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.

In this paper, we propose an original solution for the general reverse k-nearest neighbor (RkNN) search problem. Compared to the limitations of existing methods for the RkNN search, our approach works on top of any hierarchically organized tree-like index structure and, thus, is applicable to any type of data as long as a metric distance function is defined on the data objects. We will exemplarily show how our approach works on top of the most prevalent index structures for Euclidean and metric data, the R-Tree and the M-Tree, respectively. Our solution is applicable for arbitrary values of k and can also be applied in dynamic environments where updates of the database frequently occur. Although being the most general solution for the RkNN problem, our solution outperforms existing methods in terms of query execution times because it exploits different strategies for pruning false drops and identifying true hits as soon as possible.

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.