6 research outputs found
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
Advances in Distributed Graph Filtering
Graph filters are one of the core tools in graph signal processing. A central
aspect of them is their direct distributed implementation. However, the
filtering performance is often traded with distributed communication and
computational savings. To improve this tradeoff, this work generalizes
state-of-the-art distributed graph filters to filters where every node weights
the signal of its neighbors with different values while keeping the aggregation
operation linear. This new implementation, labeled as edge-variant graph
filter, yields a significant reduction in terms of communication rounds while
preserving the approximation accuracy. In addition, we characterize the subset
of shift-invariant graph filters that can be described with edge-variant
recursions. By using a low-dimensional parametrization the proposed graph
filters provide insights in approximating linear operators through the
succession and composition of local operators, i.e., fixed support matrices,
which span applications beyond the field of graph signal processing. A set of
numerical results shows the benefits of the edge-variant filters over current
methods and illustrates their potential to a wider range of applications than
graph filtering
Recommending on graphs: a comprehensive review from a data perspective
Recent advances in graph-based learning approaches have demonstrated their
effectiveness in modelling users' preferences and items' characteristics for
Recommender Systems (RSS). Most of the data in RSS can be organized into graphs
where various objects (e.g., users, items, and attributes) are explicitly or
implicitly connected and influence each other via various relations. Such a
graph-based organization brings benefits to exploiting potential properties in
graph learning (e.g., random walk and network embedding) techniques to enrich
the representations of the user and item nodes, which is an essential factor
for successful recommendations. In this paper, we provide a comprehensive
survey of Graph Learning-based Recommender Systems (GLRSs). Specifically, we
start from a data-driven perspective to systematically categorize various
graphs in GLRSs and analyze their characteristics. Then, we discuss the
state-of-the-art frameworks with a focus on the graph learning module and how
they address practical recommendation challenges such as scalability, fairness,
diversity, explainability and so on. Finally, we share some potential research
directions in this rapidly growing area.Comment: Accepted by UMUA
Graph Filters for Signal Processing and Machine Learning on Graphs
Filters are fundamental in extracting information from data. For time series
and image data that reside on Euclidean domains, filters are the crux of many
signal processing and machine learning techniques, including convolutional
neural networks. Increasingly, modern data also reside on networks and other
irregular domains whose structure is better captured by a graph. To process and
learn from such data, graph filters account for the structure of the underlying
data domain. In this article, we provide a comprehensive overview of graph
filters, including the different filtering categories, design strategies for
each type, and trade-offs between different types of graph filters. We discuss
how to extend graph filters into filter banks and graph neural networks to
enhance the representational power; that is, to model a broader variety of
signal classes, data patterns, and relationships. We also showcase the
fundamental role of graph filters in signal processing and machine learning
applications. Our aim is that this article provides a unifying framework for
both beginner and experienced researchers, as well as a common understanding
that promotes collaborations at the intersections of signal processing, machine
learning, and application domains