# Complete Trajectory Reconstruction from Sparse Mobile Phone Data

Guangshuo Chen, Aline Carneiro Viana, Marco Fiore, Carlos Sarraute

► To cite this version:

Guangshuo Chen, Aline Carneiro Viana, Marco Fiore, Carlos Sarraute. Complete Trajectory Reconstruction from Sparse Mobile Phone Data. NetMob 2019, Jul 2019, Oxford, United Kingdom. hal-04699871

HAL Id: hal-04699871

https://inria.hal.science/hal-04699871v1

Submitted on 17 Sep 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Complete Trajectory Reconstruction
from Sparse Mobile Phone Data

G. Chen (Inria), A. Carneiro Viana (Inria), M. Fiore (CNR-IEIIT), and C. Sarraute (GranData Labs)

aline.viana@inria.fr

Mobile phone data are a popular source of information
in many recent studies across multiple disciplines, and have
largely contributed to improving our understanding of human
mobility, interactions and habits [1]. Mobile phone data consist
of time-stamped and geo-referenced communication events
recorded by network operators, on a per-subscriber basis. They
offer an unprecedented possibility of monitoring populations
of millions of individuals over long periods that span months.

However, due to the uneven processes that govern mobile
communications, the sampling of user locations in mobile
phone data tends to be sparse and irregular in time, leading
to substantial gaps in the individual trajectory information.
As a result, mobile phone data offer a quite partial view of
the overall mobility of each user, with substantial continuous
periods where the positioning information is entirely absent [2].
In short, such data is usually temporarily or spatially sparse.

We address the problem of sparsity in mobile phone data, and
investigate how to solve it through *trajectory reconstruction*,
*i.e.*, the completion of individual movement information in the
data by recovering the missing positions of each individual.
To achieve our objective, we take the following steps.

First, we mine a large-scale mobile phone dataset collected
in an operational nationwide network over three months, and
provide a **characterization of the severe sparsity that affects
mobile phone data** of 1.8 million users. We quantify the
phenomenon by means of relevant metrics, including the
sampling frequency and a dedicated completeness measure of
individual trajectories in the data. Our results show that sparsity
can be dramatic: for instance, only 5% of the actual positions
that can be inferred, on average, for each user when working at
a temporal resolution of 15 minutes. An important corollary of
this result is that pre-processing techniques commonly adopted
in the literature –which perform user filtering via (even mild)
data sparsity thresholds– remove the vast majority of the
available user population from subsequent analyses, hence
introducing hard-to-estimate potential biases.

Second, we introduce an **original approach for the recon-**
**struction of trajectories from sparse mobile phone data.** Our
solution leverages well-known features of human mobility
(e.g., the temporal prevalence of static phases, the regularity
of movements, or the stability of overnight locations) to tailor
and solve a *tensor factorization* problem that befits our goal.
The proposed methodology allows transforming the highly
incomplete positioning information inferred from mobile phone
data into seamless individual trajectories that cover locations
of all users throughout the full duration of the original dataset.
We validate this strategy by using ground-truth mobile phone
data collected at high frequency for a subset of 1,450 users:

<figure><img src="image_2.png" /><figcaption>Fig. 1. Cell displacement of locations inferred via tailored tensor factorization with respect to ground truth, versus the level of completeness of the original trajectory (which are sparser at lower completeness). Candlesticks highlight the mean (light blue), median (dark blue), 25th and 75th percentiles (box), and 10th and 90th percentiles (errorbars). The horizontal line (red) highlights a one-cell displacement. This effectively means that, in the reconstructed data, a user is typically placed in the correct cell or in one that is very close to it. Such a level of accuracy is acceptable for metropolitan-scale analyses (where the urban surface is typically covered by hundreds of cells) and is excellent for national-scale studies (as inter-city mobility is perfectly captured).</figcaption></figure>

we accurately downsample the ground truth so as to mimic
the irregular sampling of typical mobile phone data, and then
reconstruct the user trajectories from the downsampled data via
our dedicated tensor factorization. Our evaluation demonstrates
that the approach achieves full reconstruction of individual
trajectories with good accuracy, as exemplified in Figure 1.

Third, we give a **demonstration of the importance of
trajectory reconstruction for human mobility analyses.** We
revisit three seminal studies by using the complete mobility
of 1.7 million users, instead of the incomplete trajectories of
a small fraction of especially active users as in the original
works. Our investigation yields the following insights: (i) travel
distances still follow a truncated power law [3] in the seamless
trajectory data of a million-strong user population, yet the cut-
off point is shifted away from the radius of gyration identified
in the original work; (ii) the high uniqueness of individual
trajectories [4] is substantially reduced in complete data, which
lets us argue that the uniqueness identified in the original
work was largely caused by the diverse temporal patterns
of the mobile communications of each user, rather than by a
distinctive mobility; (iii) the theoretical predictability of human
movements is even higher than thought [5], as considering the
whole user population removes a filtering bias that favored
highly mobile individuals with harder-to-anticipate locations.

REFERENCES

[1] V.D. Blondel et al., "A survey of results on mobile phone datasets analysis," EPJ Data Science 4(1), 2015.

[2] G. Chen et al., “Enriching sparse mobility information in call detail records,” Computer Communications 122, 2018.

[3] M.C. Gonzalez et al., “Understanding individual human mobility patterns,” Nature 453, 2008.

[4] Y.-A. de Montjoye et al., “Unique in the crowd: The privacy bounds of human mobility,” Scientific Reports 3, 2013.

[5] C. Song et al., “Limits of predictability in human mobility,” Science 327, 2010.