Matthias Renz

Advances in Spatial and Temporal Databases

Spatiotemporal reachability queries arise naturally when determining how diseases, information, physical items can propagate through a collection of moving objects; such queries are significant for many important domains like epidemiology, public health, security monitoring, surveillance, and social networks. While traditional reachability queries have been studied in graphs extensively, what makes spatiotemporal reachability queries different and challenging is that the associated graph is dynamic and space-time dependent. As the spatiotemporal dataset becomes very large over time, a solution needs to be I/O-efficient. Previous work assumes an ‘instant exchange’ scenario (where information can be instantly transferred and retransmitted between objects), which may not be the case in many real world applications. In this paper we propose the RICC (Reachability Index Construction by Contraction) approach for processing spatiotemporal reachability queries without the instant exchange assumption. We tested our algorithm on two types of realistic datasets using queries of various temporal lengths and different types (with single and multiple sources and targets). The results of our experiments show that RICC can be efficiently used for answering a wide range of spatiotemporal reachability queries on disk-resident datasets.

Probabilistic nearest-neighbor query on uncertain objects

Nearest-neighbor queries are an important query type for commonly used feature databases. In many different application areas, e.g. sensor databases, location based services or face recognition systems, distances between objects have to be computed based on vague and uncertain data. A successful approach is to express the distance between two uncertain objects by probability density functions which assign a probability value to each possible distance value. By integrating the complete probabilistic distance function as a whole directly into the query algorithm, the full information provided by these functions is exploited. The result of such a probabilistic query algorithm consists of tuples containing the result object and a probability value indicating the likelihood that the object satisfies t he query predicate. In this paper we introduce an efficient strategy for cessing probabilistic nearest-neighbor queries, as the computation of these probability values is very expensive. In a detailed experimental evaluation, we demonstrate the benefits of our probabilistic query approach. The experiments show that we can achieve high quality query results with rather low computational cost.

A generic framework for efficient subspace clustering of high-dimensional data

Subspace clustering has been investigated extensively since traditional clustering algorithms often fail to detect meaningful clusters in high-dimensional data spaces. Many recently proposed subspace clustering methods suffer from two severe problems: First, the algorithms typically scale exponentially with the data dimensionality and/or the subspace dimensionality of the clusters. Second, for performance reasons, many algorithms use a global density threshold for clustering, which is quite questionable since clusters in subspaces of significantly different dimensionality will most likely exhibit significantly varying densities. In this paper, we propose a generic framework to overcome these limitations. Our framework is based on an efficient filter-refinement architecture that scales at most quadratic w.r.t. the data dimensionality and the dimensionality of the subspace clusters. It can be applied to any clustering notions including notions that are based on a local density threshold. A broad experimental evaluation on synthetic and real-world data empirically shows that our method achieves a significant gain of runtime and quality in comparison to state-of-the-art subspace clustering algorithms.

Efficient reverse k-nearest neighbor search in arbitrary metric spaces

The reverse k-nearest neighbor (RkNN) problem, i.e. finding all objects in a data set the k-nearest neighbors of which include a specified query object, is a generalization of the reverse 1-nearest neighbor problem which has received increasing attention recently. Many industrial and scientific applications call for solutions of the RkNN problem in arbitrary metric spaces where the data objects are not Euclidean and only a metric distance function is given for specifying object similarity. Usually, these applications need a solution for the generalized problem where the value of k is not known in advance and may change from query to query. However, existing approaches, except one, are designed for the specific R1NN problem. In addition - to the best of our knowledge - all previously proposed methods, especially the one for generalized RkNN search, are only applicable to Euclidean vector data but not for general metric objects. In this paper, we propose the first approach for efficient RkNN search in arbitrary metric spaces where the value of k is specified at query time. Our approach uses the advantages of existing metric index structures but proposes to use conservative and progressive distance approximations in order to filter out true drops and true hits. In particular, we approximate the k-nearest neighbor distance for each data object by upper and lower bounds using two functions of only two parameters each. Thus, our method does not generate any considerable storage overhead. We show in a broad experimental evaluation on real-world data the scalability and the usability of our novel approach.

Probabilistic similarity join on uncertain data

An important database primitive for commonly used feature databases is the similarity join. It combines two datasets based on some similarity predicate into one set such that the new set contains pairs of objects of the two original sets. In many different application areas, e.g. sensor databases, location based services or face recognition systems, distances between objects have to be computed based on vague and uncertain data. In this paper, we propose to express the similarity between two uncertain objects by probability density functions which assign a probability value to each possible distance value. By integrating these probabilistic distance functions directly into the join algorithms the full information provided by these functions is exploited. The resulting probabilistic similarity join assigns to each object pair a probability value indicating the likelihood that the object pair belongs to the result set. As the computation of these probability values is very expensive, we introduce an efficient join processing strategy exemplarily for the distance-range join. In a detailed experimental evaluation, we demonstrate the benefits of our probabilistic similarity join. The experiments show that we can achieve high quality join results with rather low computational cost.

Route skyline queries: A multi-preference path planning approach

In recent years, the research community introduced various methods for processing skyline queries in multidimensional databases. The skyline operator retrieves all objects being optimal w.r.t. an arbitrary linear weighting of the underlying criteria. The most prominent example query is to find a reasonable set of hotels which are cheap but close to the beach. In this paper, we propose an new approach for computing skylines on routes (paths) in a road network considering multiple preferences like distance, driving time, the number of traffic lights, gas consumption, etc. Since the consideration of different preferences usually involves different routes, a skyline-fashioned answer with relevant route candidates is highly useful. In our work, we employ graph embedding techniques to enable a best-first based graph exploration considering route preferences based on arbitrary road attributes. The core of our skyline query processor is a route iterator which iteratively computes the top routes according to (at least one) preference in an efficient way avoiding that route computations need to be issued from scratch in each iteration. Furthermore, we propose pruning techniques in order to reduce the search space. Our pruning strategies aim at pruning as many route candidates as possible during the graph exploration. Therefore, we are able to prune candidates which are only partially explored. Finally, we show that our approach is able to reduce the search space significantly and that the skyline can be computed in efficient time in our experimental evaluation.

Similarity search on time series based on threshold queries

Similarity search in time series data is required in many application fields. The most prominent work has focused on similarity search considering either complete time series or similarity according to subsequences of time series. For many domains like financial analysis, medicine, environmental meteorology, or environmental observation, the detection of temporal dependencies between different time series is very important. In contrast to traditional approaches which consider the course of the time series for the purpose of matching, coarse trend information about the time series could be sufficient to solve the above mentioned problem. In particular, temporal dependencies in time series can be detected by determining the points of time at which the time series exceeds a specific threshold. In this paper, we introduce the novel concept of threshold queries in time series databases which report those time series exceeding a user-defined query threshold at similar time frames compared to the query time series. We present a new efficient access method which uses the fact that only partial information of the time series is required at query time. The performance of our solution is demonstrated by an extensive experimental evaluation on real world and artificial time series data.

Reverse k-nearest neighbor search in dynamic and general metric databases

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.

Efficient probabilistic reverse nearest neighbor query processing on uncertain data

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-of-the-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.

Probabilistic Similarity Search for Uncertain Time Series

A probabilistic similarity query over uncertain data assigns to each uncertain database object o a probability indicating the likelihood that o meets the query predicate. In this paper, we formalize the notion of uncertain time series and introduce two novel and important types of probabilistic range queries over uncertain time series. Furthermore, we propose an original approximate representation of uncertain time series that can be used to efficiently support both new query types by upper and lower bounding the Euclidean distance.