Transform-based Distributed Data Gathering

A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These transforms can be computed as data is routed towards the collection (or sink) node in the tree and exploit data correlation between nodes in the tree. Moreover, when used in wireless sensor networks, these transforms can also leverage data received at nodes via broadcast wireless communications. Various constructions of unidirectional transforms are also provided for use in data gathering in wireless sensor networks. New wavelet transforms are also proposed which provide significant improvements over existing unidirectional transforms

Adaptive distributed transforms for irregularly sampled Wireless Sensor Networks

We develop energy-efficient, adaptive distributed transforms for data gathering in wireless sensor networks. In particular, we con-sider a class of unidirectional transforms that are computed as data is forwarded to the sink along a given routing tree and develop a tree-based Karhunen-Loève Transform (KLT) that is optimal in that it achieves maximum data de-correlation among this class of trans-forms. As an alternative to this KLT (which incurs communication overhead in order to learn second order data statistics), we propose a backward adaptive filter optimization algorithm for distributed wavelet transforms that i) achieves near optimal performance and ii) has no communication overhead in learning statistics

Distributed Transforms for Efficient Data Gathering in Sensor Networks

Devices, systems, and techniques for data collecting network such as wireless sensors are disclosed. A described technique includes detecting one or more remote nodes included in the wireless sensor network using a local power level that controls a radio range of the local node. The technique includes transmitting a local outdegree. The local outdegree can be based on a quantity of the one or more remote nodes. The technique includes receiving one or more remote outdegrees from the one or more remote nodes. The technique includes determining a local node type of the local node based on detecting a node type of the one or more remote nodes, using the one or more remote outdegrees, and using the local outdegree. The technique includes adjusting characteristics, including an energy usage characteristic and a data compression characteristic, of the wireless sensor network by selectively modifying the local power level and selectively changing the local node type

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Analysis of sensory data using graph signal processing

Air pollution monitoring is an important topic that has been researched in the past few years thanks to the massive deployment of IoT platforms, as it affects the lives of both children and adults, and it kills millions of people worldwide every year. A new framework of tools called Graph Signal Processing was presented recently and it allows, among other things, the ability to predict data on a node that belongs to a network of sensors using both the data itself and the topology of the graph, which is based on the Laplacian matrix. This thesis is a comparative study on different prediction techniques for pollutant signals, such as Linear Combination, Multiple Linear Regression and GSP and it presents the results of all three methods in different scenarios, using RMSE and R2 indicators, and focusing the efforts on the understanding of how different parameters (such as the distance between nodes) affect the performances of these new tools. The results of the study show that pollutants O3 and NO2 are lowpass signals, and as the number of edges between nodes increases, GSP obtains a close performances to MRL. For PM10, we conclude that is not a low-pass signal, and the performance of the indicators drop massively compared with the previous ones. Linear combination is the worst of all three and MLR has a stable performance during all the scenarios

Contributions to Distributed Spatial Compression in Wireless Sensor Networks

Projecte final de carrera fet en col.laboració amb University of Southern CaliforniaPremi Càtedra Red.es en l’Àrea de Sistemes de la Informació al millor Projecte de Fi de Carrera d'Enginyeria de Telecomunicació. Atorgat per Càtedra Red.es. (Curs 2010-2011)This thesis presents several contributions in the field of distributed spatial compression inWireless Sensor Networks. First, since in most of the spatial compression schemes some nodes (raw nodes) need to broadcast their raw data to allow other nodes (aggregating nodes) to perform compression, we design several distributed heuristics which, via local communications, split the nodes into raw/aggregating subsets and optimize the amount of energy consumed in the network. We also extend previous work in the use of graph-based lifting transforms for data compression in distributed data gathering applications, to networks with more than one sink, and scenarios where all data has to be available at every node. Additionally, under the scope of these contributions, we design a new energy-efficient multicast routing algorithm, which is based on the minimum Steiner tree and exploits the broadcast property of wireless communications. We prove via computer-based simulations that our methods reduce the energy consumption in the network in comparison with existing approaches.Award-winnin

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science

Lifting transforms on graphs and their application to video coding

Compact representations of data are very useful in many applications such as coding, denoising or feature extraction. “Classical” transforms such as Discrete Cosine Transforms (DCT) or Discrete Wavelets Transforms (DWT) provide sparse approximations of smooth signals, but lose efficiency when they are applied to signals with large discontinuities. In such cases, directional transforms, which are able to adapt their basis functions to the underlying signal structure, improve the performance of “classical” transforms. In this PhD Thesis we describe a general class of lifting transforms on graphs that can be seen as N-dimensional directional transforms. Graphs are constructed so that every node corresponds to a specific sample point of a discrete N-dimensional signal and links between nodes represent correlation between samples. Therefore, non-correlated samples (e.g., samples across a large discontinuity in the signal) should not be linked. We propose a lifting-based directional transform that can be applied to any undirected graph. In this transform, filtering operations are performed following highcorrelation directions (indicated by the links between nodes), thus avoiding filtering across large discontinuities that give rise to large high-pass coefficients in those locations. In this way, the transform efficiently exploits the correlation that exists between data on the graph, leading to a more compact representation. We mainly focus on the design and optimization of these lifting transforms on graphs, studying and discussing the three main steps required to obtain an invertible and critically sampled transform: (i) graph construction, (ii) design of “good” graph bipartitions, and (iii) filter design. We also explain how to extend the transform to J levels of decomposition, obtaining a multiresolution analysis of the original N-dimensional signal. The proposed transform has many desirable properties, such as perfect reconstruction, critically-sampled, easy generalization to N-dimensional domains, non-separable and one-dimensional filtering operations, localization in frequency and in the original domain, and the ability to choose any filtering direction. As an application, we develop a graph-based video encoder where the goal is to obtain a compact representation of the original video sequence. To this end, we first propose a graph-representation of the video sequence and then design a 3-dimensional (spatio-temporal) non-separable directional transform. This can be viewed as an extension of wavelet transform-based video encoders that operate in the spatial and in the temporal domains independently. Our transform yields better compaction ability (in terms of non-linear approximation) than a state of the art motion-compensated temporal filtering transform (which can be interpreted as a temporal wavelet transform) and a comparable hybrid Discrete Cosine Transform (DCT)-based video encoder (which is the basis of the latest video coding standards). In order to obtain a complete video encoder, the transform coefficients and the side information (needed to obtain an invertible scheme) should be entropy coded and sent to the decoder. Therefore, we also propose a coefficient-reordering method based on the information of the graph which allows to improve the compression ability of the entropy encoder. Furthermore, we design two different low-cost approaches which aim to reduce the extensive computational complexity of the proposed system without causing significant losses of compression performance. The proposed complete system leads to an efficient encoder which significantly outperforms a comparable hybrid DCT-based encoder in rate-distortion terms. Finally, we investigate how rate-distortion optimization can be applied to the proposed coding scheme.La representación compacta de señales resulta útil en diversas aplicaciones, tales como compresión, reducción de ruido, o extracción de características. Transformadas “clásicas” como la Transformada Discreta del Coseno (DCT) o la TransformadaWavelet Discreta (DWT) logran aproximaciones compactas de señales suaves, pero pierden su eficiencia al ser aplicadas sobre se˜nales que contienen grandes discontinuidades. En estos casos, las transformadas direccionales, capaces de adaptar sus funciones base a la estructura de la señal a analizar, mejoran la eficiencia de las transformadas “clásicas”. En esta tesis nos centramos en el diseño y optimización de transformadas “lifting” sobre grafos, las cuales pueden ser interpretadas como transformadas direccionales N-dimensionales. Los grafos son construidos demanera que cada nodo se corresponde con una muestra específica de una señal discreta N-dimensional, y los enlaces entre los nodos representan correlación entre muestras. Así, muestras no correlacionadas (por ejemplo, muestras que se encuentran a ambos lados de una discontinuidad) no deberían estar unidas. Sobre el grafo formado aplicaremos transformadas basadas en el esquema “lifting”, en las que las operaciones de filtrado se realizan siguiendo las direcciones indicadas por los enlaces entre nodos (direcciones de alta correlación). De esta manera, evitaremos filtrar cruzando a través de largas discontinuidades (lo que resultaría en coeficientes con alto valor en dichas discontinuidades), dando lugar a una transformada direccional que explota la correlación que existe entre las muestras de la señal en el grafo, obteniendo una representación compacta de dicha señal. En esta tesis nos centramos, principalmente, en investigar los tres principales pasos requeridos para obtener una transformada direccional basada en el esquema “lifting” aplicado en grafos: (i) la construcción del grafo, (ii) el diseño de biparticiones del grafo, y (iii) la definición de los filtros. El buen diseño de estos tres procesos determinará, entre otras cosas, la capacidad para compactar la energía de la transformada. También explicamos cómo extender este tipo de transformadas a J niveles de descomposición, obteniendo un análisis multi-resolución de la señal N-dimensional original. La transformada propuesta tiene muchas propiedades deseables, tales como reconstrucción perfecta, muestreo crítico, fácil generalización a dominios N-dimensionales, operaciones de filtrado no separables y unidimensionales, localización en frecuencia y en el dominio original, y capacidad de elegir cualquier dirección de filtrado. Como aplicación, desarrollamos un codificador de vídeo basado en grafos donde el objetivo es obtener una versión compacta de la señal de vídeo original. Para ello, primero proponemos una representación en grafos de la secuencia de vídeo y luego diseñamos transformadas no separables direccionales 3-dimensionales (espacio-tiempo). Nuestro codificador puede interpretarse como una extensión de los codificadores de vídeo basados en “wavelets”, los cuales operan independientemente (de forma separable) en el dominio espacial y en el temporal. La transformada propuesta consigue mejores resultados (en términos de aproximación no lineal) que un método del estado del arte basado en “wavelets” temporales compensadas en movimiento, y un codificador DCT comparable (base de los últimos estándares de codificación de vídeo). Para conseguir un codificador de vídeo completo, los coeficientes resultantes de la transformada y la información secundaria (necesaria para obtener un esquema invertible) deben ser codificados entrópicamente y enviados al decodificador. Por ello, también proponemos en esta tesis un método de reordenación de los coeficientes basado en la información del grafo que permite mejorar la capacidad de compresión del codificador entrópico. El esquema de codificación propuesto mejora significativamente la eficiencia de un codificador híbrido basado en DCT en términos de tasa-distorsión. Sin embargo, nuestro método tiene la desventaja de su gran complejidad computacional. Para tratar de paliar este problema, diseñamos dos algoritmos que tratan de reducir dicha complejidad sin que ello afecte en la capacidad de compresión. Finalmente, investigamos como realizar optimización tasa-distorsión sobre el codificador basado en grafos propuesto

A Survey of Graph-based Deep Learning for Anomaly Detection in Distributed Systems

Anomaly detection is a crucial task in complex distributed systems. A thorough understanding of the requirements and challenges of anomaly detection is pivotal to the security of such systems, especially for real-world deployment. While there are many works and application domains that deal with this problem, few have attempted to provide an in-depth look at such systems. In this survey, we explore the potentials of graph-based algorithms to identify anomalies in distributed systems. These systems can be heterogeneous or homogeneous, which can result in distinct requirements. One of our objectives is to provide an in-depth look at graph-based approaches to conceptually analyze their capability to handle real-world challenges such as heterogeneity and dynamic structure. This study gives an overview of the State-of-the-Art (SotA) research articles in the field and compare and contrast their characteristics. To facilitate a more comprehensive understanding, we present three systems with varying abstractions as use cases. We examine the specific challenges involved in anomaly detection within such systems. Subsequently, we elucidate the efficacy of graphs in such systems and explicate their advantages. We then delve into the SotA methods and highlight their strength and weaknesses, pointing out the areas for possible improvements and future works.Comment: The first two authors (A. Danesh Pazho and G. Alinezhad Noghre) have equal contribution. The article is accepted by IEEE Transactions on Knowledge and Data Engineerin