The current availability of powerful computers and huge data sets is creating new opportunities in computational mathematics to bring together concepts and tools from graph theory, machine learning and signal processing, creating Data Analytics on Graphs. In discrete mathematics, a graph is merely a collection of points (nodes) and lines connecting some or all of them. The power of such graphs lies in the fact that the nodes can represent entities as diverse as the users of social networks or financial market data, and that these can be transformed into signals which can be analyzed using data analytics tools. Data Analytics on Graphs is a comprehensive introduction to generating advanced data analytics on graphs that allows us to move beyond the standard regular sampling in time and space to facilitate modelling in many important areas, including communication networks, computer science, linguistics, social sciences, biology, physics, chemistry, transport, town planning, financial systems, personal health and many others. The authors revisit graph topologies from a modern data analytics point of view, and proceed to establish a taxonomy of graph networks. With this as a basis, the authors show how the spectral analysis of graphs leads to even the most challenging machine learning tasks, such as clustering, being performed in an intuitive and physically meaningful way. The authors detail unique aspects of graph data analytics, such as their benefits for processing data acquired on irregular domains, their ability to finely-tune statistical learning procedures through local information processing, the concepts of random signals on graphs and graph shifts, learning of graph topology from data observed on graphs, and confluence with deep neural networks, multi-way tensor networks and Big Data. Extensive examples are included to render the concepts more concrete and to facilitate a greater understanding of the underlying principles. Aimed at readers with a good grasp of the fundamentals of data analytics, this book sets out the fundamentals of graph theory and the emerging mathematical techniques for the analysis of a wide range of data acquired on graph environments. Data Analytics on Graphs will be a useful friend and a helpful companion to all involved in data gathering and analysis irrespective of area of application.

This book deals with the creation of the algorithmic backbone that enables a computer to perceive humans in a monitored space. This is performed using the same signals that humans process, i.e., audio and video. Computers reproduce the same type of perception using sensors and algorithms in order to detect and track multiple interacting humans, by way of multiple cues, like bodies, faces or speech. This application domain is challenging, because audio and visual signals are cluttered by both background and foreground objects. First, particle filtering is established as the framework for tracking. Then, audio, visual and also audio-visual tracking systems are separately explained. Each modality is analyzed, starting with sensor configuration, detection for tracker initialization and the trackers themselves. Techniques to fuse the modalities are then considered. Instead of offering a monolithic approach to the tracking problem, this book also focuses on implementation by providing MATLAB code for every presented component. This way, the reader can connect every concept with corresponding code. Finally, the applications of the various tracking systems in different domains are studied.