Sparse Nonlinear MIMO Filtering and Identification

In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation

Representation learning on complex data

Machine learning has enabled remarkable progress in various fields of research and application in recent years. The primary objective of machine learning consists of developing algorithms that can learn and improve through observation and experience. Machine learning algorithms learn from data, which may exhibit various forms of complexity, which pose fundamental challenges. In this thesis, we address two major types of data complexity: First, data is often inherently connected and can be modeled by a single or multiple graphs. Machine learning methods could potentially exploit these connections, for instance, to find groups of similar users in a social network for targeted marketing or to predict functional properties of proteins for drug design. Secondly, data is often high-dimensional, for instance, due to a large number of recorded features or induced by a quadratic pixel grid on images. Classical machine learning methods perennially fail when exposed to high-dimensional data as several key assumptions cease to be satisfied. Therefore, a major challenge associated with machine learning on graphs and high-dimensional data is to derive meaningful representations of this data, which allow models to learn effectively. In contrast to conventional manual feature engineering methods, representation learning aims at automatically learning data representations that are particularly suitable for a specific task at hand. Driven by a rapidly increasing availability of data, these methods have celebrated tremendous success for tasks such as object detection in images and speech recognition. However, there is still a considerable amount of research work to be done to fully leverage such techniques for learning on graphs and high-dimensional data. In this thesis, we address the problem of learning meaningful representations for highly-effective machine learning on complex data, in particular, graph data and high-dimensional data. Additionally, most of our proposed methods are highly scalable, allowing them to learn from massive amounts of data. While we address a wide range of general learning problems with different modes of supervision, ranging from unsupervised problems on unlabeled data to (semi-)-supervised learning on annotated data sets, we evaluate our models on specific tasks from fields such as social network analysis, information security, and computer vision. The first part of this thesis addresses representation learning on graphs. While existing graph neural network models commonly perform synchronous message passing between nodes and thus struggle with long-range dependencies and efficiency issues, our first proposed method performs fast asynchronous message passing and, therefore, supports adaptive and efficient learning and additionally scales to large graphs. Another contribution consists of a novel graph-based approach to malware detection and classification based on network traffic. While existing methods classify individual network flows between two endpoints, our algorithm collects all traffic in a monitored network within a specific time frame and builds a communication graph, which is then classified using a novel graph neural network model. The developed model can be generally applied to further graph classification or anomaly detection tasks. Two further contributions challenge a common assumption made by graph learning methods, termed homophily, which states that nodes with similar properties are usually closely connected in the graph. To this end, we develop a method that predicts node-level properties leveraging the distribution of class labels appearing in the neighborhood of the respective node. That allows our model to learn general relations between a node and its neighbors, which are not limited to homophily. Another proposed method specifically models structural similarity between nodes to model different roles, for instance, influencers and followers in a social network. In particular, we develop an unsupervised algorithm for deriving node descriptors based on how nodes spread probability mass to their neighbors and aggregate these descriptors to represent entire graphs. The second part of this thesis addresses representation learning on high-dimensional data. Specifically, we consider the problem of clustering high-dimensional data, such as images, texts, or gene expression profiles. Classical clustering algorithms struggle with this type of data since it can usually not be assumed that data objects will be similar w.r.t. all attributes, but only within a particular subspace of the full-dimensional ambient space. Subspace clustering is an approach to clustering high-dimensional data based on this assumption. While there already exist powerful neural network-based subspace clustering methods, these methods commonly suffer from scalability issues and lack a theoretical foundation. To this end, we propose a novel metric learning approach to subspace clustering, which can provably recover linear subspaces under suitable assumptions and, at the same time, tremendously reduces the required numbear of model parameters and memory compared to existing algorithms.Maschinelles Lernen hat in den letzten Jahren bemerkenswerte Fortschritte in verschiedenen Forschungs- und Anwendungsbereichen ermöglicht. Das primäre Ziel des maschinellen Lernens besteht darin, Algorithmen zu entwickeln, die durch Beobachtung und Erfahrung lernen und sich verbessern können. Algorithmen des maschinellen Lernens lernen aus Daten, die verschiedene Formen von Komplexität aufweisen können, was grundlegende Herausforderungen mit sich bringt. Im Rahmen dieser Dissertation werden zwei Haupttypen von Datenkomplexität behandelt: Erstens weisen Daten oft inhärente Verbindungen, die durch einen einzelnen oder mehrere Graphen modelliert werden können. Methoden des maschinellen Lernens können diese Verbindungen potenziell ausnutzen, um beispielsweise Gruppen ähnlicher Nutzer in einem sozialen Netzwerk für gezieltes Marketing zu finden oder um funktionale Eigenschaften von Proteinen für das Design von Medikamenten vorherzusagen. Zweitens sind die Daten oft hochdimensional, z. B. aufgrund einer großen Anzahl von erfassten Merkmalen oder bedingt durch ein quadratisches Pixelraster auf Bildern. Klassische Methoden des maschinellen Lernens versagen immer wieder, wenn sie hochdimensionalen Daten ausgesetzt werden, da mehrere Schlüsselannahmen nicht mehr erfüllt sind. Daher besteht eine große Herausforderung beim maschinellen Lernen auf Graphen und hochdimensionalen Daten darin, sinnvolle Repräsentationen dieser Daten abzuleiten, die es den Modellen ermöglichen, effektiv zu lernen. Im Gegensatz zu konventionellen manuellen Feature-Engineering-Methoden zielt Representation Learning darauf ab, automatisch Datenrepräsentationen zu lernen, die für eine bestimmte Aufgabenstellung besonders geeignet sind. Angetrieben durch eine rasant steigende Datenverfügbarkeit haben diese Methoden bei Aufgaben wie der Objekterkennung in Bildern und der Spracherkennung enorme Erfolge gefeiert. Es besteht jedoch noch ein erheblicher Forschungsbedarf, um solche Verfahren für das Lernen auf Graphen und hochdimensionalen Daten voll auszuschöpfen. Diese Dissertation beschäftigt sich mit dem Problem des Lernens sinnvoller Repräsentationen für hocheffektives maschinelles Lernen auf komplexen Daten, insbesondere auf Graphen und hochdimensionalen Daten. Zusätzlich sind die meisten hier vorgeschlagenen Methoden hoch skalierbar, so dass sie aus großen Datenmengen lernen können. Obgleich eine breite Palette von allgemeinen Lernproblemen mit verschiedenen Arten der Überwachung adressiert wird, die von unüberwachten Problemen auf unannotierten Daten bis hin zum (semi-)überwachten Lernen auf annotierten Datensätzen reichen, werden die vorgestellten Metoden anhand spezifischen Anwendungen aus Bereichen wie der Analyse sozialer Netzwerke, der Informationssicherheit und der Computer Vision evaluiert. Der erste Teil der Dissertation befasst sich mit dem Representation Learning auf Graphen. Während existierende neuronale Netze für Graphen üblicherweise eine synchrone Nachrichtenübermittlung zwischen den Knoten durchführen und somit mit langreichweitigen Abhängigkeiten und Effizienzproblemen zu kämpfen haben, führt die erste hier vorgeschlagene Methode eine schnelle asynchrone Nachrichtenübermittlung durch und unterstützt somit adaptives und effizientes Lernen und skaliert zudem auf große Graphen. Ein weiterer Beitrag besteht in einem neuartigen graphenbasierten Ansatz zur Malware-Erkennung und -Klassifizierung auf Basis des Netzwerkverkehrs. Während bestehende Methoden einzelne Netzwerkflüsse zwischen zwei Endpunkten klassifizieren, sammelt der vorgeschlagene Algorithmus den gesamten Verkehr in einem überwachten Netzwerk innerhalb eines bestimmten Zeitraums und baut einen Kommunikationsgraphen auf, der dann mithilfe eines neuartigen neuronalen Netzes für Graphen klassifiziert wird. Das entwickelte Modell kann allgemein für weitere Graphenklassifizierungs- oder Anomalieerkennungsaufgaben eingesetzt werden. Zwei weitere Beiträge stellen eine gängige Annahme von Graphen-Lernmethoden in Frage, die so genannte Homophilie-Annahme, die besagt, dass Knoten mit ähnlichen Eigenschaften in der Regel eng im Graphen verbunden sind. Zu diesem Zweck wird eine Methode entwickelt, die Eigenschaften auf Knotenebene vorhersagt, indem sie die Verteilung der annotierten Klassen in der Nachbarschaft des jeweiligen Knotens nutzt. Das erlaubt dem vorgeschlagenen Modell, allgemeine Beziehungen zwischen einem Knoten und seinen Nachbarn zu lernen, die nicht auf Homophilie beschränkt sind. Eine weitere vorgeschlagene Methode modelliert strukturelle Ähnlichkeit zwischen Knoten, um unterschiedliche Rollen zu modellieren, zum Beispiel Influencer und Follower in einem sozialen Netzwerk. Insbesondere entwickeln wir einen unüberwachten Algorithmus zur Ableitung von Knoten-Deskriptoren, die darauf basieren, wie Knoten Wahrscheinlichkeitsmasse auf ihre Nachbarn verteilen, und aggregieren diese Deskriptoren, um ganze Graphen darzustellen. Der zweite Teil dieser Dissertation befasst sich mit dem Representation Learning auf hochdimensionalen Daten. Konkret wird das Problem des Clusterns hochdimensionaler Daten, wie z. B. Bilder, Texte oder Genexpressionsprofile, betrachtet. Klassische Clustering-Algorithmen haben mit dieser Art von Daten zu kämpfen, da in der Regel nicht davon ausgegangen werden kann, dass die Datenobjekte in Bezug auf alle Attribute ähnlich sind, sondern nur innerhalb eines bestimmten Unterraums des volldimensionalen Datenraums. Das Unterraum-Clustering ist ein Ansatz zum Clustern hochdimensionaler Daten, der auf dieser Annahme basiert. Obwohl es bereits leistungsfähige, auf neuronalen Netzen basierende Unterraum-Clustering-Methoden gibt, leiden diese Methoden im Allgemeinen unter Skalierbarkeitsproblemen und es fehlt ihnen an einer theoretischen Grundlage. Zu diesem Zweck wird ein neuartiger Metric Learning Ansatz für das Unterraum-Clustering vorgeschlagen, der unter geeigneten Annahmen nachweislich lineare Unterräume detektieren kann und gleichzeitig die erforderliche Anzahl von Modellparametern und Speicher im Vergleich zu bestehenden Algorithmen enorm reduziert

Design of discrete time controllers and estimators.

This thesis considers optimal linear least-squares filtering smoothing prediction and regulation for discrete-time processes. A finite interval smoothing filter is derived in the z domain giving a transfer function solution. The resulting time-invariant smoother can be applied to problems where, a time varying solution using matrix Riccati equations would diverge if the process is modelled inaccurately. A self-tuning algorithm is given for the filtering and fixed lag smoothing problems as applied to square multi-variable ARMA processes when only the order of the process is assumed known. The dynamics of the process can also be slowly time varying. If the dynamics remain constant and unknown, it is shown how the self-tuning filter or smoother algorithm converges asymptotically to the optimal Wiener solutions. LQG self-tuning regulation is considered. The LQG algorithms rely on input-output data rather than from the conventional state-space approach employing the Kalman filter. An explicit algorithm is given which is similar to certain pole placement self-tuning regulators, requiring the solution of a diophantine equation. Following this, an implicit algorithm is shown to overcome the problem of solving a diophantine equation by estimating the regulator parameters directly using recursive least squares. The LQG algorithms are shown to be able to cope with processes which are non-minimum phase, open loop unstable and with an unknown time delay

A cybernetic approach to prediction with an outline of an adaptive optical computer

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Since the pioneering work of Kolmogoroff and Wiener the use of computing devices to solve problems concerned with - the prediction of future states of a time series has stimulated a large amount of research. Despite all this, however the results have been disappointing. If significant progress were to be made in this field it would lead not only to the possibility of forecasting economic events, the weather, earthquakes, epidemics, and so on, but also -to the possibility of simulating these system. Approaches involving the programming of a computer to carry out this task run into the difficulty of defining the variables involved in a precise enough manner, whereas using the computer -to investigate all the past events of that time series requires a large processing time and an enormous memory store. This thesis examines an approach to this problem which involves the use of a device for processing information in a parallel manner. The system envisaged consists of a holographic recognition device controlled by a digital computer -a combination of analogue and digital techniques. The principle of this device is that developed by Gabor and others, and allows the system to learn to predict the future of a time series. The system learns to predict the future of a time series by using a past length of time series as a training set. Using this training set it attempts to predict the next values of the time series, which can then be compared with the actual time series. The system, then, attempts to optimize its prediction by minimizing the error between the predicted and actual values

Using contour information and segmentation for object registration, modeling and retrieval

This thesis considers different aspects of the utilization of contour information and syntactic and semantic image segmentation for object registration, modeling and retrieval in the context of content-based indexing and retrieval in large collections of images. Target applications include retrieval in collections of closed silhouettes, holistic w ord recognition in handwritten historical manuscripts and shape registration. Also, the thesis explores the feasibility of contour-based syntactic features for improving the correspondence of the output of bottom-up segmentation to semantic objects present in the scene and discusses the feasibility of different strategies for image analysis utilizing contour information, e.g. segmentation driven by visual features versus segmentation driven by shape models or semi-automatic in selected application scenarios. There are three contributions in this thesis. The first contribution considers structure analysis based on the shape and spatial configuration of image regions (socalled syntactic visual features) and their utilization for automatic image segmentation. The second contribution is the study of novel shape features, matching algorithms and similarity measures. Various applications of the proposed solutions are presented throughout the thesis providing the basis for the third contribution which is a discussion of the feasibility of different recognition strategies utilizing contour information. In each case, the performance and generality of the proposed approach has been analyzed based on extensive rigorous experimentation using as large as possible test collections

Design of a High-Speed Architecture for Stabilization of Video Captured Under Non-Uniform Lighting Conditions

Video captured in shaky conditions may lead to vibrations. A robust algorithm to immobilize the video by compensating for the vibrations from physical settings of the camera is presented in this dissertation. A very high performance hardware architecture on Field Programmable Gate Array (FPGA) technology is also developed for the implementation of the stabilization system. Stabilization of video sequences captured under non-uniform lighting conditions begins with a nonlinear enhancement process. This improves the visibility of the scene captured from physical sensing devices which have limited dynamic range. This physical limitation causes the saturated region of the image to shadow out the rest of the scene. It is therefore desirable to bring back a more uniform scene which eliminates the shadows to a certain extent. Stabilization of video requires the estimation of global motion parameters. By obtaining reliable background motion, the video can be spatially transformed to the reference sequence thereby eliminating the unintended motion of the camera. A reflectance-illuminance model for video enhancement is used in this research work to improve the visibility and quality of the scene. With fast color space conversion, the computational complexity is reduced to a minimum. The basic video stabilization model is formulated and configured for hardware implementation. Such a model involves evaluation of reliable features for tracking, motion estimation, and affine transformation to map the display coordinates of a stabilized sequence. The multiplications, divisions and exponentiations are replaced by simple arithmetic and logic operations using improved log-domain computations in the hardware modules. On Xilinx\u27s Virtex II 2V8000-5 FPGA platform, the prototype system consumes 59% logic slices, 30% flip-flops, 34% lookup tables, 35% embedded RAMs and two ZBT frame buffers. The system is capable of rendering 180.9 million pixels per second (mpps) and consumes approximately 30.6 watts of power at 1.5 volts. With a 1024×1024 frame, the throughput is equivalent to 172 frames per second (fps). Future work will optimize the performance-resource trade-off to meet the specific needs of the applications. It further extends the model for extraction and tracking of moving objects as our model inherently encapsulates the attributes of spatial distortion and motion prediction to reduce complexity. With these parameters to narrow down the processing range, it is possible to achieve a minimum of 20 fps on desktop computers with Intel Core 2 Duo or Quad Core CPUs and 2GB DDR2 memory without a dedicated hardware

Efficient Learning Machines

Computer scienc

Digital Filtering and Processing by Transform Techniques, Volume 1 Final Report

Digital filtering and processing by transform technique