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.

Abstract. Many applications require to determine the k-nearest neighbors for multiple query points simultaneously. This task is known as all-(k)-nearest-neighbor (AkNN) query. In this paper, we suggest a new method for efficient AkNN query processing which is based on spherical approximations for indexing and query set representation. In this setting, we propose trigonometric pruning which enables a significant decrease of the remaining search space for a query. Employing this new pruning method, we considerably speed up AkNN queries.

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.

In this paper, we propose a novel, effective and efficient probabilistic pruning criterion for probabilistic similarity queries on uncertain data. Our approach supports a general uncertainty model using continuous probabilistic density functions to describe the (possibly correlated) uncertain attributes of objects. In a nutshell, the problem to be solved is to compute the PDF of the random variable denoted by the probabilistic domination count: Given an uncertain database object B, an uncertain reference object R and a set D of uncertain database objects in a multi-dimensional space, the probabilistic domination count denotes the number of uncertain objects in D that are closer to R than B. This domination count can be used to answer a wide range of probabilistic similarity queries. Specifically, we propose a novel geometric pruning filter and introduce an iterative filter-refinement strategy for conservatively and progressively estimating the probabilistic domination count in an efficient way while keeping correctness according to the possible world semantics. In an experimental evaluation, we show that our proposed technique allows to acquire tight probability bounds for the probabilistic domination count quickly, even for large uncertain databases. I. INTRODUCTIONIn the past two decades, there has been a great deal of interest in developing efficient and effective methods for similarity queries, e.g. k-nearest neighbor search, reverse k-nearest neighbor search and ranking in spatial, temporal, multimedia and sensor databases. Many applications dealing with such data have to cope with uncertain or imprecise data.In this work, we introduce a novel scalable pruning approach to identify candidates for a class of probabilistic similarity queries. Generally spoken, probabilistic similarity queries compute for each database object o ∈ D the probability that a given query predicate is fulfilled. Our approach addresses probabilistic similarity queries where the query predicate is based on object (distance) relations, i.e. the event that an object B belongs to the result set depends on the relation of its distance to the query object R and the distance of another object A to the query object. Exemplarily, we apply our novel pruning method to the most prominent queries of the above mentioned class, including the probabilistic k-nearest neighbor (PkNN) query, the probabilistic reverse k-nearest neighbor (PRkNN) query and the probabilistic inverse ranking query.

Automatically determining the relative position of a single CT slice within a full body scan provides several useful functionalities. For example, it is possible to validate DICOM meta-data information. Furthermore, knowing the relative position in a scan allows the efficient retrieval of similar slices from the same body region in other volume scans. Finally, the relative position is often an important information for a non-expert user having only access to a single CT slice of a scan. In this paper, we determine the relative position of single CT slices via instance-based regression without using any meta data. Each slice of a volume set is represented by several types of feature information that is computed from a sequence of image conversions and edge detection routines on rectangular subregions of the slices. Our new method is independent from the settings of the CT scanner and provides an average localization error of less than 4.5 cm using leave-one-out validation on a dataset of 34 annotated volume scans. Thus, we demonstrate that instance-based regression is a suitable tool for mapping single slices to a standardized coordinate system and that our algorithm is competitive to other volume-based approaches with respect to runtime and prediction quality, even though only a fraction of the input information is required in comparison to other approaches.