  The problem of unicity and reidentifiability of records in large-scale
databases has been studied in different contexts and approaches, with focus on
preserving privacy or matching records from different data sources. With an
increasing number of service providers nowadays routinely collecting location
traces of their users on unprecedented scales, there is a pronounced interest
in the possibility of matching records and datasets based on spatial
trajectories. Extending previous work on reidentifiability of spatial data and
trajectory matching, we present the first large-scale analysis of user
matchability in real mobility datasets on realistic scales, i.e. among two
datasets that consist of several million people's mobility traces, coming from
a mobile network operator and transportation smart card usage. We extract the
relevant statistical properties which influence the matching process and
analyze their impact on the matchability of users. We show that for individuals
with typical activity in the transportation system (those making 3-4 trips per
day on average), a matching algorithm based on the co-occurrence of their
activities is expected to achieve a 16.8% success only after a one-week long
observation of their mobility traces, and over 55% after four weeks. We show
that the main determinant of matchability is the expected number of
co-occurring records in the two datasets. Finally, we discuss different
scenarios in terms of data collection frequency and give estimates of
matchability over time. We show that with higher frequency data collection
becoming more common, we can expect much higher success rates in even shorter
intervals.
