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.
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