Abstract-The problem of modeling and managing uncertain data has received a great deal of interest, due to its manifold applications in spatial, temporal, multimedia and sensor databases. There exists a wide range of work covering spatial uncertainty in the static (snapshot) case, where only one point of time is considered. In contrast, the problem of modeling and querying uncertain spatio-temporal data has only been treated as a simple extension of the spatial case, disregarding time dependencies between consecutive timestamps. We present a framework for efficiently modeling and querying uncertain spatio-temporal data. The key idea of our approach is to model possible object trajectories by stochastic processes. This approach has three major advantages over previous work. First it allows answering queries in accordance with the possible worlds model. Second, dependencies between object locations at consecutive points in time are taken into account. And third it is possible to reduce all queries on this model to simple matrix multiplications. Based on these concepts we propose efficient solutions for different probabilistic spatio-temporal queries for a particular stochastic process, the Markov chain. In an experimental evaluation we show that our approaches are several order of magnitudes faster than state-of-the-art competitors.

The challenges associated with handling uncertain data, in particular with querying and mining, are finding increasing attention in the research community. Here we focus on clustering uncertain data and describe a general framework for this purpose that also allows to visualize and understand the impact of uncertainty-using different uncertainty models-on the data mining results. Our framework constitutes release 0.7 of ELKI (http://elki.dbs.ifi.lmu.de/) and thus comes along with a plethora of implementations of algorithms, distance measures, indexing techniques, evaluation measures and visualization components.

Nearest neighbor (NN) queries in trajectory databases have received significant attention in the past, due to their applications in spatiotemporal data analysis. More recent work has considered the realistic case where the trajectories are uncertain; however, only simple uncertainty models have been proposed, which do not allow for accurate probabilistic search. In this paper, we fill this gap by addressing probabilistic nearest neighbor queries in databases with uncertain trajectories modeled by stochastic processes, specifically the Markov chain model. We study three nearest neighbor query semantics that take as input a query state or trajectory q and a time interval, and theoretically evaluate their runtime complexity. Furthermore we propose a sampling approach which uses Bayesian inference to guarantee that sampled trajectories conform to the observation data stored in the database. This sampling approach can be used in Monte-Carlo based approximation solutions. We include an extensive experimental study to support our theoretical results.

Given a query object q, a reverse nearest neighbor (RNN) query in a common certain database returns the objects having q as their nearest neighbor. A new challenge for databases is dealing with uncertain objects. In this paper we consider probabilistic reverse nearest neighbor (PRNN) queries, which return the uncertain objects having the query object as nearest neighbor with a sufficiently high probability. We propose an algorithm for efficiently answering PRNN queries using new pruning mechanisms taking distance dependencies into account. We compare our algorithm to state-ofthe-art approaches recently proposed. Our experimental evaluation shows that our approach is able to significantly outperform previous approaches. In addition, we show how our approach can easily be extended to PRkNN (where k > 1) query processing for which there is currently no efficient solution.

The advances in sensing and telecommunication technologies allow the collection and management of vast amounts of spatio-temporal data combining location and time information. Due to physical and resource limitations of data collection devices (e.g., RFID readers, GPS receivers and other sensors) data are typically collected only at discrete points of time. In-between these discrete time instances, the positions of tracked moving objects are uncertain. In this work, we propose novel approximation techniques in order to probabilistically bound the uncertain movement of objects; these techniques allow for efficient and effective filtering during query evaluation using an hierarchical index structure. To the best of our knowledge, this is the first approach that supports query evaluation on very large uncertain spatio-temporal databases, adhering to possible worlds semantics. We experimentally show that it accelerates the existing, scan-based approach by orders of magnitude.