=Paper=
{{Paper
|id=Vol-2068/uistda4
|storemode=property
|title=Toward Finding Latent Cities
|pdfUrl=https://ceur-ws.org/Vol-2068/uistda4.pdf
|volume=Vol-2068
|authors=Eduardo Graells-Garrido,Diego Caro,Denis Parra
|dblpUrl=https://dblp.org/rec/conf/iui/Graells-Garrido18
}}
==Toward Finding Latent Cities==
https://ceur-ws.org/Vol-2068/uistda4.pdf
Toward Finding Latent Cities
with Non-Negative Matrix Factorization
Eduardo Graells-Garrido Diego Caro
Data Science Institute Data Science Institute
Universidad del Desarrollo Universidad del Desarrollo
Telefonica R&D Telefonica R&D
Santiago, Chile Santiago, Chile
egraells@udd.cl dcaro@udd.cl
Denis Parra
Dept. of Computer Science
Faculty of Engineering
Pontificia Universidad Catolica
Santiago, Chile
dparra@ing.puc.cl
ABSTRACT available to them [12]. However, this is not enough to un-
In the last decade, digital footprints have been used to cluster derstand the city. As Charles Montgomery says in his book,
population activity into functional areas of cities. However, Happy City: “When we talk about cities, we usually end up
a key aspect has been overlooked: we experience our cities talking about how various places look and perhaps how it
not only by performing activities at specific destinations, but feels to be there in those places. But to stop there misses half
also by moving from one place to another. In this paper, we the story, because they way we experience most parts of cities
propose to analyze and cluster the city based on how people is at velocity: we glide past on the way to somewhere else.
move through it. Particularly, we introduce Mobilicities, auto- City life is as much about moving through landscapes as it is
matically generated travel patterns inferred from mobile phone about being in them” [32].
network data using NMF, a matrix factorization model. We
Since people may spend a considerable amount of time while
evaluate our method in a large city and we find that mobilic-
moving through the city, and the quality of that time has a
ities reveal latent but at the same time interpretable mobility
strong influence on mood, health, and productivity [39], it is
structures of the city. Our results provide evidence on how
important to understand city structure with respect to mobility.
clustering and visualization of aggregated phone logs could be
Given that the growth of cities is faster than the capability of
used in planning systems to interactively analyze city structure
traditional methods to understand the city, it is important to
and population activity.
have cost-effective ways to analyze the city at scale [46].
Author Keywords In this paper, inspired by Montogomery’s ideas, we estimated
Mobile Phone Networks; Urban Informatics; Urban Mobility; a characterization of the city defined by the collective experi-
Non-Negative Matrix Factorization. ence of its several areas. Particularly, we analyzed intra-city
transportation inferred from mobile phone network records,
which we represented in a Waypoints Matrix. This matrix, sim-
INTRODUCTION ilar to document-term matrices used in Information Retrieval,
The increasing availability of digital footprints, such as was decomposed using Non-Negative Matrix Factorization
Web/App access logs, user-generated content, and mobile (NMF) [11]. We interpreted and labeled the obtained com-
phone network data, has allowed to characterize the city at ponents, which we denoted Mobilicities. We evaluated our
spatio-temporal granularities never seen before. This means pipeline by performing a case study in Santiago, Chile, using
that the different functional areas of the city can be estimated, mobile phone network data from the biggest telecommunica-
based not only on how planners thought that the city would tions company in the country. Our pipeline delivered inter-
be lived, but on how people actually used the different spaces pretable results, in contrast with a well-established method.
We concluded that mobilicities can be used within an intel-
ligent user interface aimed at mobility and transportation-
analysis tasks.
BACKGROUND AND RELATED WORK
There has been a flurry of research of mobile phone network
©2018. Copyright for the individual papers remains with the authors. data known as eXtended and Call Detail Records (X/CDR), as
Copying permitted for private and academic purposes. evidenced in recent surveys on the area [4, 8]. Some examples
UISTDA ’18, March 11, 2018, Tokyo, Japan
include: understanding socio-economic factors on the popula- 3. The decomposition of W using NMF into the product of two
tion [41], understanding family and social relations [13], char- matrices, U and T , according to a number of k components,
acterizing response to emergencies and critical events [33], which we denote as mobilicities.
crime detection [5], credit scoring [40], test of urban theo-
Trip Detection. To detect trips from X/CDR traces, we resort
ries [14]; and the provision of a cost-effective way of un-
to an algorithm based on transportation rules and trajectory
derstanding population dynamics and behavior in developing
countries [21]. simplification [19]. The algorithm builds a space-time trajec-
tory from daily X/CDR events, where space is the cumula-
The mobile phone network events of a given device depict tive distance between consecutive connected towers, starting
a spatio-temporal trajectory that can be processed to infer from zero at the first connection of the day. This trajectory is
trips, by using geometric approaches based on transportation simplified using a line-simplification algorithm. Then, each
rules [19], or by clustering events in the trajectory [7]. When segment from the simplified trajectory is categorized accord-
individual trips are known, it is possible to aggregate them into ing to transportation rules, such as the relationship between
Origin-Destination (OD) matrices. This analysis is common the approximated trip distance and time, which is visually
in the literature from X/CDR [2, 23, 16, 7], and shows that inspected through the slope of the segment. In other words,
inferring individual mobility is a relevant problem. the trip detection allows us to separate X/CDR events into
the following: stationary events (the user was performing an
Other important aspects are the characterization of land use activity), trip start events (denoting the origin), trip end events
(e.g., residential areas, business areas, etc.) and functional (denoting the destination), and within-trip events (denoting
areas (i.e., delimited areas that serve specific or multiple land mobility).
uses). Since it is crucial to understand the dynamics of these
aspects, functional areas have been measured, monitored and Building the Waypoints Matrix. Ideally, characterization of
categorized using digital footprints [45, 43] and X/CDR [34, within-trips events does not need to be done using aggrega-
26, 42, 1, 18]. A similar work to ours has applied NMF to tion. For instance, GPS data allows to do rich clustering over
understand trip purpose, and build functional areas based on specific trajectories [47]. However, due to the billing purpose
the spatial distribution of such purposes [36]. of X/CDR data, it is possible that trips have few within-trip
events because of the billing cycle. Since we will focus on
The key difference between the aforementioned work and our
within-trip events, we need to aggregate such events from
proposal is the focus. Other work focuses on the destinations
an extended period of time. Furthermore, some trips do not
of trips, as well as activities performed within places. As
have within-trip events, such as those with duration near to
such, their definition of functional area is limited by those the billing cycle time, and those within zones with low tower
places that, in transportation terms, attract people [20]; yet, as density. Hence, by aggregating all within-trip events for a user
mentioned by urbanists, the city is experienced in sequence by in a period of time, the likelihood of identifying the towers
moving from one place to another [32]. Each citizen has an that characterize a specific user’s mobility increases. We use
unique version of the city, built upon the sequence of nodes, this schema to define a Waypoints Matrix W, defined as:
landmarks, and paths traversed [28]. In this paper we show
that, by using mobility inferred from X/CDR, and using NMF
to decompose/cluster the different cities experienced by mobile # of within-trip events of user ui at tower t j
wi, j =
phone users, we are able to identify the different Mobilicities # of within-trip events of user ui
that comprise a big urban city.Even though we have centered
the discussion around mobile phone network data, it is possible This schema is equivalent to the L1-normalized document-
to infer transportation and urban patterns from other sources, term matrices found in Information Retrieval, but without
particularly social media. Twitter has been shown to be a weighting with Tf-Idf [44]. We do not apply Tf-Idf because
good predictor of commuter flows [31] at several scales [27]. its purpose is to identify discriminative features; conversely,
Now, these approaches have the same limitation as previous we want to extract collective features. Additionally, note that
approaches: a focus on the origins and destinations of trips, this matrix is different to those used in related work with NMF
mainly due to their way of modelling mobility: using gravity decompositions [36]: there is a semantic difference between
and radiation models (see [29] for a comparison). Twitter within-trips and trip start/end events. To avoid this polysemic
data, while massive and longitudinal, does not allow to infer behavior, we focus only on within-trips events.
within-trip behavior.
Applying Non-Negative Matrix Factorization. To represent
how users interact with towers, we propose to decompose this
METHODS matrix into two: W = U × T , where U is a |u| × k matrix that
Our methods can be summarized in a pipeline of three steps: encodes k user latent features for |u| users, and T is a k × |t|
matrix that encode k latent tower features for |t| different cell
1. Trip detection from X/CDR data, which, for each device phone towers. Note that, by definition, all wi, j ≥ 0. NMF
in the dataset, identifies its corresponding daily trips, with allows us to decompose the matrix W into two non-negative
origin, intermediate, and destination towers. matrices, which gives a lower rank approximation for W, such
2. The construction of a Waypoint Matrix W that aggregates that W ≈ U × T [24]. This can be formalized as the following
the intermediate towers of trips, of a given period of time, optimization problem: minU,T kW − U × T kF subject to U
into a device-antenna matrix. and T be non-negative, where number of rows in U and the
Figure 2: Number of events in the dataset per day. The effect
of weekends in the number of events is easily identifiable.
Metric
# of Trips 4,213,400
# of Users 124,415
# of Users with Within-Trip events 95,027
Mean trips per user 33.87
Std. Dev. 19.62
Min 1
Percentile 25% 18
Figure 1: Choropleth map of the urban area of Santiago, Chile. Percentile 50% 34
Each municipality is colored according to their average income Percentile 75% 48
(in CLP$). Max 140
number of columns in T correspond to the desired lower-rank Table 1: Statistics with respect to the number of inferred trips.
approximation k.
Even though there is a variety of methods to decompose ma-
trices, we choose NMF, which has been applied in similar
contexts with interpretable results [36]. Then, we define a trips between 6AM and midnight, and had either a pre-paid
mobilicity mc as the weighted set of towers within the c com- or contract subscription. They generated an average of 5.33
ponent of the decomposition, i.e., the c-th column of matrix million billing records per day (c.f. Fig. 2). The average inter-
T. The parameter k must be chosen manually, and its value event times for users range within 14.71 and 30.96 minutes,
should be ideally decided jointly between data scientists and which shows a billing cycle between fifteen and thirty minutes.
domain experts according to the context. Previous strategies Telefónica has 1,464 cell phone towers in the municipalities
for choosing k have focused in measuring the stability of the under consideration. We discarded towers that were installed
components [6] and in the variation of the residual sum of in in-door contexts (e.g., malls, hospitals, etc.). This is possible
squares curve between the original matrix and its decompo- because tower meta-data includes their geographical position
sition [17, 22]. However, we prefer to manually choose the and their name. For out-door towers, the name usually contains
number of components as these methods do not allow us to the nearest crossing, while in-door towers contain the name of
incorporate external information such as the socio-economic the place they lie in. In total, there were |t| = 1,082 out-door
distribution of the city. towers (see Fig. 3, Towers). The only in-door towers that we
kept were those installed within underground metro stations.
CASE STUDY: SANTIAGO, CHILE
We performed a case study on Santiago, the capital of Chile, OpenStreetMap. OSM (http://openstreetmap.org) is a crowd-
with almost 8 million inhabitants. Its urban area covers a sur- sourced maps platform. We downloaded a dump of its data for
face of 867.75 square kilometers, and is composed of 35 inde- Chile, and then identified the highways within Santiago. We
pendent administrative units called municipalities (c.f. Fig. 1). used this information to contextualize the different mobilici-
Because this city has experienced accelerated growth, and ties identified by the NMF. We did so by finding the out-door
it is expected to keep growing at least until 2045 [38], un- towers that lie within 250 meters of each highway, as shown
derstanding its structure at scale is an important and timely in Fig. 3 (Labeled Towers).
task.
Datasets Trip Detection and Waypoints Matrix
Mobile Phone Network Data. We studied an anonymized Using the trip inference algorithm we detected 4,213,400 trips
X/CDR dataset from Telefónica Chile, the biggest telco. in for 124,415 users (c.f. Table 1 for descriptive statistics). Fig. 4
Chile, with a market share of 33% in 2016. The dataset con- shows the departure time distribution of all trips. One can see
tained records between July 27th and August 10th from 2016. that business days exhibit expected peak-times related to work
In total, we analyzed 124,414 users, who had enough connec- hours, and that weekends exhibit different patterns, such as a
tions to the cell towers under analysis to estimate their daily higher density at lunch time.
Figure 3: Maps of Santiago: cell phone tower network, highway and primary streets, the metro network, and the set of labeled
towers according to their distance to highways or metro lines.
C1 : people that live in the southern part of the city, mostly
between two metro lines. Since this area is characterized by
low income, this means that they need to take a bus to reach
the metro.
C2 : the southeast area of the city, which is characterized by
their dependency of two metro lines. This component con-
tains mixed-income municipalities.
C3 : In contrast with the previous components, this one is com-
Figure 4: Trip departure time distribution per day. pletely focused on public transportation: it fully contains
two metro lines in full, and partially other two. It also
After detecting trips, we built the W matrix, of dimensions contains bus corridors that tend to connect to metro lines.
|u| × |t|. Note that |u| = 95,027, because not all users had C4 : the northern part of the city, which is mostly residential
within-trip events. and of low income. The component also has a main street
of the city as a kind of tentacle, showing that people who
Factorization of the Waypoints Matrix lives/work in this area, but who work/lives in another, uses
To perform the NMF decomposition, we chose k = 8, because this street as a way to get into the component.
the city is usually divided into six big areas (north, south, east, C5 : the south-west part of the city, which is connected to
west, south-east, center) and, since we expect that the results downtown primarily through a highway and a metro line
exhibit relationship with modes of transportation, we wanted that is parallel to the highway.
to see the effect of private and public transportation. Thus, k = C6 : the western area of the city. This area contains one of the
8 is an arguably reasonable choice (note that we discuss the most populated municipalities in the city.
choice of k at the next section). C7 : similar to C6, but extending its reach to center areas of
the city through a metro line a bus corridors. This makes
Tower-Component Matrix. Figure 5 shows the results of this component dependent on public transport, and thus, the
the factorization, with one map for each component-tower routes followed by its inhabitants tend to cluster, in contrast
column from the matrix. One can see that there is a strong to what happens in C6.
geographical clustering of towers, which may be explained as
W is essentially a co-occurrence matrix. In summary, latent cities seem to be comprised by three kinds
of clusters of towers: those where people lives and moves,
Fig. 6 show how the sets of labeled towers (those near high- enclosed by specific limits (C0, C1, C6), those where people
ways, near surface metro and within underground metro sta- lives and work, but in different areas of the city, connected
tions) relate to each component. This allows to see that some through the transportation network (C2, C4, C5, C7), and
components tend to be more associated than others to some transportation infrastructure (C3).
modes of transportation: C1, C2, C3 and C7 are more associ-
ated to metro than highways, while C4 exhibits the opposite User-Component Matrix. The user-component matrix may
behavior. Having both figures into account, the following is suggest that users pass through different mobilicities in their
an interpretation of each mobilicity: daily lives. Fig. 7 explores this potential behavior, by display-
ing how a sample of 25,000 users cluster around the corre-
C0 : the east side of the city, including part of the center, next sponding components. One can see that, indeed, users tend
to the yellow metro line and one important highway of the to have a primary component, but they still belong to others.
city. This area is characterized for its business districts and This would be the equivalent to, for instance, living in the
high income residential areas (c.f. Fig. 3). As such, it is suburbs, and having to travel long distances to go to work.
likely that its residents do not use public transportation, nor Note that many users from C0, the wealthiest part of the city,
visit other mobilicities. Note how metro towers have lower have negligible association to other components – something
association with this component in Fig. 6.
Figure 5: The eight mobilicities of the tower-component matrix obtained by performing NMF.
Figure 6: Point-plot of the average association of the labeled sets of towers into the different mobilicities.
ized matrix. We do so by estimating mobilicities with k0 = 4
(c.f. Fig. 8) and k00 = 12 (c.f. Fig. 9).
With four mobilicities, the clustering is mostly geographic:
three components split the city. However, the fourth compo-
nent is related to public transportation: it reconstructs several
metro lines and bus corridors. In this aspect, it seems that using
k0 = 4 allows to obtain a similar result to k = 8. Then, if one
would like to differentiate cell towers with respect to general
transportation patterns, this could be a reasonable choice.
With twelve mobilicities, the geographical clustering is still
present, but the routes that connect distinct parts of the city
Figure 7: Heatmap of a random sample of 25K users and their become more evident – meaning that a mobilicity is comprised
corresponding component associations. by one or two sectors of close towers (for instance, home and
work locations), plus “bridges” that connect one mobilicity
expected due to the economical segregation of the city (c.f. to another, based on the common routes followed by people.
Fig. 3). This behavior is expected, due to the co-occurrence property
of the Waypoints Matrix.
Understanding k. We showed the eight mobilicities (c.f.
Fig. 5) to domain experts, who gave informal feedback – it In summary, several values of k allow to infer soft-partitions
made sense to split the city in this way, as we have interpreted of the city, as well as the way its inhabitants move between
earlier. Even though a formal evaluation with domain experts those partitions. A mobilicity may be a soft-partition, a soft-
is left for future work, here we discuss the patterns that emerge partition with bridges to other mobilicities, or a network of
when varying the parameter k which is the rank of the factor- those bridges – namely, a transportation network.
ization methods for positive-only data such as SLIM, which
has shown promising results in the past [25], and would allow
to understand how the choice of k influences the output and
its interpretability. On the other hand, visualization and ex-
ploratory interfaces are tools valued by domain experts [10],
and mobility has been a recurring topic in visual analytics [3].
Finally, our work did not consider the temporal aspects of
transportation. Hence, future work should consider how to
incorporate that dimension into the definition of Mobilicities.
Acknowledgements. The analysis was performed using
Jupyter Notebooks [37], jointly with the scikit-learn [35], pan-
das [30], and geopandas libraries. The maps on this paper
include data from ©OpenStreetMap contributors. We also
thank Telefónica R&D in Santiago for facilitating the data
for this study, in particular Pablo Garcı́a Briosso. The au-
thor Denis Parra has been funded by Conicyt, Fondecyt grant
11150783, as well as Fondef grant id16i10222 and the BRT+
Centre of Excellence funded by VREF. Finally, we thank the
anonymous reviewers for the insightful comments that helped
to improve this paper.
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