Entropic Characterization and Time Evolution of Complex Networks

In this thesis, we address problems encountered in complex network analysis using graph theoretic methods. The thesis specifically centers on the challenge of how to characterize the structural properties and time evolution of graphs. We commence by providing a brief roadmap for our research in Chapter 1, followed by a review of the relevant research literature in Chapter 2. The remainder of the thesis is structured as follows. In Chapter 3, we focus on the graph entropic characterizations and explore whether the von Neumann entropy recently defined only on undirected graphs, can be extended to the domain of directed graphs. The substantial contribution involves a simplified form of the entropy which can be expressed in terms of simple graph statistics, such as graph size and vertex in-degree and out-degree. Chapter 4 further investigates the uses and applications of the von Neumann entropy in order to solve a number of network analysis and machine learning problems. The contribution in this chapter includes an entropic edge assortativity measure and an entropic graph embedding method, which are developed for both undirected and directed graphs. The next part of the thesis analyzes the time-evolving complex networks using physical and information theoretic approaches. In particular, Chapter 5 provides a thermodynamic framework for handling dynamic graphs using ideas from algebraic graph theory and statistical mechanics. This allows us to derive expressions for a number of thermodynamic functions, including energy, entropy and temperature, which are shown to be efficient in identifying abrupt structural changes and phase transitions in real-world dynamical systems. Chapter 6 develops a novel method for constructing a generative model to analyze the structure of labeled data, which provides a number of novel directions to the study of graph time-series. Finally, in Chapter 7, we provide concluding remarks and discuss the limitations of our methodologies, and point out possible future research directions

Learning the Structure of Continuous Markov Decision Processes

There is growing interest in artificial, intelligent agents which can operate autonomously for an extended period of time in complex environments and fulfill a variety of different tasks. Such agents will face different problems during their lifetime which may not be foreseeable at the time of their deployment. Thus, the capacity for lifelong learning of new behaviors is an essential prerequisite for this kind of agents as it enables them to deal with unforeseen situations. However, learning every complex behavior anew from scratch would be cumbersome for the agent. It is more plausible to consider behavior to be modular and let the agent acquire a set of reusable building blocks for behavior, the so-called skills. These skills might, once acquired, facilitate fast learning and adaptation of behavior to new situations. This work focuses on computational approaches for skill acquisition, namely which kind of skills shall be acquired and how to acquire them. The former is commonly denoted as skill discovery and the latter as skill learning . The main contribution of this thesis is a novel incremental skill acquisition approach which is suited for lifelong learning. In this approach, the agent learns incrementally a graph-based representation of a domain and exploits certain properties of this graph such as its bottlenecks for skill discovery. This thesis proposes a novel approach for learning a graph-based representation of continuous domains based on formalizing the problem as a probabilistic generative model. Furthermore, a new incremental agglomerative clustering approach for identifying bottlenecks of such graphs is presented. Thereupon, the thesis proposes a novel intrinsic motivation system which enables an agent to intelligently allocate time between skill discovery and skill learning in developmental settings, where the agent is not constrained by external tasks. The results of this thesis show that the resulting skill acquisition approach is suited for continuous domains and can deal with domain stochasticity and different explorative behavior of the agent. The acquired skills are reusable and versatile and can be used in multi-task and lifelong learning settings in high-dimensional problems

A cortical model of object perception based on Bayesian networks and belief propagation.

Evidence suggests that high-level feedback plays an important role in visual perception by shaping the response in lower cortical levels (Sillito et al. 2006, Angelucci and Bullier 2003, Bullier 2001, Harrison et al. 2007). A notable example of this is reflected by the retinotopic activation of V1 and V2 neurons in response to illusory contours, such as Kanizsa figures, which has been reported in numerous studies (Maertens et al. 2008, Seghier and Vuilleumier 2006, Halgren et al. 2003, Lee 2003, Lee and Nguyen 2001). The illusory contour activity emerges first in lateral occipital cortex (LOC), then in V2 and finally in V1, strongly suggesting that the response is driven by feedback connections. Generative models and Bayesian belief propagation have been suggested to provide a theoretical framework that can account for feedback connectivity, explain psychophysical and physiological results, and map well onto the hierarchical distributed cortical connectivity (Friston and Kiebel 2009, Dayan et al. 1995, Knill and Richards 1996, Geisler and Kersten 2002, Yuille and Kersten 2006, Deneve 2008a, George and Hawkins 2009, Lee and Mumford 2003, Rao 2006, Litvak and Ullman 2009, Steimer et al. 2009). The present study explores the role of feedback in object perception, taking as a starting point the HMAX model, a biologically inspired hierarchical model of object recognition (Riesenhuber and Poggio 1999, Serre et al. 2007b), and extending it to include feedback connectivity. A Bayesian network that captures the structure and properties of the HMAX model is developed, replacing the classical deterministic view with a probabilistic interpretation. The proposed model approximates the selectivity and invariance operations of the HMAX model using the belief propagation algorithm. Hence, the model not only achieves successful feedforward recognition invariant to position and size, but is also able to reproduce modulatory effects of higher-level feedback, such as illusory contour completion, attention and mental imagery. Overall, the model provides a biophysiologically plausible interpretation, based on state-of-theart probabilistic approaches and supported by current experimental evidence, of the interaction between top-down global feedback and bottom-up local evidence in the context of hierarchical object perception

Statistical Mechanics for Network Structure and Evolution

In this thesis, we address problems in complex networks using the methods of statistical mechanics and information theory. We particularly focus on the thermodynamic characterisation of networks and entropic analysis on statistics and dynamics of network evolution. After a brief introduction of background and motivation behind the thesis in Chapter 1, we provide a review of relevant literature in Chapter 2, and elaborate the main methods from Chapter 3 to Chapter 6. In Chapter 3, we explore the normalised Laplacian matrix as the Hamiltonian operator of the network which governs the particle occupations corresponding to Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. The relevant partition functions derive the thermodynamic quantities in revealing network structural characterisations. Chapter 4 further decomposes the global network entropy in three statistics on edge-connection components. This decompensation reflects the detailed distribution of entropy across the edges of a network, and is particularly useful if the analysis of non-homogeneous networks with a strong community and hub structure is being attempted. Furthermore, Chapter 5 and Chapter 6 provide the theoretical approaches to analyse the dynamic network evolution and the application of the real-world networks. In Chapter 5, we investigate both undirected and directed network evolution using the Euler-Lagrange equation. This variational principle is based on the von Neumann entropy for time-varying network structure. The presented model not only provides an accurate simulation of the degree statistics in network evolution, but also captures the topological variations taking place when the structure of a network changes violently. Chapter 6 studies the fMRI regional brain interaction networks using directed graphs. We further develop a novel method for characterising networks using Bose-Einstein entropy and the Jensen-Shannon divergence. It offers a high discrimination among patients with suspected Alzheimer's disease. Finally, Chapter 7 concludes the thesis and discusses the limitations of our methodologies, which also supplies the potential research in the future

Research on Brain and Mind Inspired Intelligence

To address the problems of scientific theory, common technology and engineering application of multimedia and multimodal information computing, this paper is focused on the theoretical model, algorithm framework, and system architecture of brain and mind inspired intelligence (BMI) based on the structure mechanism simulation of the nervous system, the function architecture emulation of the cognitive system and the complex behavior imitation of the natural system. Based on information theory, system theory, cybernetics and bionics, we define related concept and hypothesis of brain and mind inspired computing (BMC) and design a model and framework for frontier BMI theory. Research shows that BMC can effectively improve the performance of semantic processing of multimedia and cross-modal information, such as target detection, classification and recognition. Based on the brain mechanism and mind architecture, a semantic-oriented multimedia neural, cognitive computing model is designed for multimedia semantic computing. Then a hierarchical cross-modal cognitive neural computing framework is proposed for cross-modal information processing. Furthermore, a cross-modal neural, cognitive computing architecture is presented for remote sensing intelligent information extraction platform and unmanned autonomous system

Towards accurate multi-person pose estimation in the wild

In this thesis we are concerned with the problem of articulated human pose estimation and pose tracking in images and video sequences. Human pose estimation is a task of localising major joints of a human skeleton in natural images and is one of the most important visual recognition tasks in the scenes containing humans with numerous applications in robotics, virtual and augmented reality, gaming and healthcare among others. Articulated human pose tracking requires tracking multiple persons in the video sequence while simultaneously estimating full body poses. This task is important for analysing surveillance footage, activity recognition, sports analytics, etc. Most of the prior work focused on the pose estimation of single pre-localised humans whereas here we address a case with multiple people in real world images which entails several challenges such as person-person overlaps in highly crowded scenes, unknown number of people or people entering and leaving video sequences. The first contribution is a multi-person pose estimation algorithm based on the bottom-up detection-by-grouping paradigm. Unlike the widespread top-down approaches our method detects body joints and pairwise relations between them in a single forward pass of a convolutional neural network. Multi-person parsing is performed by optimizing a joint objective based on a multicut graph partitioning framework. Secondly, we extend our pose estimation approach to articulated multi-person pose tracking in videos. Our approach performs multi-target tracking and pose estimation in a holistic manner by optimising a single objective. We further simplify and refine the formulation which allows us to reach close to the real-time performance. Thirdly, we propose a large scale dataset and a benchmark for articulated multi-person tracking. It is the first dataset of video sequences comprising complex multi-person scenes and fully annotated tracks with 2D keypoints. Our fourth contribution is a method for estimating 3D body pose using on-body wearable cameras. Our approach uses a pair of downward facing, head-mounted cameras and captures an entire body. This egocentric approach is free of limitations of traditional setups with external cameras and can estimate body poses in very crowded environments. Our final contribution goes beyond human pose estimation and is in the field of deep learning of 3D object shapes. In particular, we address the case of reconstructing 3D objects from weak supervision. Our approach represents objects as 3D point clouds and is able to learn them with 2D supervision only and without requiring camera pose information at training time. We design a differentiable renderer of point clouds as well as a novel loss formulation for dealing with camera pose ambiguity.In dieser Arbeit behandeln wir das Problem der Schätzung und Verfolgung artikulierter menschlicher Posen in Bildern und Video-Sequenzen. Die Schätzung menschlicher Posen besteht darin die Hauptgelenke des menschlichen Skeletts in natürlichen Bildern zu lokalisieren und ist eine der wichtigsten Aufgaben der visuellen Erkennung in Szenen, die Menschen beinhalten. Sie hat zahlreiche Anwendungen in der Robotik, virtueller und erweiterter Realität, in Videospielen, in der Medizin und weiteren Bereichen. Die Verfolgung artikulierter menschlicher Posen erfordert die Verfolgung mehrerer Personen in einer Videosequenz bei gleichzeitiger Schätzung vollständiger Körperhaltungen. Diese Aufgabe ist besonders wichtig für die Analyse von Video-Überwachungsaufnahmen, Aktivitätenerkennung, digitale Sportanalyse etc. Die meisten vorherigen Arbeiten sind auf die Schätzung einzelner Posen vorlokalisierter Menschen fokussiert, wohingegen wir den Fall mehrerer Personen in natürlichen Aufnahmen betrachten. Dies bringt einige Herausforderungen mit sich, wie die Überlappung verschiedener Personen in dicht gedrängten Szenen, eine unbekannte Anzahl an Personen oder Personen die das Sichtfeld der Video-Sequenz verlassen oder betreten. Der erste Beitrag ist ein Algorithmus zur Schätzung der Posen mehrerer Personen, welcher auf dem Paradigma der Erkennung durch Gruppierung aufbaut. Im Gegensatz zu den verbreiteten Verfeinerungs-Ansätzen erkennt unsere Methode Körpergelenke and paarweise Beziehungen zwischen ihnen in einer einzelnen Vorwärtsrechnung eines faltenden neuronalen Netzwerkes. Die Gliederung in mehrere Personen erfolgt durch Optimierung einer gemeinsamen Zielfunktion, die auf dem Mehrfachschnitt-Problem in der Graphenzerlegung basiert. Zweitens erweitern wir unseren Ansatz zur Posen-Bestimmung auf das Verfolgen mehrerer Personen und deren Artikulation in Videos. Unser Ansatz führt eine Verfolgung mehrerer Ziele und die Schätzung der zugehörigen Posen in ganzheitlicher Weise durch, indem eine einzelne Zielfunktion optimiert wird. Desweiteren vereinfachen und verfeinern wir die Formulierung, was unsere Methode nah an Echtzeit-Leistung bringt. Drittens schlagen wir einen großen Datensatz und einen Bewertungsmaßstab für die Verfolgung mehrerer artikulierter Personen vor. Dies ist der erste Datensatz der Video-Sequenzen von komplexen Szenen mit mehreren Personen beinhaltet und deren Spuren komplett mit zwei-dimensionalen Markierungen der Schlüsselpunkte versehen sind. Unser vierter Beitrag ist eine Methode zur Schätzung von drei-dimensionalen Körperhaltungen mittels am Körper tragbarer Kameras. Unser Ansatz verwendet ein Paar nach unten gerichteter, am Kopf befestigter Kameras und erfasst den gesamten Körper. Dieser egozentrische Ansatz ist frei von jeglichen Limitierungen traditioneller Konfigurationen mit externen Kameras und kann Körperhaltungen in sehr dicht gedrängten Umgebungen bestimmen. Unser letzter Beitrag geht über die Schätzung menschlicher Posen hinaus in den Bereich des tiefen Lernens der Gestalt von drei-dimensionalen Objekten. Insbesondere befassen wir uns mit dem Fall drei-dimensionale Objekte unter schwacher Überwachung zu rekonstruieren. Unser Ansatz repräsentiert Objekte als drei-dimensionale Punktwolken and ist im Stande diese nur mittels zwei-dimensionaler Überwachung und ohne Informationen über die Kamera-Ausrichtung zur Trainingszeit zu lernen. Wir entwerfen einen differenzierbaren Renderer für Punktwolken sowie eine neue Formulierung um mit uneindeutigen Kamera-Ausrichtungen umzugehen

Modeling cognition with generative neural networks: The case of orthographic processing

This thesis investigates the potential of generative neural networks to model cognitive processes. In contrast to many popular connectionist models, the computational framework adopted in this research work emphasizes the generative nature of cognition, suggesting that one of the primary goals of cognitive systems is to learn an internal model of the surrounding environment that can be used to infer causes and make predictions about the upcoming sensory information. In particular, we consider a powerful class of recurrent neural networks that learn probabilistic generative models from experience in a completely unsupervised way, by extracting high-order statistical structure from a set of observed variables. Notably, this type of networks can be conveniently formalized within the more general framework of probabilistic graphical models, which provides a unified language to describe both neural networks and structured Bayesian models. Moreover, recent advances allow to extend basic network architectures to build more powerful systems, which exploit multiple processing stages to perform learning and inference over hierarchical models, or which exploit delayed recurrent connections to process sequential information. We argue that these advanced network architectures constitute a promising alternative to the more traditional, feed-forward, supervised neural networks, because they more neatly capture the functional and structural organization of cortical circuits, providing a principled way to combine top-down, high-level contextual information with bottom-up, sensory evidence. We provide empirical support justifying the use of these models by studying how efficient implementations of hierarchical and temporal generative networks can extract information from large datasets containing thousands of patterns. In particular, we perform computational simulations of recognition of handwritten and printed characters belonging to different writing scripts, which are successively combined spatially or temporally in order to build more complex orthographic units such as those constituting English words