# A Survey on Differential Privacy for SpatioTemporal Data in Transportation
Research

Rahul Bhadani<EMAIL_ADDRESS>The University of Alabama in Huntsville

###### Abstract

With low-cost computing devices, improved sensor technology, and the
proliferation of data-driven algorithms, we have more data than we know what
to do with. In transportation, we are seeing a surge in spatiotemporal data
collection. At the same time, concerns over user privacy have led to research
on differential privacy in applied settings. In this paper, we look at some
recent developments in differential privacy in the context of spatiotemporal
data. Spatiotemporal data contain not only features about users but also the
geographical locations of their frequent visits. Hence, the public release of
such data carries extreme risks. To address the need for such data in research
and inference without exposing private information, significant work has been
proposed. This survey paper aims to summarize these efforts and provide a
review of differential privacy mechanisms and related software. We also
discuss related work in transportation where such mechanisms have been
applied. Furthermore, we address the challenges in the deployment and mass
adoption of differential privacy in transportation spatiotemporal data for
downstream analyses.

##  I Introduction

In the age of information, we have multiple ways to obtain data representing
human lives – from the scale of the universe to the level of genomes. The
proliferation of computing technology, sensor systems, and innovation for mass
adoption provides timeseries data in IoT, healthcare, finance, log data for an
event, transportation, genomics, and so on. Of particular interest to us is
the spatiotemporal data. Spatiotemporal data are collected across both time
and space, featuring at least one spatial and one temporal property
john2024spatiotemporal . Spatiotemporal data may be trajectory data collected
from vehicles such as speed, acceleration, brake, and throttle, along with
their GPS information bunting2022data , weather data such as temperature
pattern, precipitation, humidity, air quality, etc. radhika2022novel , species
distribution mapping in ecology study hengl2008advancing , COVID-19 dataset
spassiani2021spatiotemporal . Given that spatiotemporal data are timeseries
data with spatial components, sequence-based methods have been used for
analyses of spatiotemporal data such as Autoregressive Integrated Moving
Average (ARIMA)) model bouznad2020trend ; yan2010traj ;
rodrigues2020spatiotemporal ; li2022overview , smoothing methods
rezaeiassessment ; yang2018optimized , and machine learning methods such as
Long Short-Term Memory (LSTM) alhudhaif2024spatio ; luo2019spatiotemporal ;
li2021spatial , and Transformers abideen2020deep ; ji2023traffic ;
yang2024stfeformer . It is logistically challenging to gather or obtain
spatiotemporal data specific to particular scenarios in the transportation
domain due to the man-power required, lack of appropriate infrastructure,
risks involved, and safety-critical nature of experiments
bhadani2018dissipation ; stern2018dissipation ; lee2024traffic ; xu2022opv2v ;
schwall2020waymo . Hence, many researchers rely on data gathered by other
research groups, agencies, or companies for further analyses and secondary
research. Releasing such spatiotemporal data may expose the private
information of users and other stakeholders involved in the research, and may
have repercussions beyond the experiment in the question. Developing some kind
of privacy-preserving mechanism for such spatiotemporal is essential before
the dissemination of such datasets can be done.

Differential privacy (DP) dwork2006differential  is a class of statistical
methods to prevent an attacker from identifying a particular person from the
given dataset, possibly by associating with already available information
cowan2024handson . Several differential privacy schemes have been proposed
over the years suited for query-based data analysis from databases such as
counting, sum, frequency li2020estimating ; wang2018privacy ; yang2017survey
where privacy individuals are preserved when aggregated data are to be
released. Researchers are also seeking to make their machine-learning models
private by employing the DP mechanism in their machine-learning methods. In
machine learning training, if no privacy-preserving mechanism is employed, it
can compromise the confidentiality of the training data. A specific case of
membership attack is discussed in shokri2017membership ; yeom2018privacy
where the attacker aims to determine whether a specific data record was used
in the model’s training set. By consistently modifying these data points to
increase the model’s confidence, the actor can eventually pinpoint data
samples that are nearly identical to the actual data samples in the training
set. If a model is large, as in the case of a large language model, where
there are millions to billions of parameters, the model will most likely
memorize the training data carlini2022quantifying . In carlini2021extracting ;
mattern2023membership , a training data extraction attack is discussed where
generative output can be engineered to reproduce the training data. Such cases
were revealed from the output of some user-facing generative AI tools such as
Midjourney radauskas2024midjourney . Violations of privacy with pre-trained
machine learning models are possible and new mechanisms have been used for
thwarting such violations. Some common work on the use of differential privacy
in machine learning are Differentially Private Stochastic Gradient Descent
(DP-SGD) yu2022individual , Private Feature Selection
stoddard2014differentially , Private Classification shen2023classification ,
DP Neural Network gylberth2017differentially  to name a few.

Despite some exciting developments in the use of DP methods in data analysis
and machine learning, spatiotemporal data offers some specific challenges due
to temporal relationships as well as spatial relationships among data points.
We cannot directly use previously developed DP methods on spatiotemporal data
as protecting every single data point, or removing some samples from the
dataset may render the whole dataset useless. Correlation among features of
multivariate spatiotemporal data may also lead to privacy violations if a
well-thought method is not applied.

To the best of our knowledge, there is a lack of any review on differential
privacy for spatiotemporal transportation data. We find surveys on
spatiotemporal data mining, differential privacy in general, and differential
privacy for timeseries. However, in the domain of transportation, no such work
exists. We hope that this work will lead to renewed interest in applying
differential privacy methods on transportation spatiotemporal data to aid
researchers and users in performing private data analyses.

The rest of the paper is organized as follows: Section II introduces
spatiotemporal data analysis to the reader. Section III provides an overview
of differential privacy. Section IV provides recent developments in the use of
differential privacy on spatiotemporal data analyses. Finally, Section V
discusses open challenges and future directions in DP-based spatiotemporal
data analyses.

##  II SpatioTemporal Data

Spatial data contains information about spaces and may contain data to
represent objects like lines, circles, and polygons. Spatial data are common
in environmental studies, geographical information systems (GIS), and
location-based services using global positioning systems (GPS). Spatial data
may be map data, attribute data, or image data. Spatial data may be
represented using coordinates and may be saved in databases as raster models
or vector models. Of particular interest in transportation is HD maps. High-
definition (HD) maps are highly detailed, three-dimensional representations of
road environments used by automated vehicles (AVs) to navigate safely and
efficiently. Unlike traditional maps, HD maps provide centimeter-level
accuracy and include various layers of information critical for AV operation.
They may contain information in the form of various layers such as a base
layer; a geometric map containing 3D information of the road network; a
semantic map layer containing information on lane markings, traffic signals,
and travel direction; and map prior layers such as crowd-sourced traffic data.
It is used for autonomous navigation safely and reliably. Temporal data, also
known as timeseries are data about representing a particular feature evolving
over time. When temporal data is associated with spatial data, we obtain
spatiotemporal data. For example, timeseries information about a vehicle’s
trajectory along a highway is spatiotemporal data. We may collect
spatiotemporal data using mobile phones, social media, or sensors from moving
vehicles.

###  II.1 Analysis using SpatioTemporal Transportation Data

Spatiotemporal data in transportation can be used to predict travel demand,
travel time of transportation, traffic assignment problems, and route choices
yuan2021survey ; xie2020urban . In zhang2017probe  addresses the problem of
traffic congestion using accurate traffic forecasting using spatiotemporal
data that was collected from probe vehicles. Authors use the Gray-level Co-
occurrence Matrix (GLCM) nixon2019feature  to extract spatiotemporal features.
Using GLCM from current data and historical data, the authors calculated
Normalized Squared Differences and selected best-matched traffic patterns
nixon2019feature . In liu2019contextualized , authors address taxi origin-
destination demand prediction using a spatiotemporal data-based neural network
by adding context information – spatial context, temporal context, and global
correlation context. Authors consider taxi origin-destination demand in time
interval $t$ as a 3D matrix $X_{t}\in{\mathbb{R}}^{N\times H\times W}$, where
$H$ and $W$ are height and width of city grid map respectively, $N$ is the
total number of regions in the city. To predict the origin-destination demand,
authors train on the New York City taxi dataset using a convolution-LSTM-based
neural network. In rahman2023data , authors present a graph convolutional
neural network (GCN)-based approach to learning traffic flow patterns by
phrasing it as a traffic assignment problem. They present their transportation
network as a graph which is a suitable data type for a graph-based neural
network. Using GCN, they estimate the link flows for given travel demands.
During the estimation process, the GCN model was able to learn the traffic
flow propagation from origin nodes toward destination nodes in a
transportation network. The authors validated their results by comparing the
prediction against the analytical solution obtained from running static user
equilibrium-based traffic assignments. Spatiotemporal data can also be used
for collaborative filtering. Collaborative filtering employs the idea that
people with similar spatiotemporal data may have similar preferences. This
technique is used in creating a recommender system in transportation for
people matching similar spatiotemporal features. For example, in zhou2021smart
, authors create tourism recommendation system using spatiotemporal data.
Traditional methods often fail to consider real-time geographic conditions and
tourists’ dynamic needs, leading to suboptimal recommendations and tour
routes. The authors propose a novel tourism recommendation model that combines
cellular geospatial clustering with a multivariate weighted collaborative
filtering algorithm. Authors use Multivariate Weighted Collaborative Filtering
that enhances traditional collaborative filtering by incorporating multiple
weighted factors that reflect tourists’ preferences, such as budget, travel
time, attraction popularity, tour purpose, and transportation modes. The
algorithm calculates the similarity between tourists’ feature attributes and
historical data to provide personalized recommendations.

##  III A Primer on Differential Privacy

Differential privacy is a statistics-based formalization that measures the
amount of privacy that may be leaked if a user decides to participate in an
experiment resulting in some data collection about the user. Differential
privacy promises the user that an individual’s data does not significantly
affect the output of data analysis, and the user is not at risk more than he
would be if he decided not to participate in the experiment. By introducing
randomized algorithms that ensure outputs are statistically similar regardless
of individual data present, differential privacy mitigates risks from
auxiliary information and linkage attacks.

One kind of randomized algorithm is the Laplace mechanism where a small amount
of data drawn from the Laplace distribution is added to the dataset. Consider
a generalized data transformation algorithm as ${\mathcal{M}}$. Laplace
mechanism can be applied as follows:

$\displaystyle{\mathcal{M}}(x)=x+\textrm{Laplace(0, b)}$ (1)

where $b$ is the width parameter of the Laplace distribution (See Figure 1).

Figure 1: Probability Density Function (PDF) of the Laplace distribution with
central parameter $\mu=0$ and width parameters $b=0.5$, $b=1.0$, and $b=3.0$.

######  Definition 1.

$\epsilon$-Differential Privacy A data transformation ${\mathcal{M}}$ is
$\epsilon$-differentially private, if for a dataset $x$ and its perturbed
dataset $x^{\prime}$, we have the following condition:

$P({\mathcal{M}}(x)=y)\leq P({\mathcal{M}}(x^{\prime})=y)\cdot e^{\epsilon}$
(2)

which states that a transformation ${\mathcal{M}}$ is $\epsilon$-DP if the
probability (denoted by $P$) of any output $y$ from the original dataset $x$
is at most $e^{\epsilon}$ times the probability of the same output from a
slightly perturbed dataset $x^{\prime}$ that differs by only one data point.
This ensures that the inclusion or exclusion of any single individual’s data
has a limited impact on the outcome, thus protecting individual privacy. In
this formulation, $\epsilon$ is also referred to as privacy budget.

Considering the sensitivity $\Delta f$ of the function $f$ as

$\Delta f=\max_{x,x^{\prime}}||f(x)-f(x^{\prime})||,$

the noise to be added can be sampled from

$\textrm{Laplace}\bigg{(}\cfrac{\Delta f}{\epsilon}\bigg{)}$ (3)

######  Definition 2.

$(\epsilon,\delta)$-Differential Privacy We consider $(\epsilon,\delta)$ model
(called $(\epsilon,\delta)$-DP) as

$P({\mathcal{M}}(x)=y)\leq e^{\epsilon}\cdot
P({\mathcal{M}}(x^{\prime})=y)+\delta$ (4)

There are two models of differential privacy: the central model and the local
model. In the central model, there is the existence of a trusted curator whose
job is to apply some transformation ${\mathcal{M}}$, after obtaining data from
users or sources and then providing it for further analyses. In the local
model, there is no trusted curator, hence, it is at the source, that we are
required to apply specific transformation ${\mathcal{M}}$. An illustration of
both models is provided in Figure 3.

Figure 2: The central model and the local model for differentially private
mechanism. A trusted curator collects data from its source, applies some
transformation ${\mathcal{M}}$, and disseminates it for downstream analyses.
In the local model, the transformation is applied at the source as there may
not be a trusted curator.

###  III.1 Algorithms for Differential Privacy

Various algorithms exist for implementing differential privacy. Below, we
discussed some of those algorithms:

####  III.1.1 Randomized Response

This algorithm is suitable for a case where a binary answer is possible. The
respondent is instructed to use a randomization device, such as a coin flip or
a random number generator, to determine whether they should provide their true
answer or a randomized response. If the coin lands heads, the respondent
answers truthfully. If the coin lands tails, the respondent answers Yes with a
probability $p$ (say, 0.5) and No with a probability $1-p$. The surveyor
collects the randomized responses without knowing whether any particular
answer is truthful or randomized.

####  III.1.2 Exponential Mechanism

The exponential mechanism is used where adding noise might destroy the utility
of the data. The Exponential Mechanism selects an output from a set of
possible outcomes $r\in{\mathcal{R}}$, ${\mathcal{R}}$ being some arbitrary
range, with a probability that exponentially favors outcomes with higher
utility values, thus balancing the trade-off between utility and privacy.

Given a dataset $x$, a utility function $u(x,r)$ for each possible output
$r\in{\mathcal{R}}$ and a privacy parameter $\epsilon$, the exponential
mechanism selects an output $r$ with probability proportional to
$\exp{\epsilon u(x,r)/2\Delta u}$ where $\Delta u$ is the sensitivity of the
utility function defined as

$\Delta u=\max_{r}\max_{x,x^{\prime}}|u(x,r)-u(x^{\prime},r)|$ (5)

As an example, Consider a scenario where a company wants to select the best
location for a new store based on customer data while ensuring the decision
process is differentially private. The utility function $u(x,r)$ could
represent the expected profit from placing the store at the location $r$ given
the customer data $x$. The Exponential Mechanism would ensure that the chosen
location does not reveal sensitive information about individual customers by
making the probability of selecting each location proportional to its utility,
scaled by the privacy parameter $\epsilon$.

####  III.1.3 $\alpha$-net Mechanism

$\alpha$-net mechanism is a technique used in the context of differential
privacy to create privacy-preserving machine learning models. An $\alpha$-net
is a carefully selected subset of the original dataset that aims to preserve
the essential characteristics and patterns of the full dataset. The original
dataset is divided into smaller, non-overlapping subsets. Each subset is
analyzed to identify its key features and patterns. From each partition, a
representative subset of data points is selected based on their utility and
importance to the overall dataset. The selection process ensures that these
points capture the essential characteristics of the partition while minimizing
the risk of exposing individual data points. Controlled noise is added to the
selected data points to ensure differential privacy. The representative
subsets from each partition, collectively forming the $\alpha$-net, are used
to train the machine learning model.

There are several other algorithms to provide guaranteed differential privacy
that readers can find in the literature such as hassan2019differential ;
yang2023local .

###  III.2 Software and Tools for Differential Privacy

Research on differential privacy has led to many interesting software and
tools that can be used to incorporate differential privacy into data analyses.
We discuss some of the popular tools below.

####  III.2.1 OpenDP

OpenDP implements various statistical methods in rust with Python-binding
gaboardi2020programming . OpenDP provides a flexible, extensible, and
verifiable framework that can support a wide range of differential privacy
algorithms and applications. The software introduces interactive measurements
for adaptive queries and maintains privacy guarantees during post-processing.
Additionally, it addresses implementation concerns such as preventing side-
channel attacks and ensuring accurate arithmetic operations. The modular and
extensible design aims to facilitate community contributions while maintaining
rigorous privacy standards, providing a robust foundation for the advancement
of differential privacy algorithms.

####  III.2.2 Differential Privacy from Google

Written primarily in C++, and Go, the Differential Privacy library from Google
GoogleDifferentialPrivacy2024  provides an implementation of various
algorithms to introduce differential privacy to a data analysis task. The tool
can also be used with SQL queries.

####  III.2.3 TensorFlow Privacy

Tensorflow-Privacy papernot2019machine  is used to introduce privacy into
machine learning models. It provides a framework for privacy mechanisms at the
time of training a model that adds noise to the parameters of the model to
prevent training data from being inferred by the model’s output.

####  III.2.4 SecretFlow

SecretFlow ma2023secretflow  provides a software framework for creating
machine learning using secure multi-party computation (MPC) techniques.
However, in addition to differential privacy, SecretFlow also offers other
privacy-preserving techniques such as holomorphic encryption and Trusted
Execution Environment.

####  III.2.5 Opacus

Opacus is a software package based on Pytorch for training deep-learning
models with differential privacy. It significantly simplifies the process of
training differentially private models and achieves better performance
compared to existing solutions. A developer can also track the privacy budget
during the training process.

##  IV Differential Privacy Methods on SpatioTemporal Data in Transportation

In this section, we discuss some of the recent work in spatiotemporal
transportation data with differential privacy.

###  IV.1 Real-time Traffic Data Scenario

In transportation, real-time traffic data publishing is desirable for
congestion monitoring, crash detection, and connected vehicle control. In such
a case, $w-event$ model kellaris2014differentially  is a suitable choice. Two
spatiotemporal data $S$ and $S^{\prime}$ are $w$-event adjacent if we consider
a window of the size $w$ where the datasets are not identical, however, they
are identical outside the window as illustrated in Figure.

Figure 3: $w$-event model where two spatiotemporal data in a window of size
$w$ are not identical.

One key challenge in spatiotemporal data is how to allocate a privacy budget,
i.e. choose $\epsilon$ when employing a sliding window. In addition, one
should consider that observations made at nearby locations and timestamps may
not be independent. There may be some correlation in temporal and spatial
dimensions. Further, data distribution might change with time, leading to
ineffective privacy budget allocation. In the context of transportation data,
a dynamically allocated privacy budget might be used that takes into account
distribution change over time and location.

In wang2023dp , authors propose to use a spatiotemporal graph attention
network with a dynamic privacy budget (called P-STGAT). In P-STGAT, authors
provide a distance-based adjacent matrix on road-network data. The adjacency
matrix describes the magnitude of the correlation between nodes of the road
network. The adjacency matrix is fed to a graph-attention network that
contains a temporal attention layer and a spatial attention layer for
extracting temporal and spatial features respectively. While calculating the
new privacy budget, the last privacy budget is also taken into account, hence
updating the privacy budget recursively as follows:

$\epsilon_{new}=\epsilon+\sum_{k=i-w+1}^{i-1}\epsilon_{k}$ (6)

where $i$ is the final index in the current window of the size $w$, the
$\epsilon$ is the fixed budget. Based on the allocated privacy budget,
perturbed data using Laplace distribution is added to the original data.

###  IV.2 Trajectory Data Publication

Trajectory data publication requires DP methods that take into account the
fact that protection of only single-location data is sufficient as there are
relationships between nearby location data. One solution is to apply
differential privacy on processed data obtained from the true trajectory data.
If we convert the original trajectory data into some other form such as latent
representation (e.g. Principal Components), or low dimensional representation,
then a single data point might contain information about more than one true
data point.

In qiu2023sgtp , the authors first create K-means clusters based on the time
of the trajectory positions, a process referred to as time generalization.
After time generalization, all trajectories are generalized into $k$ temporal
location sets and equal-length trajectories. In the next step, the density
peak trajectory clustering algorithm (DPTC) is used to generalize spatial
locations. DPTC assumes that cluster centers are data points surrounded by
neighbors with lower local density and are relatively distant from any points
with higher density. Once a clustered representation of the trajectory is
obtained, Laplace distribution-based noise is added.

###  IV.3 Providing Spatiotemporal correlated Noise for Differential Privacy

As the spatiotemporal data has a correlation in the spatial domain as well as
the time domain, spatiotemporal noise is a suitable choice to prevent any
privacy attack.

In dou2020differential , the authors use correlation functions to establish
constraints on the published trajectory sequence, ensuring it maintains
spatiotemporal correlation with both the original trajectory and the added
noise. This is achieved by using the least squares method to fit the user’s
original trajectory and the overall direction of the noise sequence,
constructing a noise candidate set that ensures the added noise sequence has a
spatiotemporal correlation with the user’s trajectory. Furthermore, the method
imposes cross-correlation constraints to ensure the published trajectory
sequence satisfies both temporal and spatial correlation constraints, thereby
providing robust privacy protection.

The noise candidate set is constructed to ensure the spatial correlation
between the user’s original trajectory sequence and the added noise sequence.
The least squares method is used to fit the direction of the original
trajectory and the noise sequence as:

$\hat{b}=\frac{\sum_{i=1}^{n}x_{i}y_{i}-n\bar{x}\bar{y}}{\sum_{i=1}^{n}x_{i}^{2}-n\bar{x}^{2}}=\frac{\sum_{i=1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}$
(7)

where $\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}$ and
$\bar{y}=\frac{1}{n}\sum_{i=1}^{n}y_{i}$. To ensure the noise points are
geographically reachable, the start and end points of the noise sequence need
to satisfy,

$|\text{dis}(\text{start}_{d},\text{end}_{d})-\text{dis}(\text{start}_{\text{real}},\text{end}_{\text{real}})|\leq\delta_{\text{dis}}$
(8)

and

$|\text{time}(\text{start}_{d},\text{end}_{d})-\text{time}(\text{start}_{\text{real}},\text{end}_{\text{real}})|\leq\delta_{\text{time}}$
(9)

where $\delta_{\text{dis}}$ and $\delta_{\text{time}}$ are predefined
thresholds for distance and time, respectively. As the calculation of the
direction of the trajectory involves four data points (Equation (7)), four
groups $X_{1},X_{2},X_{3},X_{4}$ of white Gaussian noise are sampled through
Laplace distribution. Then $X=X_{1}^{2}+X_{2}^{2}-X_{3}^{2}-X_{4}^{2}$ is then
added to the original trajectory to achieve differential privacy.

##  V Open Challenges

While conducting the literature review for this paper, we found a lack of
significant work on differential privacy specifically designed for
spatiotemporal transportation data. There are interesting developments in
differential privacy, as discussed in the previous sections. However,
significant consideration is needed if we are to use spatiotemporal
transportation data for making inferences or further data analyses.

First, there is generally a high degree of correlation in spatiotemporal data.
Therefore, if a value is perturbed synthetically without considering spatial
or temporal information, it may appear anomalous and be easily identified,
undermining the principles of differential privacy. Second, spatiotemporal
transportation data often capture high-dimensional data from various sensor
modalities, which may be correlated across dimensions. Traditional methods
might be insufficient in such scenarios. Finally, the current state of the art
does not provide any evidence of successful autonomous vehicle operation using
differentially private data. The existing literature lacks significant work on
this topic.

A reasonable solution for the first two problems discussed above might be the
release of synthetic data generated from true trajectory data using generative
machine learning methods such as generative adversarial learning and
diffusion-based methods. However, the feasibility of differential privacy for
the autonomous control of vehicles is yet to be determined. There are real-
time challenges in autonomous operation, as the real-time control of a vehicle
requires control commands at a frequency of 20 Hz hayat2023traffic . An edge-
based solution may be devised to meet the privacy budget in real-time.

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