Similarity Search in Medical Data

The ongoing automation in our modern information society leads to a tremendous rise in the amount as well as complexity of collected data. In medical imaging for example the electronic availability of extensive data collected as part of clinical trials provides a remarkable potentiality to detect new relevant features in complex diseases like brain tumors. Using data mining applications for the analysis of the data raises several problems. One problem is the localization of outstanding observations also called outliers in a data set. In this work a technique for parameter-free outlier detection, which is based on data compression and a general data model which combines the Generalized Normal Distribution (GND) with independent components, to cope with existing problems like parameter settings or implicit data distribution assumptions, is proposed. Another problem in many modern applications amongst others in medical imaging is the efficient similarity search in uncertain data. At present, an adequate therapy planning of newly detected brain tumors assumedly of glial origin needs invasive biopsy due to the fact that prognosis and treatment, both vary strongly for benign, low-grade, and high-grade tumors. To date differentiation of tumor grades is mainly based on the expertise of neuroradiologists examining contrast-enhanced Magnetic Resonance Images (MRI). To assist neuroradiologist experts during the differentiation between tumors of different malignancy we proposed a novel, efficient similarity search technique for uncertain data. The feature vector of an object is thereby not exactly known but is rather defined by a Probability Density Function (PDF) like a Gaussian Mixture Model (GMM). Previous work is limited to axis-parallel Gaussian distributions, hence, correlations between different features are not considered in these similarity searches. In this work a novel, efficient similarity search technique for general GMMs without independence assumption is presented. The actual components of a GMM are approximated in a conservative but tight way. The conservativity of the approach leads to a filter-refinement architecture, which guarantees no false dismissals and the tightness of the approximations causes good filter selectivity. An extensive experimental evaluation of the approach demonstrates a considerable speed-up of similarity queries on general GMMs. Additionally, promising results for advancing the differentiation between brain tumors of different grades could be obtained by applying the approach to four-dimensional Magnetic Resonance Images of glioma patients

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

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

Active Improvement of Control Policies with Bayesian Gaussian Mixture Model

Learning from demonstration (LfD) is an intuitive framework allowing non-expert users to easily (re-)program robots. However, the quality and quantity of demonstrations have a great influence on the generalization performances of LfD approaches. In this paper, we introduce a novel active learning framework in order to improve the generalization capabilities of control policies. The proposed approach is based on the epistemic uncertainties of Bayesian Gaussian mixture models (BGMMs). We determine the new query point location by optimizing a closed-form information-density cost based on the quadratic R\'enyi entropy. Furthermore, to better represent uncertain regions and to avoid local optima problem, we propose to approximate the active learning cost with a Gaussian mixture model (GMM). We demonstrate our active learning framework in the context of a reaching task in a cluttered environment with an illustrative toy example and a real experiment with a Panda robot.Comment: Accepted for publication in IROS'2

Provably Safe Robot Navigation with Obstacle Uncertainty

As drones and autonomous cars become more widespread it is becoming increasingly important that robots can operate safely under realistic conditions. The noisy information fed into real systems means that robots must use estimates of the environment to plan navigation. Efficiently guaranteeing that the resulting motion plans are safe under these circumstances has proved difficult. We examine how to guarantee that a trajectory or policy is safe with only imperfect observations of the environment. We examine the implications of various mathematical formalisms of safety and arrive at a mathematical notion of safety of a long-term execution, even when conditioned on observational information. We present efficient algorithms that can prove that trajectories or policies are safe with much tighter bounds than in previous work. Notably, the complexity of the environment does not affect our methods ability to evaluate if a trajectory or policy is safe. We then use these safety checking methods to design a safe variant of the RRT planning algorithm.Comment: RSS 201

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

Multiple Model Methods for Cost Function Based Multiple Hypothesis Trackers

Multiple hypothesis trackers (MHTs) are widely accepted as the best means of tracking targets in clutter. This research seeks to incorporate multiple model Kalman filters into an Integral Square Error (ISE) cost-function-based MHT to increase the fidelity of target state estimation. Results indicate that the proposed multiple model methods can properly identify the maneuver mode of a target in dense clutter and ensure that an appropriately tuned filter is used. During benign portions of flight, this causes significant reductions in position and velocity RMS errors compared to a single-filter MHT. During portions of flight when the mixture mean deviates significantly from true target position, so-called deferred decision periods, the multiple model structures tend to accumulate greater RMS errors than a single-filter MHT, but this effect is inconsequential considering the inherently large magnitude of these errors (a non-MHT tracker would not be able to track during these periods at all). The multiple model MHT structures do not negatively impact track life when compared to a single-filter MHT

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