Searching and mining in enriched geo-spatial data

The emergence of new data collection mechanisms in geo-spatial applications paired with a heightened tendency of users to volunteer information provides an ever-increasing flow of data of high volume, complex nature, and often associated with inherent uncertainty. Such mechanisms include crowdsourcing, automated knowledge inference, tracking, and social media data repositories. Such data bearing additional information from multiple sources like probability distributions, text or numerical attributes, social context, or multimedia content can be called multi-enriched. Searching and mining this abundance of information holds many challenges, if all of the data's potential is to be released. This thesis addresses several major issues arising in that field, namely path queries using multi-enriched data, trend mining in social media data, and handling uncertainty in geo-spatial data. In all cases, the developed methods have made significant contributions and have appeared in or were accepted into various renowned international peer-reviewed venues. A common use of geo-spatial data is path queries in road networks where traditional methods optimise results based on absolute and ofttimes singular metrics, i.e., finding the shortest paths based on distance or the best trade-off between distance and travel time. Integrating additional aspects like qualitative or social data by enriching the data model with knowledge derived from sources as mentioned above allows for queries that can be issued to fit a broader scope of needs or preferences. This thesis presents two implementations of incorporating multi-enriched data into road networks. In one case, a range of qualitative data sources is evaluated to gain knowledge about user preferences which is subsequently matched with locations represented in a road network and integrated into its components. Several methods are presented for highly customisable path queries that incorporate a wide spectrum of data. In a second case, a framework is described for resource distribution with reappearance in road networks to serve one or more clients, resulting in paths that provide maximum gain based on a probabilistic evaluation of available resources. Applications for this include finding parking spots. Social media trends are an emerging research area giving insight in user sentiment and important topics. Such trends consist of bursts of messages concerning a certain topic within a time frame, significantly deviating from the average appearance frequency of the same topic. By investigating the dissemination of such trends in space and time, this thesis presents methods to classify trend archetypes to predict future dissemination of a trend. Processing and querying uncertain data is particularly demanding given the additional knowledge required to yield results with probabilistic guarantees. Since such knowledge is not always available and queries are not easily scaled to larger datasets due to the #P-complete nature of the problem, many existing approaches reduce the data to a deterministic representation of its underlying model to eliminate uncertainty. However, data uncertainty can also provide valuable insight into the nature of the data that cannot be represented in a deterministic manner. This thesis presents techniques for clustering uncertain data as well as query processing, that take the additional information from uncertainty models into account while preserving scalability using a sampling-based approach, while previous approaches could only provide one of the two. The given solutions enable the application of various existing clustering techniques or query types to a framework that manages the uncertainty.Das Erscheinen neuer Methoden zur Datenerhebung in räumlichen Applikationen gepaart mit einer erhöhten Bereitschaft der Nutzer, Daten über sich preiszugeben, generiert einen stetig steigenden Fluss von Daten in großer Menge, komplexer Natur, und oft gepaart mit inhärenter Unsicherheit. Beispiele für solche Mechanismen sind Crowdsourcing, automatisierte Wissensinferenz, Tracking, und Daten aus sozialen Medien. Derartige Daten, angereichert mit mit zusätzlichen Informationen aus verschiedenen Quellen wie Wahrscheinlichkeitsverteilungen, Text- oder numerische Attribute, sozialem Kontext, oder Multimediainhalten, werden als multi-enriched bezeichnet. Suche und Datamining in dieser weiten Datenmenge hält viele Herausforderungen bereit, wenn das gesamte Potenzial der Daten genutzt werden soll. Diese Arbeit geht auf mehrere große Fragestellungen in diesem Feld ein, insbesondere Pfadanfragen in multi-enriched Daten, Trend-mining in Daten aus sozialen Netzwerken, und die Beherrschung von Unsicherheit in räumlichen Daten. In all diesen Fällen haben die entwickelten Methoden signifikante Forschungsbeiträge geleistet und wurden veröffentlicht oder angenommen zu diversen renommierten internationalen, von Experten begutachteten Konferenzen und Journals. Ein gängiges Anwendungsgebiet räumlicher Daten sind Pfadanfragen in Straßennetzwerken, wo traditionelle Methoden die Resultate anhand absoluter und oft auch singulärer Maße optimieren, d.h., der kürzeste Pfad in Bezug auf die Distanz oder der beste Kompromiss zwischen Distanz und Reisezeit. Durch die Integration zusätzlicher Aspekte wie qualitativer Daten oder Daten aus sozialen Netzwerken als Anreicherung des Datenmodells mit aus diesen Quellen abgeleitetem Wissen werden Anfragen möglich, die ein breiteres Spektrum an Anforderungen oder Präferenzen erfüllen. Diese Arbeit präsentiert zwei Ansätze, solche multi-enriched Daten in Straßennetze einzufügen. Zum einen wird eine Reihe qualitativer Datenquellen ausgewertet, um Wissen über Nutzerpräferenzen zu generieren, welches darauf mit Örtlichkeiten im Straßennetz abgeglichen und in das Netz integriert wird. Diverse Methoden werden präsentiert, die stark personalisierbare Pfadanfragen ermöglichen, die ein weites Spektrum an Daten mit einbeziehen. Im zweiten Fall wird ein Framework präsentiert, das eine Ressourcenverteilung im Straßennetzwerk modelliert, bei der einmal verbrauchte Ressourcen erneut auftauchen können. Resultierende Pfade ergeben einen maximalen Ertrag basieren auf einer probabilistischen Evaluation der verfügbaren Ressourcen. Eine Anwendung ist die Suche nach Parkplätzen. Trends in sozialen Medien sind ein entstehendes Forscchungsgebiet, das Einblicke in Benutzerverhalten und wichtige Themen zulässt. Solche Trends bestehen aus großen Mengen an Nachrichten zu einem bestimmten Thema innerhalb eines Zeitfensters, so dass die Auftrittsfrequenz signifikant über den durchschnittlichen Level liegt. Durch die Untersuchung der Fortpflanzung solcher Trends in Raum und Zeit präsentiert diese Arbeit Methoden, um Trends nach Archetypen zu klassifizieren und ihren zukünftigen Weg vorherzusagen. Die Anfragebearbeitung und Datamining in unsicheren Daten ist besonders herausfordernd, insbesondere im Hinblick auf das notwendige Zusatzwissen, um Resultate mit probabilistischen Garantien zu erzielen. Solches Wissen ist nicht immer verfügbar und Anfragen lassen sich aufgrund der \P-Vollständigkeit des Problems nicht ohne Weiteres auf größere Datensätze skalieren. Dennoch kann Datenunsicherheit wertvollen Einblick in die Struktur der Daten liefern, der mit deterministischen Methoden nicht erreichbar wäre. Diese Arbeit präsentiert Techniken zum Clustering unsicherer Daten sowie zur Anfragebearbeitung, die die Zusatzinformation aus dem Unsicherheitsmodell in Betracht ziehen, jedoch gleichzeitig die Skalierbarkeit des Ansatzes auf große Datenmengen sicherstellen

Uncertain voronoi cell computation based on space decomposition

LNCS v. 9239 entitled: Advances in Spatial and Temporal Databases: 14th International Symposium, SSTD 2015 ... ProceedingsThe problem of computing Voronoi cells for spatial objects whose locations are not certain has been recently studied. In this work, we propose a new approach to compute Voronoi cells for the case of objects having rectangular uncertainty regions. Since exact computation of Voronoi cells is hard, we propose an approximate solution. The main idea of this solution is to apply hierarchical access methods for both data and object space. Our space index is used to efficiently find spatial regions which must (not) be inside a Voronoi cell. Our object index is used to efficiently identify Delauny relations, i.e., data objects which affect the shape of a Voronoi cell. We develop three algorithms to explore index structures and show that the approach that descends both index structures in parallel yields fast query processing times. Our experiments show that we are able to approximate uncertain Voronoi cells much more effectively than the state-of-the-art, and at the same time, improve run-time performance.postprin

UV-Diagram: A Voronoi Diagram for Uncertain Spatial Databases

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Handling location uncertainty in probabilistic location-dependent queries

Location-based services have motivated intensive research in the field of mobile computing, and particularly on location-dependent queries. Existing approaches usually assume that the location data are expressed at a fine geographic precision (physical coordinates such as GPS). However, many positioning mechanisms are subject to an inherent imprecision (e.g., the cell-id mechanism used in cellular networks can only determine the cell where a certain moving object is located). Moreover, even a GPS location can be subject to an error or be obfuscated for privacy reasons. Thus, moving objects can be considered to be associated not to an exact location, but to an uncertainty area where they can be located. In this paper, we analyze the problem introduced by the imprecision of the location data available in the data sources by modeling them using uncertainty areas. To do so, we propose to use a higher-level representation of locations which includes uncertainty, formalizing the concept of uncertainty location granule. This allows us to consider probabilistic location-dependent queries, among which we will focus on probabilistic inside (range) constraints. The adopted model allows us to develop a systematic and efficient approach for processing this kind of queries. An experimental evaluation shows that these probabilistic queries can be supported efficiently

Complex queries and complex data

With the widespread availability of wearable computers, equipped with sensors such as GPS or cameras, and with the ubiquitous presence of micro-blogging platforms, social media sites and digital marketplaces, data can be collected and shared on a massive scale. A necessary building block for taking advantage from this vast amount of information are efficient and effective similarity search algorithms that are able to find objects in a database which are similar to a query object. Due to the general applicability of similarity search over different data types and applications, the formalization of this concept and the development of strategies for evaluating similarity queries has evolved to an important field of research in the database community, spatio-temporal database community, and others, such as information retrieval and computer vision. This thesis concentrates on a special instance of similarity queries, namely k-Nearest Neighbor (kNN) Queries and their close relative, Reverse k-Nearest Neighbor (RkNN) Queries. As a first contribution we provide an in-depth analysis of the RkNN join. While the problem of reverse nearest neighbor queries has received a vast amount of research interest, the problem of performing such queries in a bulk has not seen an in-depth analysis so far. We first formalize the RkNN join, identifying its monochromatic and bichromatic versions and their self-join variants. After pinpointing the monochromatic RkNN join as an important and interesting instance, we develop solutions for this class, including a self-pruning and a mutual pruning algorithm. We then evaluate these algorithms extensively on a variety of synthetic and real datasets. From this starting point of similarity queries on certain data we shift our focus to uncertain data, addressing nearest neighbor queries in uncertain spatio-temporal databases. Starting from the traditional definition of nearest neighbor queries and a data model for uncertain spatio-temporal data, we develop efficient query mechanisms that consider temporal dependencies during query evaluation. We define intuitive query semantics, aiming not only at returning the objects closest to the query but also their probability of being a nearest neighbor. After theoretically evaluating these query predicates we develop efficient querying algorithms for the proposed query predicates. Given the findings of this research on nearest neighbor queries, we extend these results to reverse nearest neighbor queries. Finally we address the problem of querying large datasets containing set-based objects, namely image databases, where images are represented by (multi-)sets of vectors and additional metadata describing the position of features in the image. We aim at reducing the number of kNN queries performed during query processing and evaluate a modified pipeline that aims at optimizing the query accuracy at a small number of kNN queries. Additionally, as feature representations in object recognition are moving more and more from the real-valued domain to the binary domain, we evaluate efficient indexing techniques for binary feature vectors.Nicht nur durch die Verbreitung von tragbaren Computern, die mit einer Vielzahl von Sensoren wie GPS oder Kameras ausgestattet sind, sondern auch durch die breite Nutzung von Microblogging-Plattformen, Social-Media Websites und digitale Marktplätze wie Amazon und Ebay wird durch die User eine gigantische Menge an Daten veröffentlicht. Um aus diesen Daten einen Mehrwert erzeugen zu können bedarf es effizienter und effektiver Algorithmen zur Ähnlichkeitssuche, die zu einem gegebenen Anfrageobjekt ähnliche Objekte in einer Datenbank identifiziert. Durch die Allgemeinheit dieses Konzeptes der Ähnlichkeit über unterschiedliche Datentypen und Anwendungen hinweg hat sich die Ähnlichkeitssuche zu einem wichtigen Forschungsfeld, nicht nur im Datenbankumfeld oder im Bereich raum-zeitlicher Datenbanken, sondern auch in anderen Forschungsgebieten wie dem Information Retrieval oder dem Maschinellen Sehen entwickelt. In der vorliegenden Arbeit beschäftigen wir uns mit einem speziellen Anfrageprädikat im Bereich der Ähnlichkeitsanfragen, mit k-nächste Nachbarn (kNN) Anfragen und ihrem Verwandten, den Revers k-nächsten Nachbarn (RkNN) Anfragen. In einem ersten Beitrag analysieren wir den RkNN Join. Obwohl das Problem von reverse nächsten Nachbar Anfragen in den letzten Jahren eine breite Aufmerksamkeit in der Forschungsgemeinschaft erfahren hat, wurde das Problem eine Menge von RkNN Anfragen gleichzeitig auszuführen nicht ausreichend analysiert. Aus diesem Grund formalisieren wir das Problem des RkNN Joins mit seinen monochromatischen und bichromatischen Varianten. Wir identifizieren den monochromatischen RkNN Join als einen wichtigen und interessanten Fall und entwickeln entsprechende Anfragealgorithmen. In einer detaillierten Evaluation vergleichen wir die ausgearbeiteten Verfahren auf einer Vielzahl von synthetischen und realen Datensätzen. Nach diesem Kapitel über Ähnlichkeitssuche auf sicheren Daten konzentrieren wir uns auf unsichere Daten, speziell im Bereich raum-zeitlicher Datenbanken. Ausgehend von der traditionellen Definition von Nachbarschaftsanfragen und einem Datenmodell für unsichere raum-zeitliche Daten entwickeln wir effiziente Anfrageverfahren, die zeitliche Abhängigkeiten bei der Anfragebearbeitung beachten. Zu diesem Zweck definieren wir Anfrageprädikate die nicht nur die Objekte zurückzugeben, die dem Anfrageobjekt am nächsten sind, sondern auch die Wahrscheinlichkeit mit der sie ein nächster Nachbar sind. Wir evaluieren die definierten Anfrageprädikate theoretisch und entwickeln effiziente Anfragestrategien, die eine Anfragebearbeitung zu vertretbaren Laufzeiten gewährleisten. Ausgehend von den Ergebnissen für Nachbarschaftsanfragen erweitern wir unsere Ergebnisse auf Reverse Nachbarschaftsanfragen. Zuletzt behandeln wir das Problem der Anfragebearbeitung bei Mengen-basierten Objekten, die zum Beispiel in Bilddatenbanken Verwendung finden: Oft werden Bilder durch eine Menge von Merkmalsvektoren und zusätzliche Metadaten (zum Beispiel die Position der Merkmale im Bild) dargestellt. Wir evaluieren eine modifizierte Pipeline, die darauf abzielt, die Anfragegenauigkeit bei einer kleinen Anzahl an kNN-Anfragen zu maximieren. Da reellwertige Merkmalsvektoren im Bereich der Objekterkennung immer öfter durch Bitvektoren ersetzt werden, die sich durch einen geringeren Speicherplatzbedarf und höhere Laufzeiteffizienz auszeichnen, evaluieren wir außerdem Indexierungsverfahren für Binärvektoren

Similarity search and data mining techniques for advanced database systems.

Modern automated methods for measurement, collection, and analysis of data in industry and science are providing more and more data with drastically increasing structure complexity. On the one hand, this growing complexity is justified by the need for a richer and more precise description of real-world objects, on the other hand it is justified by the rapid progress in measurement and analysis techniques that allow the user a versatile exploration of objects. In order to manage the huge volume of such complex data, advanced database systems are employed. In contrast to conventional database systems that support exact match queries, the user of these advanced database systems focuses on applying similarity search and data mining techniques. Based on an analysis of typical advanced database systems — such as biometrical, biological, multimedia, moving, and CAD-object database systems — the following three challenging characteristics of complexity are detected: uncertainty (probabilistic feature vectors), multiple instances (a set of homogeneous feature vectors), and multiple representations (a set of heterogeneous feature vectors). Therefore, the goal of this thesis is to develop similarity search and data mining techniques that are capable of handling uncertain, multi-instance, and multi-represented objects. The first part of this thesis deals with similarity search techniques. Object identification is a similarity search technique that is typically used for the recognition of objects from image, video, or audio data. Thus, we develop a novel probabilistic model for object identification. Based on it, two novel types of identification queries are defined. In order to process the novel query types efficiently, we introduce an index structure called Gauss-tree. In addition, we specify further probabilistic models and query types for uncertain multi-instance objects and uncertain spatial objects. Based on the index structure, we develop algorithms for an efficient processing of these query types. Practical benefits of using probabilistic feature vectors are demonstrated on a real-world application for video similarity search. Furthermore, a similarity search technique is presented that is based on aggregated multi-instance objects, and that is suitable for video similarity search. This technique takes multiple representations into account in order to achieve better effectiveness. The second part of this thesis deals with two major data mining techniques: clustering and classification. Since privacy preservation is a very important demand of distributed advanced applications, we propose using uncertainty for data obfuscation in order to provide privacy preservation during clustering. Furthermore, a model-based and a density-based clustering method for multi-instance objects are developed. Afterwards, original extensions and enhancements of the density-based clustering algorithms DBSCAN and OPTICS for handling multi-represented objects are introduced. Since several advanced database systems like biological or multimedia database systems handle predefined, very large class systems, two novel classification techniques for large class sets that benefit from using multiple representations are defined. The first classification method is based on the idea of a k-nearest-neighbor classifier. It employs a novel density-based technique to reduce training instances and exploits the entropy impurity of the local neighborhood in order to weight a given representation. The second technique addresses hierarchically-organized class systems. It uses a novel hierarchical, supervised method for the reduction of large multi-instance objects, e.g. audio or video, and applies support vector machines for efficient hierarchical classification of multi-represented objects. User benefits of this technique are demonstrated by a prototype that performs a classification of large music collections. The effectiveness and efficiency of all proposed techniques are discussed and verified by comparison with conventional approaches in versatile experimental evaluations on real-world datasets

Similarity search and data mining techniques for advanced database systems.

Modern automated methods for measurement, collection, and analysis of data in industry and science are providing more and more data with drastically increasing structure complexity. On the one hand, this growing complexity is justified by the need for a richer and more precise description of real-world objects, on the other hand it is justified by the rapid progress in measurement and analysis techniques that allow the user a versatile exploration of objects. In order to manage the huge volume of such complex data, advanced database systems are employed. In contrast to conventional database systems that support exact match queries, the user of these advanced database systems focuses on applying similarity search and data mining techniques. Based on an analysis of typical advanced database systems — such as biometrical, biological, multimedia, moving, and CAD-object database systems — the following three challenging characteristics of complexity are detected: uncertainty (probabilistic feature vectors), multiple instances (a set of homogeneous feature vectors), and multiple representations (a set of heterogeneous feature vectors). Therefore, the goal of this thesis is to develop similarity search and data mining techniques that are capable of handling uncertain, multi-instance, and multi-represented objects. The first part of this thesis deals with similarity search techniques. Object identification is a similarity search technique that is typically used for the recognition of objects from image, video, or audio data. Thus, we develop a novel probabilistic model for object identification. Based on it, two novel types of identification queries are defined. In order to process the novel query types efficiently, we introduce an index structure called Gauss-tree. In addition, we specify further probabilistic models and query types for uncertain multi-instance objects and uncertain spatial objects. Based on the index structure, we develop algorithms for an efficient processing of these query types. Practical benefits of using probabilistic feature vectors are demonstrated on a real-world application for video similarity search. Furthermore, a similarity search technique is presented that is based on aggregated multi-instance objects, and that is suitable for video similarity search. This technique takes multiple representations into account in order to achieve better effectiveness. The second part of this thesis deals with two major data mining techniques: clustering and classification. Since privacy preservation is a very important demand of distributed advanced applications, we propose using uncertainty for data obfuscation in order to provide privacy preservation during clustering. Furthermore, a model-based and a density-based clustering method for multi-instance objects are developed. Afterwards, original extensions and enhancements of the density-based clustering algorithms DBSCAN and OPTICS for handling multi-represented objects are introduced. Since several advanced database systems like biological or multimedia database systems handle predefined, very large class systems, two novel classification techniques for large class sets that benefit from using multiple representations are defined. The first classification method is based on the idea of a k-nearest-neighbor classifier. It employs a novel density-based technique to reduce training instances and exploits the entropy impurity of the local neighborhood in order to weight a given representation. The second technique addresses hierarchically-organized class systems. It uses a novel hierarchical, supervised method for the reduction of large multi-instance objects, e.g. audio or video, and applies support vector machines for efficient hierarchical classification of multi-represented objects. User benefits of this technique are demonstrated by a prototype that performs a classification of large music collections. The effectiveness and efficiency of all proposed techniques are discussed and verified by comparison with conventional approaches in versatile experimental evaluations on real-world datasets

Similarity search and mining in uncertain spatial and spatio-temporal databases

Both the current trends in technology such as smart phones, general mobile devices, stationary sensors and satellites as well as a new user mentality of utilizing this technology to voluntarily share information produce a huge flood of geo-spatial and geo-spatio-temporal data. This data flood provides a tremendous potential of discovering new and possibly useful knowledge. In addition to the fact that measurements are imprecise, due to the physical limitation of the devices, some form of interpolation is needed in-between discrete time instances. From a complementary perspective - to reduce the communication and bandwidth utilization, along with the storage requirements, often the data is subjected to a reduction, thereby eliminating some of the known/recorded values. These issues introduce the notion of uncertainty in the context of spatio-temporal data management - an aspect raising an imminent need for scalable and flexible data management. The main scope of this thesis is to develop effective and efficient techniques for similarity search and data mining in uncertain spatial and spatio-temporal data. In a plethora of research fields and industrial applications, these techniques can substantially improve decision making, minimize risk and unearth valuable insights that would otherwise remain hidden. The challenge of effectiveness in uncertain data is to correctly determine the set of possible results, each associated with the correct probability of being a result, in order to give a user a confidence about the returned results. The contrary challenge of efficiency, is to compute these result and corresponding probabilities in an efficient manner, allowing for reasonable querying and mining times, even for large uncertain databases. The paradigm used to master both challenges, is to identify a small set of equivalent classes of possible worlds, such that members of the same class can be treated as equivalent in the context of a given query predicate or data mining task. In the scope of this work, this paradigm will be formally defined, and applied to the most prominent classes of spatial queries on uncertain data, including range queries, k-nearest neighbor queries, ranking queries and reverse k-nearest neighbor queries. For this purpose, new spatial and probabilistic pruning approaches are developed to further speed up query processing. Furthermore, the proposed paradigm allows to develop the first efficient solution for the problem of frequent co-location mining on uncertain data. Special emphasis is taken on the temporal aspect of applications using modern data collection technologies. While the aforementioned techniques work well for single points of time, the prediction of query results over time remains a challenge. This thesis fills this gap by modeling an uncertain spatio-temporal object as a stochastic process, and by applying the above paradigm to efficiently query, index and mine historical spatio-temporal data.Moderne Technologien, z.B. Sattelitentechnologie und Technologie in Smart Phones, erzeugen eine Flut räumlicher Geo-Daten. Zudem ist in der Gesellschaft ein Trend zu beobachten diese erzeugten Daten freiwillig auf öffentlich zugänglichen Plattformen zur Verfügung zu stellen. Diese Datenflut hat immenses Potential, um neues und nützliches Wissen zu entdecken. Diese Daten sind jedoch grundsätzlich unsichere räumliche Daten. Die Unsicherheit ergibt sich aus mehreren Aspekten. Zum einen kommt es bei Messungen grundsätzlich zu Messungenauigkeiten, zum anderen ist zwischen diskreten Messzeitpunkten eine Interpolation nötig, die zusätzliche Unsicherheit erzeugt. Auerdem werden die Daten oft absichtlich reduziert, um Speicherplatz und Transfervolumen einzusparen, wodurch weitere Information verloren geht. Diese Unsicherheit schafft einen sofortigen Bedarf für skalierbare und flexible Methoden zur Verwaltung und Auswertung solcher Daten. Im Rahmen dieser Arbeit sollen effektive und effiziente Techniken zur Ähnlichkeitssuche und zum Data Mining bei unsicheren räumlichen und unsicheren räumlich-zeitlichen Daten erarbeitet werden. Diese Techniken liefern wertvolles Wissen, das auf verschiedenen Forschungsgebieten, als auch bei industriellen Anwendungen zur Entscheidungsfindung genutzt werden kann. Bei der Entwicklung dieser Techniken gibt es zwei Herausforderungen. Einerseits müssen die entwickelten Techniken effektiv sein, um korrekte Ergebnisse und Wahrscheinlichkeiten dieser Ergebnisse zurückzugeben. Andererseits müssen die entwickelten Techniken effizient sein, um auch in sehr großen Datenbanken Ergebnisse in annehmbarer Zeit zu liefern. Die Dissertation stellt ein neues Paradigma vor, das beide Herausforderungen meistert. Dieses Paradigma identifiziert mögliche Datenbankwelten, die bezüglich des gegebenen Anfrageprädikats äquivalent sind. Es wird formal definiert und auf die relevantesten räumlichen Anfragetypen angewendet, um effiziente Lösungen zu entwickeln. Dazu gehören Bereichanfragen, k-Nächste-Nachbarnanfragen, Rankinganfragen und Reverse k-Nächste-Nachbarnanfragen. Räumliche und probabilistische Pruningkriterien werden entwickelt, um insignifikante Ergebnisse früh auszuschlieen. Zudem wird die erste effiziente Lösung für das Problem des "Spatial Co-location Minings" auf unsicheren Daten präsentiert. Ein besonderer Schwerpunkt dieser Arbeit liegt auf dem temporalen Aspekt moderner Geo-Daten. Während obig genannte Techniken dieser Arbeit für einzelne Zeitpunkt sehr gut funktionieren, ist die effektive und effiziente Verwaltung von unsicheren räumlich zeitlichen Daten immer noch ein weitestgehend ungelöstes Problem. Diese Dissertation löst dieses Problem, indem unsichere räumlich-zeitliche Daten durch stochastische Prozesse modeliert werden. Auf diese stochastischen Prozesse lässt sich das oben genannte Paradigma anwenden, um unsichere räumlich-zeitliche Daten effizient anzufragen, zu indexieren, und zu minen