (a)

For point tags (e.g., locations of different services), count the number of
target types within the catchment area.

    * (b)

For polygon tags (e.g., parks, buildings), calculate the proportion of the
catchment area that these tags cover.

We have used a 1 km radius for the catchment area in our analysis. As our
focus is on demonstrating the use of heterogeneous graph models, a comparison
of different catchment radii and their impacts is left to future work.

Table 3: POI categories and their specific tags for labelling land use. Category |  Tags | Data types
---|---|---
Office |  Government, Association, Company, Consulting, Financial, Coworking, Lawyer, Estate, Insurance, Telecommunication | Points
Sustenance |  Restaurant, Cafe, Bar, Pub, Fast Food | Points
Transport |  Bicycle, Subway, Transport, Taxi, Parking, Ferry, Tram | Points and Polygons
Retail |  Convenience, Supermarket, Mall, Department, Bakery, Butcher, Clothes, Hardware, Furniture, Electronics | Points
Leisure |  Park, Sports, Playground, Swimming, Pitch, Track, Fitness, Garden, Nature | Points and Polygons
Residence |  Residential, House, Detached, Apartments, Population | Points and Polygons

###  5.2 Baseline models for comparison

In our framework, we compare our proposed HGT model against several baseline
methods, including:

  * 1.

Neural Network (NN): A basic neural network model, serving as a foundational
benchmark against more complex graph-based models.

  * 2.

Graph Convolutional Network (GCN): Utilises convolutional processes directly
on the graph structure to capture neighbourhood information [77].

  * 3.

Graph Attention Network (GAT): Incorporates attention mechanisms into graph
neural networks, enabling nuanced weighting of node contributions from
neighbours [48].

  * 4.

GraphSage: A scalable graph neural network method that generates embeddings by
sampling and aggregating features from a node’s local neighbourhood [47].

  * 5.

Relational Graph Convolutional Network (RGCN): Extends GCNs to manage graph
heterogeneity by incorporating various relational types among nodes during the
learning process [78].

Each of these models represents a unique approach to incorporating graph
structure into the learning process, which makes them suitable baselines for
assessing the performance of our proposed HGT model.

###  5.3 Measurement metrics

To evaluate the performance of our regression models, we employ three widely
recognised metrics: Mean Absolute Error (MAE), Root Mean Square Error (RMSE),
and the Coefficient of Determination ($R^{2}$). These metrics are essential
for assessing the accuracy and predictive quality of the models. They are
defined as follows, where $n$ is the number of observations in the test set,
$y_{i}$ represents the actual values, and $\hat{y}_{i}$ are the predicted
values.

  * 1.

Mean Absolute Error (MAE): MAE quantifies the average absolute difference
between the predicted values and the actual values, giving an insight into the
overall error magnitude without the influence of error direction.

$\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}|y_{i}-\hat{y}_{i}|$

  * 2.

Root Mean Square Error (RMSE): RMSE is a quadratic scoring rule that
calculates the square root of the average of squared differences between the
predicted and actual values. It emphasises larger errors, which can be
particularly important in certain contexts.

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

  * 3.

Coefficient of Determination (R-Squared): $R^{2}$ is a statistical measure
that indicates the proportion of the variance in the dependent variable that
is predictable from the independent variables. It is used to measure how well
the model captures the variability of the dataset.

$\displaystyle\text{R}^{2}=1-\frac{\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}}{\sum_{i=1}^{n}(y_{i}-\overline{y})^{2}}$

where $\overline{y}$ is the mean of the actual values $y_{i}$.

###  5.4 Results

These experiments were undertaken on a Linux Ubuntu system, utilising CUDA
Version 11.4 with NVIDIA RTX A5000 GPU for deep learning model optimisation.
Computations were executed on Python 3.10 within a dedicated virtual
environment (Readers can check “requirement.txt” on the GitHub website of this
project). For comprehensive model evaluation and testing, we randomly
allocated 70% of the samples for training, with the remaining 15% for
validation and 15% for testing. To ensure fair comparisons against multiple
baseline models, we used the same hyper-parameters to model, train, and test
them, as detailed in Table 4.

Table 4: Summary of Hyper-Parameter Settings. Parameter | Value
---|---
Hidden Layer Numbers | 2
Hidden Layer Dimension | 128
Activation Function | ReLU
Attention-Head Numbers | 2
Optimiser | AdamW [79]
Epoch Number | 200
Batch-Size | 64
Learning Rate | 0.002
Sampling for Homo-Graph | Neighbor Loader [47]
Sampling for Hetero-Graph | HGT Loader [80]
Graph Hop Number | 1

####  5.4.1 Overall accuracy

This section offers a comprehensive evaluation of various deep learning
methods using the London mobility datasets across multiple urban domains.
Models evaluated include the proposed HGT framework compared with baseline
methods mentioned in Section 5.2. The improvement percentage (Impr.) over the
baseline neural network model underscores the effectiveness of these models in
inferring land use.

Table 5: Performance metrics and improvements across different land use targets. Indicators | Metrics | NN | GCN | GraphSage | GAT | RGCN | HGT
---|---|---|---|---|---|---|---
Office | MAE | 0.086 | 0.043 | 0.043 | 0.039 | 0.035 | 0.031
Impr. | - | 50.00% | 50.00% | 54.65% | 59.30% | 63.95%
RMSE | 0.124 | 0.060 | 0.058 | 0.054 | 0.051 | 0.047
Impr. | - | 51.61% | 53.23% | 56.45% | 58.87% | 62.10%
Sustenance | MAE | 0.079 | 0.033 | 0.032 | 0.034 | 0.031 | 0.025
Impr. | - | 58.23% | 59.49% | 56.96% | 60.76% | 68.35%
RMSE | 0.116 | 0.046 | 0.045 | 0.049 | 0.044 | 0.039
Impr. | - | 60.34% | 61.21% | 57.76% | 62.07% | 66.38%
Transport | MAE | 0.097 | 0.046 | 0.043 | 0.039 | 0.039 | 0.033
Impr. | - | 52.58% | 55.67% | 59.79% | 59.79% | 65.98%
RMSE | 0.139 | 0.063 | 0.059 | 0.054 | 0.054 | 0.050
Impr. | - | 54.68% | 57.55% | 61.15% | 61.15% | 64.03%
Retail | MAE | 0.103 | 0.057 | 0.053 | 0.050 | 0.046 | 0.039
Impr. | - | 44.66% | 48.54% | 51.46% | 55.34% | 62.14%
RMSE | 0.134 | 0.077 | 0.070 | 0.068 | 0.065 | 0.058
Impr. | - | 42.54% | 47.76% | 49.25% | 51.49% | 56.72%
Leisure | MAE | 0.106 | 0.064 | 0.060 | 0.058 | 0.051 | 0.044
Impr. | - | 39.62% | 43.40% | 45.28% | 51.89% | 58.49%
RMSE | 0.141 | 0.086 | 0.083 | 0.080 | 0.069 | 0.067
Impr. | - | 39.01% | 41.13% | 43.26% | 51.06% | 52.48%
Residence | MAE | 0.123 | 0.062 | 0.058 | 0.054 | 0.051 | 0.042
Impr. | - | 49.59% | 52.85% | 56.10% | 58.54% | 65.85%
RMSE | 0.158 | 0.083 | 0.078 | 0.074 | 0.070 | 0.062
Impr. | - | 47.47% | 50.63% | 53.16% | 55.70% | 60.76%

The results in Table 5 indicate a consistent improvement in performance when
transitioning from general deep learning models to complex graph-based models.
The HGT model consistently delivers the highest improvement percentages across
all categories, showing its capability to handle heterogeneous graph data.
Specifically, the ‘Sustenance’ indicator has substantial benefits from graph-
based models, with the HGT achieving MAE improvements of 68.35%. The RGCN and
HGT models consistently outperform others, probably due to their ability to
capture heterogeneous relationships within the mobility and topology
structure. The smallest improvement is noted in the ‘leisure’ land use
indicator, suggesting that there might be unobserved information which could
boost predictive accuracy.

####  5.4.2 Spatial residual distribution

To better understand the function of heterogeneous graph models at the
individual level, we compare the geographical distribution of residuals in the
geometric map between GCN and HGT. Figure 4 illustrates an example of one of
the land use indicators –‘Residence’, where the size of the circular markers
indicates the absolute value of the residuals. The colour of each marker
indicates whether the residual is positive or negative: red for over-predicted
values and blue for underestimated values. Similar comparisons of other land
use indicators can be found in Figure 10 in B.

A comparison in Figure 4 reveals that the circular markers in HGT are smaller
overall than those in GCN. Additionally, a continuous distribution of red and
blue colours in the GCN map suggests that the model consistently overestimates
or underestimates certain areas or roads. This suggests unobserved
heterogeneity is hindering the model’s performance. HGT significantly improves
this issue, displaying a more uniform colour distribution in its corresponding
maps. According to Figure 10, the same observations applied in other land use
indicators like ‘leisure’ and ‘retail’.

Figure 4: Spatial distribution of residual of residence: GCN (left) and HGT
(right)

####  5.4.3 Ablation analysis on connectivity in the graph

Given the significant improvement of GNN models illustrated in Table 5, this
section delves into the role of connectivity and neighbouring nodes.
Specifically, we constructed four scenarios by removing some of the nodes and
connections: a) all nodes and edges; b) only bus and bike nodes with their
edges; c) only bus and tube nodes with their edges; d) only bus nodes with
their edges. Owing to the limited number of bike and tube nodes, these modes
were not assessed as separate scenarios. We use R-square as the measurement
for comparison as shown in Figure 5.

Figure 5: $R^{2}$ of six land use indicators in four scenarios: (a) bus, bike,
and tube; (b) bus and bike; (c) bus and tube; (d) bus

According to Figure 5, we can draw two conclusions. First, increased
connectivity enhances performance across all metrics in all graph models.
Specifically, moving from chart (a) to chart (d) reveals a noticeable decrease
in performance metrics across domains like transport, retail, and residential
areas. Second, the heterogeneous information acts as complementary for
prediction, especially for areas under sparse connectivity. As noted
previously, inferring land use for leisure is challenging because vehicular
and cycling mobility data poorly represent non-commuting activities like
leisurely travelling. However, we observed that heterogeneous graph models
(HGT and RGCN) significantly improve the accuracy performance in the ‘leisure’
land use.

####  5.4.4 Feature attribution analysis

This section examines feature attributions – the impact of the daily mobility
distribution on the outcome using the Approximate Integrated Gradients index.
The results are displayed in a heatmap format, where red indicates a positive
correlation and blue a negative correlation between input features of
different 15-time intervals and land use indicators, as shown in Figure 6.

Figure 6: Heatmap of the distribution of Integrated-gradients importance of
HGT model.

The feature attribution results in Figure 6 closely align with the general
understanding of human activities in London, illustrated in three categories
with different characteristics. The first category, comprising transport,
office, and sustenance, is primarily associated with work-related activities.
This category shows a high sensitivity to commuter inflow during peak hours.
Specifically, inflow is lower in the morning (10:00-11:00 AM) and
significantly higher in the evening (5:00-6:00 PM). This indicates that areas
with these land uses attract more commuters returning from work in the evening
than departing in the morning. Besides, a subtler trend shows that Category 1
(work-related) stations experience reduced feature importance in the early
evening (6:45-7:45 PM) and increased importance later at night (8:45-9:45 PM).
This likely reflects a common urban lifestyle pattern, where individuals
engage in leisure and entertainment activities after returning home from work.

In contrast, the second category, consisting of residential land use areas,
exhibits a reverse trend with higher morning inflow and lower evening inflow.
This reflects typical residential patterns where people leave for work in the
morning and return in the evening.

The third category, including leisure and retail, is less affected by inflows
at peak hours. Notably, these areas show minimal variation in inflow during
peak hours but have varied activity during other times, such as evenings
(presumably after work), which aligns with shopping and leisure activities.

It is important to note that various feature attribution methods might produce
different outcomes. Our comparison of two methods, Integrated Gradients
(Figure 6) and InputX-Gradient (Figure 11 in appendix), illustrates this
point. Integrated Gradients are generally considered more reliable because
they account for changes over a broader range, offering a more comprehensive
understanding of feature importance. Conversely, InputX-Gradient, focusing on
a single point gradient, failed to align with the general context. As shown in
this case, the importance of heatmap from the Integrated Gradient method
aligns more closely with the characteristics of human activity in London,
reflecting our understanding of the comparative performance of the methods.

####  5.4.5 Counterfactual explanation analysis

In the previous section, we focused on the explainability of our model by
analysing the feature attribution of node features. Although this analysis
offered valuable insights into individual node attributes, it did not account
for the importance of other critical factors such as node types, edge types,
and the overall graph structure. To overcome this limitation, this section
introduces counterfactual analysis for a more comprehensive understanding of
our model. We set ‘mixed’ as an expected scenario. Mixed land use refers to an
area with balanced facilities and diverse activities, crucial for enhancing
urban vitality, reducing commute distances, and promoting sustainable
development [76]. Mathematically, given the predicted land use intensity
$y_{i,j}$ from the main models, we applied the Shannon diversity index to
quantify the diversity of land uses within each area. The Shannon diversity
(SD) is calculated as follows:

$\text{SD}_{i}=-\sum_{j\in\mathcal{T}}\frac{y_{i,j}}{\sum_{j\in\mathcal{T}}y_{i,j}}\ln(\frac{y_{i,j}}{\sum_{j\in\mathcal{T}}y_{i,j}})$
(8)

where $y_{i,j}/\sum_{j\in\mathcal{T}}y_{i,j}$ represents the proportion of
land use of type $i$ in the area. This formula provides a diversity score for
each area to reflect the variety of land uses present. After calculating the
diversity scores for all areas, we ranked them in descending order. The areas
with the highest diversity scores, representing the top 10% of all nodes, were
classified as ‘mixed’ land use types. This approach ensures that we focus on
regions that already demonstrate a high level of land use diversity.

Based on the mixed land use based Counterfactual Explanations (CEs), this
counterfactual analysis is conducted in two parts. Initially, we perform a
local-level analysis to demonstrate the practical application of CEs. In this
analysis, we select a specific input node and target a ‘mixed’ land use
prediction as the desired outcome. We identify a CE for this node and compare
it with the original input to underscore the necessary changes for achieving
the target prediction. Secondly, we conduct an aggregated-level analysis to
demonstrate how dissimilarity measures for CEs can illuminate the importance
of factors such as node features, node types, edge types, and graph structure.

##### Local-level analysis

We present CEs for two example input nodes which do not belong to the ‘mixed’
land use area; these are the inputs 1 and 2 which are located in Central and
East London respectively (Figure 7). We compute CEs for the two nodes which
reveal the minimum changes to make from the input (subgraph) in order to
achieve the ‘mixed’ land use. The node feature differences between the input
nodes and the CE subgraphs are illustrated in Figure 8, and the node type,
edge type, and graph structure differences are listed in Table 6. For input 1,
as can be observed from the magnitudes in Figure 8(a), the required changes
are mostly in the node features, while the differences are small for the items
in Table 6. Indeed, this intuition is demonstrated by the dissimilarity
measures, which for the four data modalities are respectively 0.271, 0.056,
0.043, and 0.043. The high node feature dissimilarity emphasises the
importance of changing node features for input 1. For input 2, however, the
dissimilarities are 0.047, 0.0, 0.133, and 0.069, meaning that the change of
edge (road) type is the primary factor in achieving the ‘mixed’ land use. The
magnitudes of node feature changes are relatively small (Figure 8(b)), while
the edge type changes are more significant.

Figure 7: Two local-level cases: (a) Input 1: a bus stop in the central London
area with a high level of ‘transport’ prediction; (b) Input 2: a bus stop in
the eastern area with a high level of ‘leisure’ prediction

(a) Input 1: Charing Cross stop E, and its CE

(b) Input 2: Andrew Street Stop Q, and it CE

Figure 8: Node feature differences. Each line (in different colours) is a vector of node features of a node, the line highlighted in red is for the input node, while the other lines in blue-like colours are for the nodes in the CE subgraph.  Table 6: Node type, edge type, graph structure differences between example inputs and their CE, both in the form of 1-hop complete subgraph. Subgraph | Node type | Avg. Edge Type | Structure
---|---|---|---
Input 1 | 0 tube, 14 bus, 4 bike | 0.52 | 141
CE 1 | 0 tube, 13 bus, 4 bike | 0.70 | 135
Input 2 | 0 tube, 11 bus, 0 bike | 1.68 | 72
CE 2 | 0 tube, 11 bus, 0 bike | 1.15 | 67

##### Aggregated-level analysis

Given a closed ‘mixed’ subgraph for each sample’s subgraph, we specify four
types of differences: node feature, node type, edge type and graph structure.
These differences can be regarded as relevant importance determining the
minimal effort required to transition to a mixed land use type. All the values
have been scaled into the 0-1 range, as shown in Table 7.

Table 7: Counterfactual scores of different elements in a graph.  Indicators | Node feature | Node type | Edge type | Structure
---|---|---|---|---
office |  0.637 $\pm$ 0.132 |  0.422 $\pm$ 0.139 |  0.030 $\pm$ 0.030 |  0.021 $\pm$ 0.023
sustenance |  0.449 $\pm$ 0.212 |  0.457 $\pm$ 0.089 |  0.049 $\pm$ 0.045 |  0.039 $\pm$ 0.033
transport |  0.287 $\pm$ 0.234 |  0.370 $\pm$ 0.121 |  0.038 $\pm$ 0.034 |  0.048 $\pm$ 0.052
retail |  0.262 $\pm$ 0.302 |  0.399 $\pm$ 0.130 |  0.033 $\pm$ 0.021 |  0.042 $\pm$ 0.038
leisure |  0.284 $\pm$ 0.260 |  0.269 $\pm$ 0.143 |  0.058 $\pm$ 0.044 |  0.048 $\pm$ 0.046
residence |  0.216 $\pm$ 0.202 |  0.286 $\pm$ 0.141 |  0.045 $\pm$ 0.039 |  0.048 $\pm$ 0.052

According to Table 7, In terms of the average values, node feature and node
type are the primary source of discrepancies, while edge type and graph
structure have lower impact. Specifically, in leisure and residence tasks, the
impact of node features is significantly reduced, which is aligned with the
relatively low accuracy of these two tasks, as shown in Section 5.4.1.
Conversely, these tasks slightly increase the influence of edge types and
graph structure. Additionally, the standard deviation indicates that node
features contribute minimally to the difference for some sample regions,
especially for indicators like ‘retail’, ‘leisure’ and ‘residence’. These
patterns indicate that although node features are generally crucial, graph
structural aspects and node relationships become more significant in leisure
and residence contexts.

##  6 Conclusions

This paper builds an explainable graph-based framework for inferring land use
from multi-modal mobility data in complex urban scenarios. In this framework,
a Heterogeneous Graph Transformer model is introduced to fuse multi-modal
mobility information for land use inference tasks. Next, two types of
explainable AI methods enhance the models’ transparency and extrapolability.

The overall accuracy indicates that the use of GNNs significantly improves
accuracy. Furthermore, ablation analysis shows that HGNs effectively enhance
network structure information and outperform homogeneous graph models,
especially in challenging tasks like identifying ‘leisure’.

Feature attribution analysis assesses the importance of input factors and
verifies the model’s explainability by checking if the importance distribution
aligns with expert experience. As shown in the feature attribution analysis,
the symmetrical nature of the ‘residence’ and ‘work’ categories aligns well
with the commuter’s ‘work’; and ‘recreation’ activities in London, giving some
confidence in the suitability of proposed model for the land use setting.
Meanwhile, counterfactual explanations highlight the efforts needed to alter
any node’s prediction from a micro perspective, allowing experts to assess the
GNNs’ explainability based on differences between subgraphs. The analysis of
the counterfactual explanations in Section 5.4.5 reveals that in areas with
different functions and historical backgrounds (e.g., Central London and East
London), the different types of information in the heterogeneous graph data,
which represent various elements in the sub-map, have significantly different
forms of contribution. This is consistent with the planner’s understanding of
these regions, thus validating the usefulness of fusing data from different
sources. We posit that these insights will help to build user trust in GNNs by
providing a clear, evidence-based rationale for each prediction, which is
crucial for users in urban planning and management to trust the proposed
methods.

There are several limitations and opportunities for future research. The
current model uses simplistic meta-relations that consider only 1-hop
relationships. Future work could focus on more complex relationships (e.g.,
multi-steps of transfers) among urban mobility facilities. Due to the limited
data collected, the nodes’ features are only represented by outflow rather
than inflow and outflow, potentially limiting the comprehensiveness of our
findings. Future research will benefit from the growing availability of open
graph-structured urban data, enabling comparative studies to enhance our
understanding of urban dynamics in different countries and societies. Cross-
validation could potentially enhance this model’s performance; however, due to
limited hardware computational capacity, only standard training methods were
utilised in this paper. Further, incorporating multiple explainable AI
techniques will increase the model’s transparency and strengthen support for
urban planning decisions, offering a more trustworthy analysis of urban land
use dynamics.

##  7 Declaration of generative AI and AI-assisted technologies in the writing
process

During the preparation of this work, the author(s) used Chatgpt in order to
improve readability. After using this tool/service, the author(s) reviewed and
edited the content as needed and take(s) full responsibility for the content
of the publication.

##  Appendix A Labels processing

Figure 9: POI and population data for building the labels

##  Appendix B Supplementary results

Figure 10: Special distribution of residual among six land use indicators
Figure 11: Heatmap of the distribution of InputX-gradient

## References

  * [1] J. L. Toole, M. Ulm, D. Bauer, M. C. Gonzalez, Inferring land use from mobile phone activity, proceedings of the acm sigkdd international workshop on urban computing (2012).
  * [2] J. Yuan, Y. Zheng, X. Xie, Discovering regions of different functions in a city using human mobility and pois, in: Acm Sigkdd International Conference on Knowledge Discovery & Data Mining, 2012, p. 186.
  * [3] J. Zhao, W. Fan, X. Zhai, Identification of land-use characteristics using bicycle sharing data: A deep learning approach, Journal of Transport Geography 82 (2020).
  * [4] S. Gao, K. Janowicz, H. Couclelis, Extracting urban functional regions from points of interest and human activities on location-based social networks, Transactions in GIS 21 (3) (2017) 446–467.
  * [5] X. Zhang, W. Li, F. Zhang, R. Liu, Z. Du, Identifying urban functional zones using public bicycle rental records and point-of-interest data, ISPRS international journal of geo-information 7 (12) (2018) 459.
  * [6] F. Yuan, K. E. Sawaya, B. C. Loeffelholz, M. E. Bauer, Land cover classification and change analysis of the twin cities (minnesota) metropolitan area by multitemporal landsat remote sensing, Remote sensing of Environment 98 (2-3) (2005) 317–328.
  * [7] B. Zhou, K. M. Kockelman, Neighborhood impacts on land use change: A multinomial logit model of spatial relationships, The Annals of Regional Science 42 (2008) 321–340.
  * [8] R. B. Matthews, N. G. Gilbert, A. Roach, J. G. Polhill, N. M. Gotts, Agent-based land-use models: a review of applications, Landscape Ecology 22 (2007) 1447–1459.
  * [9] C. M. de Almeida, M. Batty, A. M. V. Monteiro, G. Câmara, B. S. Soares-Filho, G. C. Cerqueira, C. L. Pennachin, Stochastic cellular automata modeling of urban land use dynamics: empirical development and estimation, Computers, environment and urban systems 27 (5) (2003) 481–509.
  * [10] M. A. Fadhel, A. M. Duhaim, A. Saihood, A. Sewify, M. N. Al-Hamadani, A. Albahri, L. Alzubaidi, A. Gupta, S. Mirjalili, Y. Gu, Comprehensive systematic review of information fusion methods in smart cities and urban environments, Information Fusion (2024) 102317.
  * [11] V. Snášel, M. Štěpnička, V. Ojha, P. N. Suganthan, R. Gao, L. Kong, Large-scale data classification based on the integrated fusion of fuzzy learning and graph neural network, Information Fusion 102 (2024) 102067.
  * [12] Y. Casali, N. Y. Aydin, T. Comes, Machine learning for spatial analyses in urban areas: a scoping review, Sustainable cities and society 85 (2022) 104050.
  * [13] J. Yuan, Y. Zheng, X. Xie, Discovering regions of different functions in a city using human mobility and pois, in: Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining, 2012, pp. 186–194.
  * [14] C. R. Bhat, S. Sen, N. Eluru, The impact of demographics, built environment attributes, vehicle characteristics, and gasoline prices on household vehicle holdings and use, Transportation Research Part B: Methodological 43 (1) (2009) 1–18.
  * [15] R. Ewing, R. Cervero, Travel and the built environment: A meta-analysis, Journal of the American planning association 76 (3) (2010) 265–294.
  * [16] T. Yigitcanlar, N. Sipe, R. Evans, M. Pitot, A gis-based land use and public transport accessibility indexing model, Australian planner 44 (3) (2007) 30–37.
  * [17] S. Hu, S. Gao, L. Wu, Y. Xu, Z. Zhang, H. Cui, X. Gong, Urban function classification at road segment level using taxi trajectory data: A graph convolutional neural network approach, Computers, Environment and Urban Systems 87 (2021) 101619.
  * [18] J. Choi, W. No, M. Park, Y. Kim, Inferring land use from spatialtemporal taxi ride data, Applied Geography 142 (2022) 102688.
  * [19] J. Kleinberg, H. Lakkaraju, J. Leskovec, J. Ludwig, S. Mullainathan, Human decisions and machine predictions, The quarterly journal of economics 133 (1) (2018) 237–293.
  * [20] Z. Sun, Z. Peng, Y. Yu, H. Jiao, Deep convolutional autoencoder for urban land use classification using mobile device data, International Journal of Geographical Information Science 36 (11) (2022) 2138–2168.
  * [21] Y. Yuan, M. Raubal, Y. Liu, Correlating mobile phone usage and travel behavior – a case study of harbin, china, Computers Environment & Urban Systems 36 (2) (2012) 118–130.
  * [22] Z. Du, X. Zhang, W. Li, F. Zhang, R. Liu, A multi-modal transportation data-driven approach to identify urban functional zones: An exploration based on hangzhou city, china, Transactions in GIS 24 (1) (2020) 123–141.
  * [23] Q. Liu, W. Huan, M. Deng, X. Zheng, H. Yuan, Inferring urban land use from multi-source urban mobility data using latent multi-view subspace clustering, ISPRS International Journal of Geo-Information 10 (5) (2021) 274.
  * [24] Z. Deng, X. You, Z. Shi, H. Gao, X. Hu, Z. Yu, L. Yuan, Identification of urban functional zones based on the spatial specificity of online car-hailing traffic cycle, ISPRS International Journal of Geo-Information 11 (8) (2022) 435.
  * [25] H. Jiao, S. Huang, Y. Zhou, Understanding the land use function of station areas based on spatiotemporal similarity in rail transit ridership: A case study in shanghai, china, Journal of Transport Geography 109 (2023) 103568.
  * [26] M. G. Demissie, L. Kattan, Understanding the temporal and spatial interactions between transit ridership and urban land-use patterns: an exploratory study, Public Transport 14 (2) (2022) 385–417.
  * [27] X. Zhang, X. Liu, K. Chen, F. Guan, M. Luo, H. Huang, Inferring building function: A novel geo-aware neural network supporting building-level function classification, Sustainable Cities and Society 89 (2023) 104349.
  * [28] S. Ali, T. Abuhmed, S. H. A. El-Sappagh, K. Muhammad, J. M. Alonso-Moral, R. Confalonieri, R. Guidotti, J. D. Ser, N. D. Rodríguez, F. Herrera, Explainable artificial intelligence (XAI): what we know and what is left to attain trustworthy artificial intelligence, Inf. Fusion 99 (2023) 101805.  doi:10.1016/J.INFFUS.2023.101805.
URL https://doi.org/10.1016/j.inffus.2023.101805

  * [29] A. Jacovi, A. Marasovic, T. Miller, Y. Goldberg, Formalizing trust in artificial intelligence: Prerequisites, causes and goals of human trust in AI, in: FAccT ’21: 2021 ACM Conference on Fairness, Accountability, and Transparency, Virtual Event / Toronto, Canada, March 3-10, 2021, 2021, pp. 624–635.  doi:10.1145/3442188.3445923.
URL https://doi.org/10.1145/3442188.3445923

  * [30] J. Schoeffer, N. Kühl, Y. Machowski, ”there is not enough information”: On the effects of explanations on perceptions of informational fairness and trustworthiness in automated decision-making, in: FAccT ’22: 2022 ACM Conference on Fairness, Accountability, and Transparency, Seoul, Republic of Korea, June 21 - 24, 2022, 2022, pp. 1616–1628.  doi:10.1145/3531146.3533218.
URL https://doi.org/10.1145/3531146.3533218

  * [31] A. Ferrario, M. Loi, How explainability contributes to trust in AI, in: FAccT ’22: 2022 ACM Conference on Fairness, Accountability, and Transparency, Seoul, Republic of Korea, June 21 - 24, 2022, 2022, pp. 1457–1466.  doi:10.1145/3531146.3533202.
URL https://doi.org/10.1145/3531146.3533202

  * [32] J. Zerilli, U. Bhatt, A. Weller, How transparency modulates trust in artificial intelligence, Patterns 3 (4) (2022) 100455.  doi:10.1016/J.PATTER.2022.100455.
URL https://doi.org/10.1016/j.patter.2022.100455

  * [33] C. Panigutti, A. Beretta, F. Giannotti, D. Pedreschi, Understanding the impact of explanations on advice-taking: a user study for ai-based clinical decision support systems, in: CHI ’22: CHI Conference on Human Factors in Computing Systems, New Orleans, LA, USA, 29 April 2022 - 5 May 2022, 2022, pp. 568:1–568:9.  doi:10.1145/3491102.3502104.
URL https://doi.org/10.1145/3491102.3502104

  * [34] T. Papadakis, I. T. Christou, C. Ipektsidis, J. Soldatos, A. Amicone, Explainable and transparent artificial intelligence for public policymaking, Data & Policy 6 (2024) e10.
  * [35] C. Jin, T. Ruan, D. Wu, L. Xu, T. Dong, T. Chen, S. Wang, Y. Du, M. Wu, Hetgat: a heterogeneous graph attention network for freeway traffic speed prediction, Journal of Ambient Intelligence and Humanized Computing (2021) 1–12.
  * [36] G. Li, Z. Zhao, X. Guo, L. Tang, H. Zhang, J. Wang, Towards integrated and fine-grained traffic forecasting: A spatio-temporal heterogeneous graph transformer approach, Information Fusion 102 (2024) 102063.
  * [37] K. T. Chui, B. B. Gupta, R. W. Liu, P. Vasant, Handling data heterogeneity in electricity load disaggregation via optimized complete ensemble empirical mode decomposition and wavelet packet transform, Sensors 21 (9) (2021) 3133.
  * [38] D. Wang, D. Zhong, A. Souri, Energy management solutions in the internet of things applications: Technical analysis and new research directions, Cognitive Systems Research 67 (2021) 33–49.
  * [39] N. Schwalbe, B. Wahl, Artificial intelligence and the future of global health, The Lancet 395 (10236) (2020) 1579–1586.
  * [40] Y. Zheng, Z. Xu, X. Wang, The fusion of deep learning and fuzzy systems: A state-of-the-art survey, IEEE Transactions on Fuzzy Systems 30 (8) (2021) 2783–2799.
  * [41] L. Du, R. Gao, P. N. Suganthan, D. Z. Wang, Bayesian optimization based dynamic ensemble for time series forecasting, Information Sciences 591 (2022) 155–175.
  * [42] Y. Wang, Y. Liu, Bayesian entropy network for fusion of different types of information, Reliability Engineering & System Safety 195 (2020) 106747.
  * [43] M. A. Ganaie, M. Hu, A. K. Malik, M. Tanveer, P. N. Suganthan, Ensemble deep learning: A review, Engineering Applications of Artificial Intelligence 115 (2022) 105151.
  * [44] Y. Ren, L. Zhang, P. N. Suganthan, Ensemble classification and regression-recent developments, applications and future directions, IEEE Computational intelligence magazine 11 (1) (2016) 41–53.
  * [45] Y. Liang, Z. Zhao, F. Ding, Y. Tang, Z. He, Time-dependent trip generation for bike sharing planning: A multi-task memory-augmented graph neural network, Information Fusion (2024) 102294.
  * [46] F. Zhou, T. Wang, T. Zhong, G. Trajcevski, Identifying user geolocation with hierarchical graph neural networks and explainable fusion, Information Fusion 81 (2022) 1–13.
  * [47] W. Hamilton, Z. Ying, J. Leskovec, Inductive representation learning on large graphs, Advances in neural information processing systems 30 (2017).
  * [48] P. Veličković, G. Cucurull, A. Casanova, A. Romero, P. Lio, Y. Bengio, Graph attention networks, arXiv preprint arXiv:1710.10903 (2017).
  * [49] C. Shi, B. Hu, W. X. Zhao, S. Y. Philip, Heterogeneous information network embedding for recommendation, IEEE transactions on knowledge and data engineering 31 (2) (2018) 357–370.
  * [50] Y. Wu, Y. Chen, Z. Yin, W. Ding, I. King, A survey on graph embedding techniques for biomedical data: Methods and applications, Information Fusion 100 (2023) 101909.
  * [51] X. Wang, D. Bo, C. Shi, S. Fan, Y. Ye, S. Y. Philip, A survey on heterogeneous graph embedding: methods, techniques, applications and sources, IEEE Transactions on Big Data 9 (2) (2022) 415–436.
  * [52] S. Yang, B. Yang, An inductive heterogeneous graph attention-based multi-agent deep graph infomax algorithm for adaptive traffic signal control, Information fusion 88 (2022) 249–262.
  * [53] M. Sundararajan, A. Taly, Q. Yan, Axiomatic attribution for deep networks, in: International conference on machine learning, PMLR, 2017, pp. 3319–3328.
  * [54] S. M. Lundberg, S.-I. Lee, A unified approach to interpreting model predictions, Advances in neural information processing systems 30 (2017).
  * [55] Z. Yan, W. L. Hamilton, M. Blanchette, Graph neural representational learning of rna secondary structures for predicting rna-protein interactions, Bioinformatics 36 (Supplement_1) (2020) i276–i284.
  * [56] Y. Bi, D. Xiang, Z. Ge, F. Li, C. Jia, J. Song, An interpretable prediction model for identifying n7-methylguanosine sites based on xgboost and shap, Molecular Therapy-Nucleic Acids 22 (2020) 362–372.
  * [57] M. Dobrojevic, M. Zivkovic, A. Chhabra, N. S. Sani, N. Bacanin, M. M. Amin, Addressing internet of things security by enhanced sine cosine metaheuristics tuned hybrid machine learning model and results interpretation based on shap approach, PeerJ Computer Science 9 (2023) e1405.
  * [58] S. Wachter, B. D. Mittelstadt, C. Russell, Counterfactual explanations without opening the black box: Automated decisions and the GDPR, Harv. JL & Tech. 31 (2017) 841.
  * [59] D. Numeroso, D. Bacciu, Meg: Generating molecular counterfactual explanations for deep graph networks, in: 2021 International Joint Conference on Neural Networks (IJCNN), IEEE, 2021, pp. 1–8.
  * [60] Z. Chen, F. Silvestri, J. Wang, Y. Zhang, Z. Huang, H. Ahn, G. Tolomei, Grease: Generate factual and counterfactual explanations for gnn-based recommendations, arXiv preprint arXiv:2208.04222 (2022).
  * [61] X. Jiang, Y. Shen, Y. Wang, H. Shen, C. Xu, S. Ma, Meta-path based social relation reasoning in a deep and robust way, in: International Conference on Database Systems for Advanced Applications, Springer, 2023, pp. 3–20.
  * [62] P. Pezeshkpour, S. Jain, S. Singh, B. C. Wallace, Combining feature and instance attribution to detect artifacts, CoRR abs/2107.00323 (2021).  arXiv:2107.00323.
URL https://arxiv.org/abs/2107.00323

  * [63] C. Meng, L. Trinh, N. Xu, J. Enouen, Y. Liu, Interpretability and fairness evaluation of deep learning models on MIMIC-IV dataset, Scientific Reports 12 (2022).
  * [64] A. Shrikumar, P. Greenside, A. Shcherbina, A. Kundaje, Not just a black box: Learning important features through propagating activation differences, arXiv preprint arXiv:1605.01713 (2016).
  * [65] M. Sundararajan, A. Taly, Q. Yan, Axiomatic attribution for deep networks, in: D. Precup, Y. W. Teh (Eds.), Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia, 6-11 August 2017, Vol. 70 of Proceedings of Machine Learning Research, PMLR, 2017, pp. 3319–3328.
URL http://proceedings.mlr.press/v70/sundararajan17a.html

  * [66] M. Ancona, E. Ceolini, C. Öztireli, M. Gross, Towards better understanding of gradient-based attribution methods for deep neural networks, in: 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 - May 3, 2018, Conference Track Proceedings, OpenReview.net, 2018.
URL https://openreview.net/forum?id=Sy21R9JAW

  * [67] D. Balduzzi, M. Frean, L. Leary, J. Lewis, K. W.-D. Ma, B. McWilliams, The shattered gradients problem: If resnets are the answer, then what is the question?, in: International Conference on Machine Learning, PMLR, 2017, pp. 342–350.
  * [68] Z. Ying, D. Bourgeois, J. You, M. Zitnik, J. Leskovec, Gnnexplainer: Generating explanations for graph neural networks, in: H. M. Wallach, H. Larochelle, A. Beygelzimer, F. d’Alché-Buc, E. B. Fox, R. Garnett (Eds.), Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada, 2019, pp. 9240–9251.
URL
https://proceedings.neurips.cc/paper/2019/hash/d80b7040b773199015de6d3b4293c8ff-
Abstract.html

  * [69] M. A. Prado-Romero, B. Prenkaj, G. Stilo, F. Giannotti, A survey on graph counterfactual explanations: Definitions, methods, evaluation, and research challenges, ACM Comput. Surv. 56 (7) (2024) 171:1–171:37.  doi:10.1145/3618105.
URL https://doi.org/10.1145/3618105

  * [70] Y. Casali, N. Y. Aydin, T. Comes, Machine learning for spatial analyses in urban areas: a scoping review, Sustainable cities and society 85 (2022) 104050.
  * [71] L. d. F. Costa, Further generalizations of the jaccard index, arXiv preprint arXiv:2110.09619 (2021).
  * [72] D. Brughmans, P. Leyman, D. Martens, Nice: an algorithm for nearest instance counterfactual explanations, Data mining and knowledge discovery (2023) 1–39.
  * [73] R. Poyiadzi, K. Sokol, R. Santos-Rodríguez, T. D. Bie, P. A. Flach, FACE: feasible and actionable counterfactual explanations, in: A. N. Markham, J. Powles, T. Walsh, A. L. Washington (Eds.), AIES ’20: AAAI/ACM Conference on AI, Ethics, and Society, New York, NY, USA, February 7-8, 2020, ACM, 2020, pp. 344–350.  doi:10.1145/3375627.3375850.
URL https://doi.org/10.1145/3375627.3375850

  * [74] J. Jiang, F. Leofante, A. Rago, F. Toni, Robust counterfactual explanations in machine learning: A survey, in: Proceedings of the 33rd International Joint Conference on Artificial Intelligence, IJCAI, 2024.
  * [75] D. Farr, Sustainable urbanism: Urban design with nature, John Wiley & Sons, 2011.
  * [76] S. Lehmann, Sustainable urbanism: towards a framework for quality and optimal density?, Future cities and environment 2 (2016) 1–13.
  * [77] T. N. Kipf, M. Welling, Semi-supervised classification with graph convolutional networks, arXiv preprint arXiv:1609.02907 (2016).
  * [78] M. Schlichtkrull, T. N. Kipf, P. Bloem, R. Van Den Berg, I. Titov, M. Welling, Modeling relational data with graph convolutional networks, in: The semantic web: 15th international conference, ESWC 2018, Heraklion, Crete, Greece, June 3–7, 2018, proceedings 15, Springer, 2018, pp. 593–607.
  * [79] I. Loshchilov, F. Hutter, Decoupled weight decay regularization, arXiv preprint arXiv:1711.05101 (2017).
  * [80] Z. Hu, Y. Dong, K. Wang, Y. Sun, Heterogeneous graph transformer, in: Proceedings of the web conference 2020, 2020, pp. 2704–2710.