Lifted Bayesian filtering in multi-entity systems

This thesis focuses on Bayesian filtering for systems that consist of multiple, interacting entites (e.g. agents or objects), which can naturally be described by Multiset Rewriting Systems (MRSs). The main insight is that the state space that is underling an MRS exhibits a certain symmetry, which can be exploited to increase inference efficiency. We provide an efficient, lifted filtering algorithm, which is able to achieve a factorial reduction in space and time complexity, compared to conventional, ground filtering.Diese Arbeit betrachtet Bayes'sche Filter in Systemen, die aus mehreren, interagierenden Entitäten (z.B. Agenten oder Objekten) bestehen. Die Systemdynamik solcher Systeme kann auf natürliche Art durch Multiset Rewriting Systems (MRS) spezifiziert werden. Die wesentliche Erkenntnis ist, dass der Zustandraum Symmetrien aufweist, die ausgenutzt werden können, um die Effizienz der Inferenz zu erhöhen. Wir führen einen effizienten, gelifteten Filter-Algorithmus ein, dessen Zeit- und Platzkomplexität gegenüber dem grundierten Algorithmus um einen faktoriellen Faktor reduziert ist

Unsupervised Selection and Estimation of Non-Gaussian Mixtures for High Dimensional Data Analysis

Lately, the enormous generation of databases in almost every aspect of life has created a great demand for new, powerful tools for turning data into useful information. Therefore, researchers were encouraged to explore and develop new machine learning ideas and methods. Mixture models are one of the machine learning techniques receiving considerable attention due to their ability to handle efficiently and effectively multidimensional data. Generally, four critical issues have to be addressed when adopting mixture models in high dimensional spaces: (1) choice of the probability density functions, (2) estimation of the mixture parameters, (3) automatic determination of the number of components M in the mixture, and (4) determination of what features best discriminate among the different components. The main goal of this thesis is to summarize all these challenging interrelated problems in one unified model. In most of the applications, the Gaussian density is used in mixture modeling of data. Although a Gaussian mixture may provide a reasonable approximation to many real-world distributions, it is certainly not always the best approximation especially in computer vision and image processing applications where we often deal with non-Gaussian data. Therefore, we propose to use three highly flexible distributions: the generalized Gaussian distribution (GGD), the asymmetric Gaussian distribution (AGD), and the asymmetric generalized Gaussian distribution (AGGD). We are motivated by the fact that these distributions are able to fit many distributional shapes and then can be considered as a useful class of flexible models to address several problems and applications involving measurements and features having well-known marked deviation from the Gaussian shape. Recently, researches have shown that model selection and parameter learning are highly dependent and should be performed simultaneously. For this purpose, many approaches have been suggested. The vast majority of these approaches can be classified, from a computational point of view, into two classes: deterministic and stochastic methods. Deterministic methods estimate the model parameters for a set of candidate models using the Expectation-Maximization (EM) framework, then choose the model that maximizes a model selection criterion. Stochastic methods such as Markov chain Monte Carlo (MCMC) can be used in order to sample from the full a posteriori distribution with M considered unknown. Hence, in this thesis, we propose three learning techniques capable of automatically determining model complexity while learning its parameters. First, we incorporate a Minimum Message Length (MML) penalty in the model learning step performed using the EM algorithm. Our second approach employs the Rival Penalized EM (RPEM) algorithm which is able to select an appropriate number of densities by fading out the redundant densities from a density mixture. Last but not least, we incorporate the nonparametric aspect of mixture models by assuming a countably infinite number of components and using Markov Chain Monte Carlo (MCMC) simulations for the estimation of the posterior distributions. Hence, the difficulty of choosing the appropriate number of clusters is sidestepped by assuming that there are an infinite number of mixture components. Another essential issue in the case of statistical modeling in general and finite mixtures in particular is feature selection (i.e. identification of the relevant or discriminative features describing the data) especially in the case of high-dimensional data. Indeed, feature selection has been shown to be a crucial step in several image processing, computer vision and pattern recognition applications not only because it speeds up learning but also because it improves model accuracy and generalization. Moreover, the learning of the mixture parameters ( i.e. both model selection and parameters estimation) is greatly affected by the quality of the features used. Hence, in this thesis, we are trying to solve the feature selection problem in unsupervised learning by casting it as an estimation problem, thus avoiding any combinatorial search. Finally, the effectiveness of our approaches is evaluated by applying them to different computer vision and image processing applications

Applications

Volume 3 describes how resource-aware machine learning methods and techniques are used to successfully solve real-world problems. The book provides numerous specific application examples: in health and medicine for risk modelling, diagnosis, and treatment selection for diseases in electronics, steel production and milling for quality control during manufacturing processes in traffic, logistics for smart cities and for mobile communications

Applications

Volume 3 describes how resource-aware machine learning methods and techniques are used to successfully solve real-world problems. The book provides numerous specific application examples: in health and medicine for risk modelling, diagnosis, and treatment selection for diseases in electronics, steel production and milling for quality control during manufacturing processes in traffic, logistics for smart cities and for mobile communications

Information Analysis for Steganography and Steganalysis in 3D Polygonal Meshes

Information hiding, which embeds a watermark/message over a cover signal, has recently found extensive applications in, for example, copyright protection, content authentication and covert communication. It has been widely considered as an appealing technology to complement conventional cryptographic processes in the field of multimedia security by embedding information into the signal being protected. Generally, information hiding can be classified into two categories: steganography and watermarking. While steganography attempts to embed as much information as possible into a cover signal, watermarking tries to emphasize the robustness of the embedded information at the expense of embedding capacity. In contrast to information hiding, steganalysis aims at detecting whether a given medium has hidden message in it, and, if possible, recover that hidden message. It can be used to measure the security performance of information hiding techniques, meaning a steganalysis resistant steganographic/watermarking method should be imperceptible not only to Human Vision Systems (HVS), but also to intelligent analysis. As yet, 3D information hiding and steganalysis has received relatively less attention compared to image information hiding, despite the proliferation of 3D computer graphics models which are fairly promising information carriers. This thesis focuses on this relatively neglected research area and has the following primary objectives: 1) to investigate the trade-off between embedding capacity and distortion by considering the correlation between spatial and normal/curvature noise in triangle meshes; 2) to design satisfactory 3D steganographic algorithms, taking into account this trade-off; 3) to design robust 3D watermarking algorithms; 4) to propose a steganalysis framework for detecting the existence of the hidden information in 3D models and introduce a universal 3D steganalytic method under this framework. %and demonstrate the performance of the proposed steganalysis by testing it against six well-known 3D steganographic/watermarking methods. The thesis is organized as follows. Chapter 1 describes in detail the background relating to information hiding and steganalysis, as well as the research problems this thesis will be studying. Chapter 2 conducts a survey on the previous information hiding techniques for digital images, 3D models and other medium and also on image steganalysis algorithms. Motivated by the observation that the knowledge of the spatial accuracy of the mesh vertices does not easily translate into information related to the accuracy of other visually important mesh attributes such as normals, Chapters 3 and 4 investigate the impact of modifying vertex coordinates of 3D triangle models on the mesh normals. Chapter 3 presents the results of an empirical investigation, whereas Chapter 4 presents the results of a theoretical study. Based on these results, a high-capacity 3D steganographic algorithm capable of controlling embedding distortion is also presented in Chapter 4. In addition to normal information, several mesh interrogation, processing and rendering algorithms make direct or indirect use of curvature information. Motivated by this, Chapter 5 studies the relation between Discrete Gaussian Curvature (DGC) degradation and vertex coordinate modifications. Chapter 6 proposes a robust watermarking algorithm for 3D polygonal models, based on modifying the histogram of the distances from the model vertices to a point in 3D space. That point is determined by applying Principal Component Analysis (PCA) to the cover model. The use of PCA makes the watermarking method robust against common 3D operations, such as rotation, translation and vertex reordering. In addition, Chapter 6 develops a 3D specific steganalytic algorithm to detect the existence of the hidden messages embedded by one well-known watermarking method. By contrast, the focus of Chapter 7 will be on developing a 3D watermarking algorithm that is resistant to mesh editing or deformation attacks that change the global shape of the mesh. By adopting a framework which has been successfully developed for image steganalysis, Chapter 8 designs a 3D steganalysis method to detect the existence of messages hidden in 3D models with existing steganographic and watermarking algorithms. The efficiency of this steganalytic algorithm has been evaluated on five state-of-the-art 3D watermarking/steganographic methods. Moreover, being a universal steganalytic algorithm can be used as a benchmark for measuring the anti-steganalysis performance of other existing and most importantly future watermarking/steganographic algorithms. Chapter 9 concludes this thesis and also suggests some potential directions for future work