1,841 research outputs found

    Range Queries on Uncertain Data

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    Given a set PP of nn uncertain points on the real line, each represented by its one-dimensional probability density function, we consider the problem of building data structures on PP to answer range queries of the following three types for any query interval II: (1) top-11 query: find the point in PP that lies in II with the highest probability, (2) top-kk query: given any integer knk\leq n as part of the query, return the kk points in PP that lie in II with the highest probabilities, and (3) threshold query: given any threshold τ\tau as part of the query, return all points of PP that lie in II with probabilities at least τ\tau. We present data structures for these range queries with linear or nearly linear space and efficient query time.Comment: 26 pages. A preliminary version of this paper appeared in ISAAC 2014. In this full version, we also present solutions to the most general case of the problem (i.e., the histogram bounded case), which were left as open problems in the preliminary versio

    Indexing and knowledge discovery of gaussian mixture models and multiple-instance learning

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    Due to the increasing quantity and variety of generated and stored data, the manual and automatic analysis becomes a more and more challenging task in many modern applications, like biometric identification and content-based image retrieval. In this thesis, we consider two very typical, related inherent structures of objects: Multiple-Instance (MI) objects and Gaussian Mixture Models (GMM). In both approaches, each object is represented by a set. For MI, each object is a set of vectors from a multi-dimensional space. For GMM, each object is a set of multi-variate Gaussian distribution functions, providing the ability to approximate arbitrary distributions in a concise way. Both approaches are very powerful and natural as they allow to express (1) that an object is additively composed from several components or (2) that an object may have several different, alternative kinds of behavior. Thus we can model e.g. an image which may depict a set of different things (1). Likewise, we can model a sports player who has performed differently at different games (2). We can use GMM to approximate MI objects and vice versa. Both ways of approximation can be appealing because GMM are more concise whereas for MI objects the single components are less complex. A similarity measure quantifies similarities between two objects to assess how much alike these objects are. On this basis, indexing and similarity search play essential roles in data mining, providing efficient and/or indispensable supports for a variety of algorithms such as classification and clustering. This thesis aims to solve challenges in the indexing and knowledge discovery of complex data using MI objects and GMM. For the indexing of GMM, there are several techniques available, including universal index structures and GMM-specific methods. However, the well-known approaches either suffer from poor performance or have too many limitations. To make use of the parameterized properties of GMM and tackle the problem of potential unequal length of components, we propose the Gaussian Components based Index (GCI) for efficient queries on GMM. GCI decomposes GMM into their components, and stores the n-lets of Gaussian combinations that have uniform length of parameter vectors in traditional index structures. We introduce an efficient pruning strategy to filter unqualified GMM using the so-called Matching Probability (MP) as the similarity measure. MP sums up the joint probabilities of two objects all over the space. GCI achieves better performance than its competitors on both synthetic and real-world data. To further increase its efficiency, we propose a strategy to store GMM components in a normalized way. This strategy improves the ability of filtering unqualified GMM. Based on the normalized transformation, we derive a set of novel similarity measures for GMM. Since MP is not a metric (i.e., a symmetric, positive definite distance function guaranteeing the triangle inequality), which would be essential for the application of various analysis techniques, we introduce Infinite Euclidean Distance (IED) for probability distribution functions, a metric with a closed-form expression for GMM. IED allows us to store GMM in well-known metric trees like the Vantage-Point tree or M-tree, which facilitate similarity search in sublinear time by exploiting the triangle inequality. Moreover, analysis techniques that require the properties of a metric (e.g. Multidimensional Scaling) can be applied on GMM with IED. For MI objects which are not well-approximated by GMM, we introduce the potential densities of instances for the representation of MI objects. Based on that, two joint Gaussian based measures are proposed for MI objects and we extend GCI on MI objects for efficient queries as well. To sum up, we propose in this thesis a number of novel similarity measures and novel indexing techniques for GMM and MI objects, enabling efficient queries and knowledge discovery on complex data. In a thorough theoretic analysis as well as extensive experiments we demonstrate the superiority of our approaches over the state-of-the-art with respect to the run-time efficiency and the quality of the result.Angesichts der steigenden Quantität und Vielfalt der generierten und gespeicherten Daten werden manuelle und automatisierte Analysen in vielen modernen Anwendungen eine zunehmend anspruchsvolle Aufgabe, wie z.B. biometrische Identifikation und inhaltbasierter Bildzugriff. In dieser Arbeit werden zwei sehr typische und relevante inhärente Strukturen von Objekten behandelt: Multiple-Instance-Objects (MI) und Gaussian Mixture Models (GMM). In beiden Anwendungsfällen wird das Objekt in Form einer Menge dargestellt. Bei MI besteht jedes Objekt aus einer Menge von Vektoren aus einem multidimensionalen Raum. Bei GMM wird jedes Objekt durch eine Menge von multivariaten normalverteilten Dichtefunktionen repräsentiert. Dies bietet die Möglichkeit, beliebige Wahrscheinlichkeitsverteilungen in kompakter Form zu approximieren. Beide Ansätze sind sehr leistungsfähig, denn sie basieren auf einfachsten Ideen: (1) entweder besteht ein Objekt additiv aus mehreren Komponenten oder (2) ein Objekt hat unterschiedliche alternative Verhaltensarten. Dies ermöglicht es uns z.B. ein Bild zu repräsentieren, welches unterschiedliche Objekte und Szenen zeigt (1). In gleicher Weise können wir einen Sportler modellieren, der bei verschiedenen Wettkämpfen unterschiedliche Leistungen gezeigt hat (2). Wir können MI-Objekte durch GMM approximieren und auch der umgekehrte Weg ist möglich. Beide Vorgehensweisen können sehr ansprechend sein, da GMM im Vergleich zu MI kompakter sind, wogegen in MI-Objekten die einzelnen Komponenten weniger Komplexität aufweisen. Ein ähnlichkeitsmaß dient der Quantifikation der Gemeinsamkeit zwischen zwei Objekten. Darauf basierend spielen Indizierung und ähnlichkeitssuche eine wesentliche Rolle für die effiziente Implementierung von einer Vielzahl von Klassifikations- und Clustering-Algorithmen im Bereich des Data Minings. Ziel dieser Arbeit ist es, die Herausforderungen bei Indizierung und Wissensextraktion von komplexen Daten unter Verwendung von MI Objekten und GMM zu bewältigen. Für die Indizierung der GMM stehen verschiedene universelle und GMM-spezifische Indexstrukuren zur Verfügung. Jedoch leiden solche bekannten Ansätze unter schwacher Leistung oder zu vielen Einschränkungen. Um die parametrisieren Eigenschaften der GMM auszunutzen und dem Problem der möglichen ungleichen Komponentenlänge entgegenzuwirken, präsentieren wir das Verfahren Gaussian Components based Index (GCI), welches effizienten Abfrage auf GMM ermöglicht. GCI zerlegt dabei ein GMM in Parameterkomponenten und speichert alle möglichen Kombinationen mit einheitlicher Vektorlänge in traditionellen Indexstrukturen. Wir stellen ein effizientes Pruningverfahren vor, um ungeeignete GMM unter Verwendung der sogenannten Matching Probability (MP) als ähnlichkeitsma\ss auszufiltern. MP errechnet die Summe der gemeinsamen Wahrscheinlichkeit zweier Objekte aus dem gesamten Raum. CGI erzielt bessere Leistung als konkurrierende Verfahren, sowohl in Bezug auf synthetische, als auch auf reale Datensätze. Um ihre Effizienz weiter zu verbessern, stellen wir eine Strategie zur Speicherung der GMM-Komponenten in normalisierter Form vor. Diese Strategie verbessert die Fähigkeit zum Ausfiltern ungeeigneter GMM. Darüber hinaus leiten wir, basierend auf dieser Transformation, neuartige ähnlichkeitsmaße für GMM her. Da MP keine Metrik (d.h. eine symmetrische, positiv definite Distanzfunktion, die die Dreiecksungleichung garantiert) ist, dies jedoch unentbehrlich für die Anwendung mehrerer Analysetechniken ist, führen wir Infinite Euclidean Distance (IED) ein, ein Metrik mit geschlossener Ausdrucksform für GMM. IED erlaubt die Speicherung der GMM in Metrik-Bäumen wie z.B. Vantage-Point Trees oder M-Trees, die die ähnlichkeitssuche in sublinear Zeit mit Hilfe der Dreiecksungleichung erleichtert. Außerdem können Analysetechniken, die die Eigenschaften einer Metrik erfordern (z.B. Multidimensional Scaling), auf GMM mit IED angewandt werden. Für MI-Objekte, die mit GMM nicht in außreichender Qualität approximiert werden können, stellen wir Potential Densities of Instances vor, um MI-Objekte zu repräsentieren. Darauf beruhend werden zwei auf multivariater Gaußverteilungen basierende Maße für MI-Objekte eingeführt. Außerdem erweitern wir GCI für MI-Objekte zur effizienten Abfragen. Zusammenfassend haben wir in dieser Arbeit mehrere neuartige ähnlichkeitsmaße und Indizierungstechniken für GMM- und MI-Objekte vorgestellt. Diese ermöglichen effiziente Abfragen und die Wissensentdeckung in komplexen Daten. Durch eine gründliche theoretische Analyse und durch umfangreiche Experimente demonstrieren wir die überlegenheit unseres Ansatzes gegenüber anderen modernen Ansätzen bezüglich ihrer Laufzeit und Qualität der Resultate

    Transparent Forecasting Strategies in Database Management Systems

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    Whereas traditional data warehouse systems assume that data is complete or has been carefully preprocessed, increasingly more data is imprecise, incomplete, and inconsistent. This is especially true in the context of big data, where massive amount of data arrives continuously in real-time from vast data sources. Nevertheless, modern data analysis involves sophisticated statistical algorithm that go well beyond traditional BI and, additionally, is increasingly performed by non-expert users. Both trends require transparent data mining techniques that efficiently handle missing data and present a complete view of the database to the user. Time series forecasting estimates future, not yet available, data of a time series and represents one way of dealing with missing data. Moreover, it enables queries that retrieve a view of the database at any point in time - past, present, and future. This article presents an overview of forecasting techniques in database management systems. After discussing possible application areas for time series forecasting, we give a short mathematical background of the main forecasting concepts. We then outline various general strategies of integrating time series forecasting inside a database and discuss some individual techniques from the database community. We conclude this article by introducing a novel forecasting-enabled database management architecture that natively and transparently integrates forecast models

    A methodology for the efficient integration of transient constraints in the design of aircraft dynamic systems

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    Transient regimes experienced by dynamic systems may have severe impacts on the operation of the aircraft. They are often regulated by dynamic constraints, requiring the dynamic signals to remain within bounds whose values vary with time. The verification of these peculiar types of constraints, which generally requires high-fidelity time-domain simulation, intervenes late in the system development process, thus potentially causing costly design iterations. The research objective of this thesis is to develop a methodology that integrates the verification of dynamic constraints in the early specification of dynamic systems. In order to circumvent the inefficiencies of time-domain simulation, multivariate dynamic surrogate models of the original time-domain simulation models are generated using wavelet neural networks (or wavenets). Concurrently, an alternate approach is formulated, in which the envelope of the dynamic response, extracted via a wavelet-based multiresolution analysis scheme, is subject to transient constraints. Dynamic surrogate models using sigmoid-based neural networks are generated to emulate the transient behavior of the envelope of the time-domain response. The run-time efficiency of the resulting dynamic surrogate models enables the implementation of a data farming approach, in which the full design space is sampled through a Monte-Carlo Simulation. An interactive visualization environment, enabling what-if analyses, is developed; the user can thereby instantaneously comprehend the transient response of the system (or its envelope) and its sensitivities to design and operation variables, as well as filter the design space to have it exhibit only the design scenarios verifying the dynamic constraints. The proposed methodology, along with its foundational hypotheses, is tested on the design and optimization of a 350VDC network, where a generator and its control system are concurrently designed in order to minimize the electrical losses, while ensuring that the transient undervoltage induced by peak demands in the consumption of a motor does not violate transient power quality constraints.Ph.D.Committee Chair: Mavris, Dimitri; Committee Member: Charrier, Jean-Jacques; Committee Member: Garcia, Elena; Committee Member: Grijalva, Santiago; Committee Member: Schrage, Danie

    Doctor of Philosophy

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    dissertationWe are living in an age where data are being generated faster than anyone has previously imagined across a broad application domain, including customer studies, social media, sensor networks, and the sciences, among many others. In some cases, data are generated in massive quantities as terabytes or petabytes. There have been numerous emerging challenges when dealing with massive data, including: (1) the explosion in size of data; (2) data have increasingly more complex structures and rich semantics, such as representing temporal data as a piecewise linear representation; (3) uncertain data are becoming a common occurrence for numerous applications, e.g., scientific measurements or observations such as meteorological measurements; (4) and data are becoming increasingly distributed, e.g., distributed data collected and integrated from distributed locations as well as data stored in a distributed file system within a cluster. Due to the massive nature of modern data, it is oftentimes infeasible for computers to efficiently manage and query them exactly. An attractive alternative is to use data summarization techniques to construct data summaries, where even efficiently constructing data summaries is a challenging task given the enormous size of data. The data summaries we focus on in this thesis include the histogram and ranking operator. Both data summaries enable us to summarize a massive dataset to a more succinct representation which can then be used to make queries orders of magnitude more efficient while still allowing approximation guarantees on query answers. Our study has focused on the critical task of designing efficient algorithms to summarize, query, and manage massive data

    Monte Carlo Method with Heuristic Adjustment for Irregularly Shaped Food Product Volume Measurement

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    Volume measurement plays an important role in the production and processing of food products. Various methods have been proposed to measure the volume of food products with irregular shapes based on 3D reconstruction. However, 3D reconstruction comes with a high-priced computational cost. Furthermore, some of the volume measurement methods based on 3D reconstruction have a low accuracy. Another method for measuring volume of objects uses Monte Carlo method. Monte Carlo method performs volume measurements using random points. Monte Carlo method only requires information regarding whether random points fall inside or outside an object and does not require a 3D reconstruction. This paper proposes volume measurement using a computer vision system for irregularly shaped food products without 3D reconstruction based on Monte Carlo method with heuristic adjustment. Five images of food product were captured using five cameras and processed to produce binary images. Monte Carlo integration with heuristic adjustment was performed to measure the volume based on the information extracted from binary images. The experimental results show that the proposed method provided high accuracy and precision compared to the water displacement method. In addition, the proposed method is more accurate and faster than the space carving method
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