Graph-based Data Modeling and Analysis for Data Fusion in Remote Sensing

Hyperspectral imaging provides the capability of increased sensitivity and discrimination over traditional imaging methods by combining standard digital imaging with spectroscopic methods. For each individual pixel in a hyperspectral image (HSI), a continuous spectrum is sampled as the spectral reflectance/radiance signature to facilitate identification of ground cover and surface material. The abundant spectrum knowledge allows all available information from the data to be mined. The superior qualities within hyperspectral imaging allow wide applications such as mineral exploration, agriculture monitoring, and ecological surveillance, etc. The processing of massive high-dimensional HSI datasets is a challenge since many data processing techniques have a computational complexity that grows exponentially with the dimension. Besides, a HSI dataset may contain a limited number of degrees of freedom due to the high correlations between data points and among the spectra. On the other hand, merely taking advantage of the sampled spectrum of individual HSI data point may produce inaccurate results due to the mixed nature of raw HSI data, such as mixed pixels, optical interferences and etc. Fusion strategies are widely adopted in data processing to achieve better performance, especially in the field of classification and clustering. There are mainly three types of fusion strategies, namely low-level data fusion, intermediate-level feature fusion, and high-level decision fusion. Low-level data fusion combines multi-source data that is expected to be complementary or cooperative. Intermediate-level feature fusion aims at selection and combination of features to remove redundant information. Decision level fusion exploits a set of classifiers to provide more accurate results. The fusion strategies have wide applications including HSI data processing. With the fast development of multiple remote sensing modalities, e.g. Very High Resolution (VHR) optical sensors, LiDAR, etc., fusion of multi-source data can in principal produce more detailed information than each single source. On the other hand, besides the abundant spectral information contained in HSI data, features such as texture and shape may be employed to represent data points from a spatial perspective. Furthermore, feature fusion also includes the strategy of removing redundant and noisy features in the dataset. One of the major problems in machine learning and pattern recognition is to develop appropriate representations for complex nonlinear data. In HSI processing, a particular data point is usually described as a vector with coordinates corresponding to the intensities measured in the spectral bands. This vector representation permits the application of linear and nonlinear transformations with linear algebra to find an alternative representation of the data. More generally, HSI is multi-dimensional in nature and the vector representation may lose the contextual correlations. Tensor representation provides a more sophisticated modeling technique and a higher-order generalization to linear subspace analysis. In graph theory, data points can be generalized as nodes with connectivities measured from the proximity of a local neighborhood. The graph-based framework efficiently characterizes the relationships among the data and allows for convenient mathematical manipulation in many applications, such as data clustering, feature extraction, feature selection and data alignment. In this thesis, graph-based approaches applied in the field of multi-source feature and data fusion in remote sensing area are explored. We will mainly investigate the fusion of spatial, spectral and LiDAR information with linear and multilinear algebra under graph-based framework for data clustering and classification problems

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

A Comparison of Image Denoising Methods

The advancement of imaging devices and countless images generated everyday pose an increasingly high demand on image denoising, which still remains a challenging task in terms of both effectiveness and efficiency. To improve denoising quality, numerous denoising techniques and approaches have been proposed in the past decades, including different transforms, regularization terms, algebraic representations and especially advanced deep neural network (DNN) architectures. Despite their sophistication, many methods may fail to achieve desirable results for simultaneous noise removal and fine detail preservation. In this paper, to investigate the applicability of existing denoising techniques, we compare a variety of denoising methods on both synthetic and real-world datasets for different applications. We also introduce a new dataset for benchmarking, and the evaluations are performed from four different perspectives including quantitative metrics, visual effects, human ratings and computational cost. Our experiments demonstrate: (i) the effectiveness and efficiency of representative traditional denoisers for various denoising tasks, (ii) a simple matrix-based algorithm may be able to produce similar results compared with its tensor counterparts, and (iii) the notable achievements of DNN models, which exhibit impressive generalization ability and show state-of-the-art performance on various datasets. In spite of the progress in recent years, we discuss shortcomings and possible extensions of existing techniques. Datasets, code and results are made publicly available and will be continuously updated at https://github.com/ZhaomingKong/Denoising-Comparison.Comment: In this paper, we intend to collect and compare various denoising methods to investigate their effectiveness, efficiency, applicability and generalization ability with both synthetic and real-world experiment

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