=Paper=
{{Paper
|id=Vol-2841/BMDA_10
|storemode=property
|title=City Indicators for Mobility Data Mining
|pdfUrl=https://ceur-ws.org/Vol-2841/BMDA_10.pdf
|volume=Vol-2841
|authors=Mirco Nanni,Agnese Bonavita,Riccardo Guidotti
|dblpUrl=https://dblp.org/rec/conf/edbt/NanniBG21
}}
==City Indicators for Mobility Data Mining==
https://ceur-ws.org/Vol-2841/BMDA_10.pdf
City Indicators for Mobility Data Mining
Mirco Nanni Agnese Bonavita Riccardo Guidotti
ISTI-CNR, Pisa Scuola Normale Superiore University of Pisa
Pisa, Italy Pisa, Italy Pisa, Italy
mirco.nanni@isti.cnr.it agnese.bonavita@sns.it riccardo.guidotti@di.unipi.it
ABSTRACT from networks that represent the places and movement of single
Classifying cities and other geographical units is a classical task in users; last, characteristics of road networks and how traffic is
urban geography, typically carried out through manual analysis distributed in them. The group of global city indicators, instead,
of specific characteristics of the area. The primary objective of looks at the mobility between cities as a graph, where each city
this paper is to contribute to this process through the definition is represented by a node, and extracts network features for each
of a wide set of city indicators that capture different aspects node. Both the complete network and the ego-network for each
of the city, mainly based on human mobility and automatically city are considered.
computed from a set of data sources, including mobility traces After describing all the city indicators we introduce a mobility
and road networks. The secondary objective is to prove that such prediction problem, and we use it to test how much predictive
set of characteristics is indeed rich enough to support a simple models are transferable across different regions. In particular, we
task of geographical transfer learning, namely identifying which study the relationship between transferability between two areas,
groups of geographical areas can share with each other a basic i.e. the performances of a model built on one area and used to
traffic prediction model. The experiments show that similarity in make predictions on the other one, and their similarity in terms
terms of our city indicators also means better transferability of of city indicators. The results confirm our hypothesis that cities
predictive models, opening the way to the development of more with similar indicators are more likely to be transfer-compliant,
sophisticated solutions that leverage city indicators. this providing a first guide to understand which predictive models
can be reused in other areas.
Finally, a key feature of this work is that all methods are
1 INTRODUCTION implemented in a way that makes it possible to automatically
Classifying a geographical territory into semantic categories is calculate all characteristics for hundreds of different cities and
one of the most common tasks in research areas such as urban entire regions. The resulting software (a Python library) enables
geography, urban planning and mobility data analytics [7]. Char- the user to process an unlimited amount of data simply by passing
acterizing human mobility is a key component of this process, a database with trajectories and a list containing the positions of
and it is well known that mobility often does not work the same the geographical areas of interest as an input.
way across different regions. A movement pattern in a moun- The rest of this paper is organized as follows. Section 2 in-
tainous countryside may have other implications than the same troduces some related works; Section 3 presents the dataset and
pattern has in the suburbs of a large town. The movement trajec- geographical areas used as testbed in the paper; Sections 4 and
tories in a planned city with rectangular streets and strict zoning 5 describe, respectively, the local and global city indicators; Sec-
laws might be completely different than the ones in a town that tion 6 presents our case study on evaluating the relations between
has grown organically without any clear structure. Therefore, geographical transferability of a simple predictive model between
any kind of property that was learned in a particular area, in any pair of areas and their similarity based on our indicators;
general cannot simply be assumed to hold in another one. finally, Section 7 closes the paper with conclusive remarks.
This paper aims at making a first step towards the characteri-
zation of a geographical area. That is achieved through a range 2 RELATED WORK
of quantitative measures that provide a multilayer description Chracterizing urban spaces is a fundamental task of urban ge-
of urban regions and are a means for displaying differences be- ography, which considers the spatial distribution of spaces and
tween cities, municipalities, or other geographical units. Such a patterns of movement, focusing both on structural properties
numerical description of urban areas can have a wide spectrum of and how the different parts interact [7]. Historically, determining
applications. Among them, the measures presented in this work such characteristics was usually a domain expert-driven process,
can be used as an input for geographical transfer learning, that that required a huge amount of time, and also particular care to
is the transformation of knowledge gained in one geographical ensure that results are comparable across different places. Ge-
region in order to apply it to another region. This problem will ographical Information Science introduced several innovations
be considered as a case study for the extracted indicators. that helped also to automatize and extend the approach, includ-
We consider two main approaches: (i) computing features that ing statistical methods for geography [33] and computational
describe each area isolated from the others, that we call local city tools for managing large databases of information.
indicators; and (ii) computing features that describe its relation On another direction, city indicators have a important applica-
with the others, named global city indicators. The first group tion in defining the sustainability characteristics of urban areas.
covers four different families of measures: spatial concentration Various attempts have been made to design indicators for moni-
indexes of human activities; network features of intra-city traffic toring sustainability at various levels, such as national [11] and
flows; mobility characteristics of the individual mobility, obtained city level [32]. As described in the review paper [17], the litera-
© 2021 Copyright for this paper by its author(s). Published in the Workshop Proceed- ture covers a wide range of aspects, including mobility-related
ings of the EDBT/ICDT 2021 Joint Conference (March 23–26, 2021, Nicosia, Cyprus) ones (e.g. mobility space usage and functional diversity). How-
on CEUR-WS.org. Use permitted under Creative Commons License Attribution 4.0
International (CC BY 4.0) ever, very few attempts were made to systematically exploit big
data sources to estimate them. One example was the Air Quality
4.1 Spatial Concentration
Spatial concentration is one of the most important aspects in the
description of urban regions and answer the question how the
density of people and activities vary across the area? This question
was traditionally focused on people’s residency and workplace,
since that was the only available data, mostly coming from census
or government records. More recent research is profiting from
the availability of more detailed data from mobile phones, vehicle
trackers and satellite imaging [2, 22, 39]. Spatial concentration
is used in a vast range of different fields [16, 19, 20, 23, 36]. In
this work, the concept of spatial concentration is focused on the
overall amount of mobility, undifferentiated by types of activity.
The question of interest is: are the activities concentrated in cluster-
like centers of high density or are they spread-out across the map?
Figure 1: The areas of study: 10×10km squares centered on In the following, we present three approaches to answer this
each municipality in Tuscany. question: spatial entropy, Moran’s measure, and the average near-
est neighbor distance. The first two approaches can only be calcu-
lated after the geographical space has been partitioned into a set
of disjoint areas. In this work, we do that adopting an equally-
Now EU project [9], which used vehicular and public transport
spaced grid, and divide the 100𝑘𝑚 2 region representing each area
data to infer some measures. Yet, that is limited to direct and sim-
using different resolutions, including a grid of 10x10 (i.e. each
ple ones, such as traffic, speeds and exposure to pollution. The
cell is a square of side 1 km), 20x20 and 50x50 cells.
literature also considers mobility indicators and road network
properties as potential measures to adopt, which is aligned with 4.1.1 Entropy. It can be used to measures how equally activi-
our approach [38]. ties are distributed across the grid. Let 𝑋 be a discrete random
Finally, exploiting big mobility data to understand the proper- variable modeling the positions of an individual ending up in 𝑛
ties of geographical spaces is a very active area. It includes data different fields [5]. The entropy is defined as [35]:
mining methods to find mobility patterns and regularities [15], 𝑛
Õ
simulations to estimate various indicators, like the impact of 𝐸 (𝑋 ) = − 𝑃 (𝑥𝑖 ) log 𝑃 (𝑥𝑖 )
alternative transportation means as car pooling [20], the visual 𝑖=1
exploration of patterns and contextual features [13], etc. How-
where {𝑥 1, . . . , 𝑥𝑛 } are the possible values of 𝑋 and 𝑃 (𝑥𝑖 ) is the
ever, to the best of our knowledge, no existing work tried to
probability of 𝑋 being in state 𝑖. For maximum entropy (𝑙𝑜𝑔(𝑛))
collect a wide set of complex indicators in a systematic and re-
there is an equal amount of activity in all fields; for minimum
producible way, directly aimed to make cities comparable in a
entropy (0) all the activity is amassed in a single field. In order
computational way.
to compare entropy scores of different-sized grids, the measure
must be normalized by dividing it by the expected entropy of a
3 DATASET uniform distribution, i.e., 𝑙𝑜𝑔(𝑛).
The testbed considered in this paper is a dataset of GPS traces of
private vehicles provided within the Track &Know project1 mov- 4.1.2 Moran’s I. It overcomes the entropy weakness by con-
ing in the Tuscany region, Italy. The experiments were performed sidering how the fields are positioned in space: spatial autocorre-
on a sample of 18.9 million trajectories of 250,239 cars, which lation [33] that represents the degree to which the fields’ values
were collected during a period of seven weeks. The geographical are correlated to the value of neighboring fields. For spatial au-
unit adopted to model a “city” is the municipality. tocorrelation, the nearness between all pairs of fields must be
All measures were calculated separately for each of the 276 defined with a so-called weight matrix 𝑤, where 𝑤𝑖 𝑗 is the near-
municipalities of Tuscany. For the sake of simplicity and applica- ness between nodes 𝑖 and 𝑗. A simple form of weight matrix is
bility to a wider range of situations, the areas to investigate were an adjacency matrix, with the value 1 if fields are adjacent, 0
chosen to be a 10 × 10 km rectangle for each municipality, with otherwise. An important difference to the entropy is that spatial
the sides approximately parallel to the meridians and parallels, autocorrelation has two directions. A high autocorrelation indi-
centered around the town or village center (see Figure 1). cates that values of the same magnitude are prone to be next to
It should be noted that, for the purpose of this work, only a each other, while a low autocorrelation means that similar values
partial subset of trajectories is considered, namely those starting are less likely to be near each other than under random posi-
and ending in Tuscany, and lasting less than 24 hours (indeed, tioning. Somewhere in between lies a value of autocorrelation in
longer trips are exceptional and not very representative). which the population of the fields is how one would expect it to
be under a random distribution with no spatial autocorrelation.
The most famous autocorrelation measures is Moran’s I [26]:
4 LOCAL CITY INDICATORS Í Í
Here we introduce the local city indicators designed individually
¯ 𝑗 − 𝑥)
𝑁 𝑖 𝑗 𝑤𝑖 𝑗 (𝑥𝑖 − 𝑥)(𝑥 ¯
𝐼 (𝑋 ) = Í 2
for each municipality. They are grouped in spatial concentration 𝑊 ¯
𝑖 (𝑥𝑖 − 𝑥)
measures, flows measure, individual mobility and street network. where 𝑁 is the number of fields, 𝑥 is the amount of activity or
population, 𝑥¯ is the average field value, and 𝑊 is the sum of all
the weights. The minimum and maximum values of Moran’s I
1 https://trackandknowproject.eu/
depend on the weight matrix. We highlight that the absence of
autocorrelation is given at Moran’s I equals to −1/(𝑁 − 1), that have the same expected weight. We highlight that the direction
tends to zero in grids with an high amounts of fields. of traffic flow is not important here. Thus, the grid networks in
this work are transformed into non-directed networks before the
4.1.3 Nearest Neighbor Distance. The Average Nearest Neigh-
modularity is calculated. Modularity does not describe a network
bor Distance (ANND) is not dependent on a grid and its param-
on its own, but a network along with its partition. In order to
eters. For every point, the distance to its nearest neighbor is
quantify how well an urban region is separable into different sub-
calculated. The mean of those values is the ANND :
Í areas we adopt the Louvain Algorithm [6] that does not guarantee
𝑚𝑖𝑛(𝑑𝑖 ) an optimal solution but it performs well empirically.
ANND = 𝑖
𝑁
where 𝑑𝑖 is a vector containing the distances of point 𝑖 to all 4.2.3 Interaction Models. The flow network allows us to test
the other points, and 𝑁 is the amount of points. The lower the how well the empirical data aligns with two established mod-
ANND , the higher is the average spatial concentration in the els that describe human interaction in space. The Gravitation
areas surrounding the points. We highlight that this definition Model [1] idea is that the traffic flow from place 𝑖 to place 𝑗
bears a similar weakness as the entropy. The expected ANND depends on the origin population 𝑚𝑖 and the destination popula-
under assumption of a uniform distribution of points across the tion 𝑛 𝑗 . Highly populated places, attract flow towards them. The
area is the Mean classic model predicts the traffic flow from 𝑖 to 𝑗 which have a dis-
p Random Nearest Neighbor Distance (MRNND) 𝛽
MRNND = 0.5 𝐴/𝑁 , where 𝐴 is the surface of the area and 𝑁 tance of 𝑟 as 𝐺𝑖 𝑗 = 𝐴𝑚𝑖𝛼 𝑛 𝑗 /𝑟 𝛾 , where 𝐴 is a normalization factor,
the amount of points. By dividing the ANND by MRNND we and 𝛼, 𝛽, 𝛾 are the model’s parameters. They can be optimized by
obtain the Nearest Neighbor Index (NNI ) which is comparable multiple regression when fitting data to the model. In this work
among samples with different sizes and areas. A NNI smaller we adopt a simpler model [25] with 𝛼 = 𝛽 = 1. The Radiation
than 1 indicates a higher spatial concentration than in a random Model [37] updates 𝐺𝑖 𝑗 by introducing 𝑠𝑖 𝑗 that is the population
case, whilst value above 1 shows that the points are spread out within a circle around place 𝑖, with a radius of its distance to
across the map more than one expects in a random scenario. place 𝑗, minus 𝑚𝑖 and 𝑛 𝑗 . The intuition is that outgoing trips are
being attracted by nearby populations [25]. It predicts the flow
4.2 Flows in a Grid Network 𝑇𝑖 𝑗 as 𝑇𝑚 𝑖 𝑚𝑖 𝑛 𝑗
where 𝑇𝑖 is the sum of outflows
1− 𝑀𝑖 (𝑚𝑖 +𝑠Í
𝑖 𝑗 ) (𝑚𝑖 +𝑛 𝑗 +𝑠𝑖 𝑗 )
In order to capture the information about flows in urban regions, from 𝑖, and 𝑀 = 𝑖 𝑚𝑖 is the total sample population.
the data can be transformed into a directed weighted graph that
represents the flow of the people’s trajectories: 4.3 Individual Mobility
• a set of nodes 𝑉 representing places that are origins and
Here we consider the mobility at level of individual users. From
destinations of trajectories,
this perspective, urban regions can be described by aggregated
• a set of edges 𝐸 representing the directed connections
values of their inhabitants’ mobility, therefore a set of statistics
between the nodes,
are calculated for each individual from their trajectories:
• a weight function 𝑤 : 𝐸 → R that maps each edge to a
weight, which indicates the amount of trajectories that • Average distance and duration per trip
occur along the edge. • Average driving distance and duration per day
The map is split into fields of a grid and all origins and destina- • Average amount of trips per day
tions of the trajectories in the area are assigned to the field in Also, following the methods described in [21, 31], individu-
which they lie. The network is created by assigning every node to als’ mobility data can be transformed into Individual Mobility
a cell, and to each edge the weight the amount of flows occurring Networks (IMN ), which is a representation of a person’s travel
along the edge. The weight function 𝑤 is equivalent to an origin behavior in the form of a weighted directed network, where the
destination matrix. The network allows us to gain knowledge set of nodes 𝑉 represents places that are visited once or repeat-
about the structure of a region by looking at the properties of edly by the individual, and the edges 𝐸 represent trajectories
the resulting network described in the following. from one of those places to another. The edge’s weights model
the amount of times was followed a trajectory from one node
4.2.1 Node Degrees. A basic property of the network is the
to another. From an IMN , we can describe the individuals travel
distribution of its degrees. Degree is hereby defined as the total
behavior with the following indicators:
traffic (sum of in- and out-flow) of a grid field. This measure is
sometimes also referred to as node-flux [34]. • Size of the network: number of nodes and edges.
• Temporal-uncorrelated entropy: measure how equally the
4.2.2 Louvain Modularity. An interesting quality of networks
different places of the IMN are visited.
is the degree to which nodes can be partitioned into groups,
• Radius of gyration [28]: approximates the average distance
such that the connectivity is high within those groups, and low
of an individual from its center of mass [18].
in between. In the context of urban regions, the corresponding
• Regularity of trajectories: percentage of trips that are driven
question is: can the city be split into areas that are relatively
more often than a certain threshold per time [19, 21].
autonomous and have only low interaction between them? In
• Modularity: the Louvain Algorithm [6] applied to the IMN .
network science, modularity measures this property for a given
partitioning: a graph partitioning separates the graph’s nodes into
non-overlapping communities. Modularity shows the difference 4.4 Roads and Traffic
between the relative amount of inner-community links and the 4.4.1 Static Road Network. This section focuses on the road
expected relative amount under random linking in a non-directed network modeled as a directed graph (𝐺 = (𝐸, 𝑉 ), where 𝑉 is
weighted graph [4]. The modularity goes from −1 to +1, where 0 a set of nodes representing roads intersections, 𝐸 is the set of
marks the value expected in a network where all possible edges directed edges which model the the road segments, and 𝑙 : 𝐸 → R
maps each edge to its length in meters. Some basic statistics of
the road network can be calculated:
(1) amount of edges and nodes/node density
(2) amount of intersections/intersection density
(3) average node degree/average intersection degree
(4) total length of edges/mean edge length
In addition, since nodes in any network can be evaluated w.r.t.
their centrality, we evaluate the road network’s closeness centrality
in terms of the length of the shortest path to any given node. The
average of those path lengths is a node’s average farness from
other nodes. The reciprocal of this value is a node’s closeness
centrality 𝐶 (𝑥) = Í 𝑑1(𝑦,𝑥) , where 𝑥 and 𝑦 are nodes and the 𝑑
𝑦
returns the length of the shortest path between its arguments.
As distance function we consider the length as the summed road Figure 2: Disconnected nodes vs. flow threshold.
lengths of the edges of the shortest path [30].
4.4.2 Traffic in the Road Network. To investigate how traffic is through Figure 2. The plot shows the number of disconnected
distributed in a road network one must map match the sequences nodes corresponding to a selected threshold. The fraction of
of GPS locations that represent the trajectories to nodes and “isolated” cities grows as the threshold increases, but there is
edges in the road network. There is a variety of algorithms that a little plateau between 110 and 130, which led to our choice.
handle this problem, such as hidden Markov models [27]. In the With the selected threshold, the final graph consists of 276 nodes
case study of this work, a simpler algorithm was implemented (corresponding to municipalities), 22 of which are disconnected
due to the high reliability of the data. It independently maps from the giant component.
every point of a trajectory to a node in the road network. The The properties related to each node of the network constitute
nodes are then connected and build a path that describes the the first set of attributes to be considered for clustering:
individual’s trajectory.
Given a map matching, it is possible to create a function that • Self-loops: # trajectories starting and ending in that node.
reveals the fraction of total traffic that flows through a given • In/Out degree: fraction of nodes its incoming/outgoing
percentage of the most dense roads. For this purpose, all edges are edges are connected to.
sorted by their traffic flow in a non-ascending order. Cumulative • Closeness: the closeness centrality of a node 𝑢 is the recip-
traffic, measured as #𝑐𝑎𝑟𝑠 × 𝑚𝑒𝑡𝑒𝑟𝑠, is calculated for the end rocal of the average shortest path distance (see Section 4.4).
of every edge by multiplying the edge length with the amount • Betweenness: the betweenness of a node 𝑣 is the sum of
of traffic flow and adding the result to the previous amount of the fraction of all-pairs shortest paths that pass through 𝑣.
cumulative traffic. The intermediary values within edges can • Clustering coefficient: the local clustering coefficient 𝐶𝑖
be calculated by linear interpolation. For any given percentage for a vertex 𝑣𝑖 is given by the proportion of links between
of roads, the percentage of traffic in those roads is calculated the vertices within its neighborhood divided by the num-
by dividing the cumulative traffic until that point by the total ber of links that could possibly exist between them.
amount of traffic. • Radius of Gyration: q the radius of gyration of a city 𝑐 is
1
defined as 𝑟𝑔 (𝑐) = 𝑁 𝑖 𝑤𝑖 (𝑟𝑖 − 𝑟𝑐𝑚 ) 2 , where 𝑁 is the
Í𝑁
5 GLOBAL CITY INDICATORS total number of travels from 𝑐, 𝑤𝑖 is the number of travels
In this section we introduce the global city indicators designed from 𝑐 to 𝑖, 𝑟𝑖 is the pair of coordinates of location 𝑖 and
to compare two cities. To compare and cluster cities in groups, 𝑟𝑐𝑚 is the center of mass (i.e., the average position) of the
we need some quantitative features. Therefore, we have to define visited cities starting from 𝑐.
some metrics describing a city with respect to traffic. A possible • Random Entropy: the random entropy captures the de-
approach is to exploit again a network structure where each city gree of predictability of the destination starting from a
(in our case study, 276 municipalities in Tuscany) is a node, and city 𝑖 if each location is visited with equal probability
edges are drawn based on the trajectories between them. Starting 𝑆𝑟𝑎𝑛 = log2 𝑀, where 𝑀 is the number of distinct cities
from the trajectories we infer descriptive attributes from two visited starting from city 𝑖;
perspectives: (i) graph measures from the complete network of • Uncorrelated Entropy: the temporal-uncorrelated entropy
cities; (ii) graph measures from the ego-network of each city. is the historical probability that a location 𝑗 was visited
starting from a city 𝑖, characterizing the heterogeneity its
Í
5.1 Complete Network of Cities of visitation patterns 𝑆𝑢𝑛𝑐 = − 𝑁 𝑗 𝑝 𝑗 log 𝑝 𝑗 where 𝑝 𝑗 is
We can derive a set of global indicators through a network of 𝑖’s probability of visiting location 𝑗. We can also normalize
cities as described in the following. Given the trajectories on the uncorrelated entropy by dividing it by log2 𝑁 .
the territory, we can derive an Origin-Destination Matrix (OD),
which measures the number of trips that starts from city 𝐴 and 5.2 Ego-Networks
ends in city 𝐵 for each pair (𝐴, 𝐵). Since connections established In Social Network Analysis, it is usual to refer to Ego Networks
through very few trajectories might be not significant, a threshold as social networks made of an individual (called ego) along with
is needed to establish if an edge should be drawn. In our case all the social links he has with other users (called alters)[3, 10].
study, after empirical evaluation, we fixed this threshold to 110 Several fundamental properties of social relationships can be char-
trajectories by analyzing the results yielded by different values acterized by studying them. Adapting the terms to the present
context, we can obtain an ego network for each city, where the
ego is the city itself and the alters are its neighbors. The additional
set of attributes obtained consists of:
• Number of nodes of the ego network.
• Number of edges of the ego network.
• Average clustering coefficient: the clustering coefficient
is the average 𝐶 = 𝑛1 𝑣 ∈𝐺 𝑐 𝑣 , where 𝑛 is the nbr. of nodes
Í
in 𝐺 and 𝑐 𝑣 is the clustering coefficient of each node;.
• Diameter: is the longest shortest path of the ego network.
• Assortativity: is measured as the Pearson correlation co-
efficient of degree between pairs of linked nodes. It mea-
sures the preference for a network’s nodes to attach to
others that are similar in some way.
Figure 3: Network of correlations for the first set of at-
6 CASE STUDY: TRANSFER-COMPLIANT tributes (total graph).
GEOGRAPHICAL LOCATIONS
The huge amount of urban data generated by smartphones, vehi-
cles, and infrastructures (e.g., traffic cameras, air quality moni-
toring stations) opens up new opportunities to learn about city
dynamics from a variety of perspectives and facilitates various
smart city applications for traffic monitoring, public safety, urban
planning, etc. – all contributing to what is called urban computing.
However, there are some questions that remains still almost
unexplored: what if the administration of a city wanted to predict
the impact of an event on the urban mobility without having
historical data on it? Is it possible to infer some useful insights
exploiting the experience gained by other municipalities? Can
knowledge be transferred from any city or are there some con-
straints? How can you compare two cities, for example in terms of
urban mobility? Lately there have been different attempts to over-
come the data scarcity issue in “new” urban contexts. All these
studies have in common the application of Transfer Learning, a Figure 4: Dendogram and selected clusters.
very broad family of approaches which focuses on developing
methods to transfer knowledge learned in one or more “source
tasks”, and use it to improve learning in a related “target task”. Preprocessing and Feature Selection. Since the range of differ-
This section studies these questions in the context of Machine ent indicators varies widely, we applied a form of normalization
Learning (ML) and big data analytics for mobility data. In partic- to make them homogeneous. We adopted the min-max scaling,
ular, our goal it to verify the feasibility of a model transfer, i.e., a where feature are re-scaled in the interval [0, 1]. Then, we per-
ML model is trained in the source domain and then transferred formed a study of correlation on each set of features (local and
to the target domain, in the prediction of urban traffic, exploiting global) to eliminate unnecessary ones. To efficiently filter them,
the city indicators developed in the previous sections. we adopted a network-based correlations finder, where the fea-
The basic idea is that cities that are similar can be represented tures are interpreted as nodes of a graph, and a link is drawn
by the same model more easily than very different cities. For between two features if they are highly correlated. As evaluation
instance, a highly populated city with heavy traffic and users metrics, the standard Pearson’s Correlation Coefficient is used [29].
that frequently make long trips is expected to have mobility Considering each couple of features (𝑖, 𝑗), an edge is drawn if
dynamics very different from small, country-side cities with low 𝜌𝑖,𝑗 > 0.65. The result obtained on the global features is shown
traffic. The approach proposed in this section is developed in as example in Figure 3. The removal of features is an iterative
three steps: first, using a similarity measure between cities based process that removes the node (feature) with the highest degree
on the indicators presented in Sections 4 and 5, cities are clustered (thus is correlated to the highest number of non-filtered features)
into similarity groups; next, for each city a traffic prediction task and repeats until the average degree of the network is 0. The
is defined, which is approached through a standard machine remaining nodes are the features which are preserved. This pre-
learning solution (XGBoost regression [8]); finally, the prediction processing step is applied to global and local indicators separately,
model of a city is applied to make predictions in each of the and then on the set of survived features of both categories. Apply-
others, aiming to test whether cities in the same cluster show a ing the procedure to our case study, the initial set of indicators,
better transferability of their models. composed of a total of 178 measures, was reduced to 21 features.
Hierarchical Clustering. The city clustering step has been re-
alized through a Hierarchical agglomerative clustering schema,
6.1 City Clustering
adopting Ward’s linkage criterion, which at each step of aggre-
In this step, the city indicators built in the previous sections are gation aims to minimize the total within-cluster variance. In our
first preprocessed and filtered, and then used to cluster cities. case study, a small fraction of cities resulted to be disconnected
cluster id # of cities % of cities
0 22 8.0
1 53 19.2
2 47 17.0
3 110 39.9
4 44 15.9
Table 1: Cluster Population
Figure 6: Selected cells for some municipalities.
from outside or going outside. Indeed, they have high values
for entropy and low values for Moran’s I, the highest number of
nodes regularly visited from users and a large ego network radius.
This cluster is the most populated, comprising almost 40% of the
dataset. Finally, cluster 4 was called Hubs, since it comprises all
the biggest cities, encompassing most of the busiest roads in
Tuscany. Municipalities are pretty similar to those belonging to
cluster 3, excepted that they have a large Moran’s I, which reflects
the presence of specific patterns within the city.
6.2 Traffic Forecasting in City Grids
Urban traffic prediction is a discipline that aims to exploit ML
models to capture hidden traffic characteristics from substantial
historical mobility data, making then use of trained models to
Figure 5: Map of clustered municipalities. Colors white, predict traffic conditions in the future [24]. However, there is
yellow, orange, red and dark red correspond resp. to clus- a main problem to face: is it possible to extract specific traffic
ters 0, 1, 2, 3 and 4. patterns that reflect the peculiarities of a city structure?
A Grid to Split the City. Following one of the most used ap-
from all the others in terms of flows, thus making them outliers proach in traffic prediction problems [24], we divide every geo-
w.r.t. the global features (e.g., the assortativity measure is null). graphical area corresponding to municipalities in adjacent squared
Therefore, we decided to put them in a separate cluster, and apply cells having side of 0.5 km, and our predictive objective is to fore-
the hierarchical clustering on the remaining ones. The results cast the traffic flow that crosses a given cell. In our case study we
of applying the clustering to our dataset is shown in Figure 4 as select a subset of representative cells and, in order to avoid the
a dendogram of the hierarchical clusters found (notice that the possible issues emerging when a random or top-frequency subset
dendogram is truncated, in order to show only the last 12 aggre- is selected, we adopt a mixed approach, randomly selecting 5 cells
gations. Based on the gaps between splits/merge points in the among those having a traffic volume above the 90𝑡ℎ percentile
dendogram, the aggregation is stopped at distance 4.0, yielding over the municipality, and other 5 cells among those having a
four clusters. To these, we add another cluster (id 0) containing traffic volume between the 80𝑡ℎ and the 90𝑡ℎ percentiles.
the isolated cities. A summary of clusters’ size is in Table 1.
Time Series Preprocessing. Based on the trajectories that cross
An analysis of the properties of each cluster reveals that they
the representative cells identified above, we compute a time series
may be distinguished based on the kind of traffic flows they
for each cell with a 1-hour sampling rate, by counting the number
involve. Also, clusters are depicted on the map in Figure 5. Cluster
of vehicles that crossed the cell within each hour of each day.
0 was named Disconnected, since it is composed by the nodes not
A first operation performed was to compute a moving-average
connected in the inter-city flows network. These municipalities
smoothing of the time series, since a preliminary test with the
also have a low entropy and low Moran’s I score, meaning a
Augmented Dickey-Fuller test (ADF) [14] reveals that they are not
not significant pattern of traffic, and most of them are located at
stationary, i.e. it could not be rejected the null hypothesis that a
the boundary of Tuscany and in the country-side areas, where
unit root is present in the time series sample (ADF=-2.38 against
there is a lower concentration of roads. Cluster 1, named Self
a critical 90% threshold at -2.57). On the contrary, after smooth-
Sufficient, is characterized by high entropy, high modularity and
ing, the null hypothesis is rejected with a very large confidence
high fraction of regular trips, yet a low radius of gyration and
(ADF=-5.57 against a 99% threshold at -3.43, p-value = 2 · 10−5 ).
low diameter of the associated ego networks. Also, they are
mostly far from the highways that cross the region. Cluster 2, Predictive Features. Similarly to what done by several time
called Visited Sites, have a very low entropy (almost as low as series forecasting solutions [12], we base our predictions for the
those in the disconnected group), low modularity and the lowest next value of the time series on more recent observations of the
fraction of regular trips, and yet a relatively high betweenness. same time series. In particular, we adopt as basic features the
Cluster 3 was named Drive Through, as these cities are crossed 24 most recent lagged values, i.e., the observations of the last
by a great flow of traffic, which is however basically coming 24 hours. We remark that in this simplified approach we do not
Figure 7: XGBoost traffic forecasting on Florence (green)
against real values (blue). The two curves differ in very
few points.
include features about other time series in the same municipal-
ity, as done in more complex solutions that exploit the spatial
autocorrelation of this kind of phenomena. Figure 8: Transfer scores matrix with cluster separation
Another important property that can be encoded is related to (red lines). Each row/column represents a municipality.
the weekday; at this regard, we introduce the Boolean feature
is_weekend that is true if the weekday is Saturday or Sunday and
false otherwise, since we expect to see different behaviors in the
weekends. Finally, we can encode information about a weekday
by inserting the average traffic volume at that day.
Having a total of 26 new features, we can now try to forecast
the smoothed time series.
Predictive Model. As regressive model, we selected the popular
and effective algorithm XGBoost [8]. XGBoost has proved to be
highly reliable in regression tasks, providing in general a good
accuracy of predictions and remarkable speed of execution, yield-
ing good results in term of robustness with its default settings,
which simplifies our task. XGBoost adopts a Boosting procedure,
i.e., is a ML ensemble meta-algorithm for primarily reducing bias
and variance in supervised learning, where a set of weak learners
is turned into a single strong learner.
In Figure 7 we can see an example of XGBoost predictions ex-
ploiting the features previously introduced over the municipality
of Florence, which shows results very close to the real values. The Figure 9: NMRSE mean values for all train-test pairs.
model performance is evaluated through the standardq Normal-
( 𝑦ˆ −𝑦 ) 2
Í𝑇
𝑡 =1 𝑡 𝑡
ized Root Mean Squared Error, defined as RMSE = 𝑇 , of prediction scores where on the rows there are the cities in
having predicted values 𝑦ˆ𝑡 for times 𝑡 of a regression’s dependent which the model is trained and in the columns those where the
variable 𝑦𝑡 , with variables observed over 𝑇 times. RMSE is always model is tested. The algorithm implemented iteratively trains
non-negative, the lower is the value the better are the predictions. a model on each city, tests it against all the cities and fills the
Since RMSE is scale-dependent, we adopt the Normalized RMSE score matrix with the corresponding NRMSE score obtained. To
(NRMSE), computed as: NRMSE = RMSE 𝜎 , where 𝜎 is the standard enable a more meaningful comparison, NRMSE scores are log-
deviation of the observed values. transformed to reduce the skewness.
Empirical evaluation shows that the most important feature is The final result is visually shown Figure 8 which shows the
the value of traffic 1 hour before, as expected, while the previous transfer scores by sorting the cities based on their cluster be-
hours have all a comparable influence. Instead, it is apparently longing. Keeping in mind that the squares around the diagonal
almost irrelevant to know if a day is a week-end day or not. represent training and testing on cities of the same cluster, while
the other rectangles depict training and testing on different clus-
6.3 Testing Model Transferability ters, we can observe:
In this section we study the transferability of the predictive mod- (1) the transfer is far better between cities of the same cluster
els built above, and its relation with the similarity groups found (the NRMSE values obtained making predictions on a mu-
through clustering. The hypothesis we want to test is that the nicipality using a model built on a different one is lower
similarity based on our city indicators is indeed useful to identify if the two belong to the same cluster);
groups of areas such that any model built from an area in the (2) it is worth noting that also cluster 0, that we built up
cluster is usable in other areas within the same cluster. artificially behave exactly as the others;
The first step is to split the traffic time series of each city in (3) the matrix is not symmetric: training on city 𝐴 and testing
training and test sets. In this way it is possible to obtain a matrix on 𝐵 is different from training on 𝐵 and testing on 𝐴.
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