Mining of spatial data is an enabling technology for mobile services, Internet-connected cars and the Internet of Things. But the very distinctiveness of spatial data that drives utility can cost user privacy. Past work has focused upon points and trajectories for differentially private release. In this work, we continue the tradition of privacy-preserving spatial analytics, focusing not on point or path data, but on planar spatial regions. Such data represent the area of a user’s most frequent visitation—such as “around home and nearby shops”. Specifically we consider the differentially private release of data structures that support range queries for counting users’ spatial regions. Counting planar regions leads to unique challenges not faced in existing work. A user’s spatial region that straddles multiple data structure cells can lead to duplicate counting at query time. We provably avoid this pitfall by leveraging the Euler characteristic for the first time with differential privacy. To address the increased sensitivity of range queries to spatial region data, we calibrate privacy-preserving noise using bounded user region size and a constrained inference that uses robust least absolute deviations. Our novel constrained inference reduces noise and promotes covertness by (privately) imposing consistency. We provide a full end-to-end theoretical analysis of both differential privacy and high-probability utility for our approach using concentration bounds. A comprehensive experimental study on several real-world datasets establishes practical validity.
Aggregation under range queries has emerged as a fundamental primitive in spatial and spatio-temporal analytics @cite_14 @cite_7 @cite_20 @cite_3 @cite_53 . Originally motivated by statistical and computational efficiency, aggregation is now also used for qualitative privacy.
@cite_14 @cite_7 @cite_53 @cite_3 @cite_20
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Spatial databases store information about the position of individual objects in space. In many applications however, such as traffic supervision or mobile communications, only summarized data, like the number of cars in an area or phones serviced by a cell, is required. Although this information can be obtained from transactional spatial databases, its computation is expensive, rendering online processing inapplicable. Driven by the non-spatial paradigm, spatial data warehouses can be constructed to accelerate spatial OLAP operations. In this paper we consider the star-schema and we focus on the spatial dimensions. Unlike the non-spatial case, the groupings and the hierarchies can be numerous and unknown at design time, therefore the well-known materialization techniques are not directly applicable. In order to address this problem, we construct an ad-hoc grouping hierarchy based on the spatial index at the finest spatial granularity. We incorporate this hierarchy in the lattice model and present efficient methods to process arbitrary aggregations. We finally extend our technique to moving objects by employing incremental update methods. Several spatio-temporal applications require the retrieval of summarized information about moving objects that lie in a query region during a query interval (e.g., the number of mobile users covered by a cell, traffic volume in a district, etc.). Existing solutions have the distinct counting problem: if an object remains in the query region for several timestamps during the query interval, it will be counted multiple times in the result. We solve this problem by integrating spatio-temporal indexes with sketches, traditionally used for approximate query processing. The proposed techniques can also be applied to reduce the space requirements of conventional spatio-temporal data and to mine spatio-temporal association rules. In this paper we present a formal framework for modelling a trajectory data warehouse (TDW), namely a data warehouse aimed at storing aggregate information on trajectories of moving objects, which also offers visual OLAP operations for data analysis. The data warehouse model includes both temporal and spatial dimensions, and it is flexible and general enough to deal with objects that are either completely free or constrained in their movements (e.g., they move along a road network). In particular, the spatial dimension and the associated concept hierarchy reflect the structure of the environment in which the objects travel. Moreover, we cope with some issues related to the efficient computation of aggregate measures, as needed for implementing roll-up operations. The TDW and its visual interface allow one to investigate the behaviour of objects inside a given area as well as the movements of objects between areas in the same neighbourhood. A user can easily navigate the aggregate measures obtained from OLAP queries at different granularities, and get overall views in time and in space of the measures, as well as a focused view on specific measures, spatial areas, or temporal intervals. We discuss two application scenarios of our TDW, namely road traffic and vessel movement analysis, for which we built prototype systems. They mainly differ in the kind of information available for the moving objects under observation and their movement constraints. In this paper we discuss how data warehousing technology can be used to store aggregate information about trajectories and perform OLAP operations over them. To this end, we define a data cube with spatial and temporal dimensions, discretized according to a regular grid. We investigate in depth some issues related to the computation of a holistic aggregate function, i.e, the presence, which returns the number of distinct trajectories occurring in a given spatio-temporal area. In particular, we introduce a novel way to compute an approximate, but nevertheless very accurate, presence aggregate function, which uses only a bounded amount of measures stored in the base cells of our cuboid. We also concentrate on the loading phase of our data warehouse, which has to deal with an unbounded stream of trajectory observations. We suggest how the complexity of this phase can be reduced, and we analyse the errors that this procedure induces at the level of the sub-aggregates stored in the base cells. These errors and the accuracy of our approximate aggregate functions are carefully evaluated by means of tests performed on synthetic trajectory datasets. Spatiotemporal databases are becoming increasingly more common. Typically, applications modeling spatiotemporal objects need to process vast amounts of data. In such cases, generating aggregate information from the data set is more useful than individually analyzing every entry. In this paper, we study the most relevant techniques for the evaluation of aggregate queries on spatial, temporal, and spatiotemporal data. We also present a model that reduces the evaluation of aggregate queries to the problem of selecting qualifying tuples and the grouping of these tuples into collections on which an aggregate function is to be applied. This model gives us a framework that allows us to analyze and compare the different existing techniques for the evaluation of aggregate queries. At the same time, it allows us to identify opportunities for research on types of aggregate queries that have not been studied.