Loading...
Filter Design on Graphs
Killian, Joseph Jr
Killian, Joseph Jr
Citations
Altmetric:
Journal Title
Keywords
Readers/Advisors
Reale, Michael, Adriamanalimanana, Bruno, Chiang, Chen-Fu
Journal Title
Term and Year
Publication Date
2022-12
Type
Book Title
Publication Volume
Publication Issue
Publication Begin
Publication End
Number of pages
Files
Research Projects
Organizational Units
Journal Issue
Abstract
Graphs are a fundamental tool in Computer Science in a variety of areas such as Artificial Intelligence,
Machine Learning, Networking, Signal Processing, Brain Mapping, Social Networks, and many others. Many
of these graphs can have millions of nodes, so some sort of filtering is usually in order to extract the useful
information. The aim of this thesis is develop the mathematical background and building blocks that are
fundamental to designing these filters, as well as lay out a clear blueprint for how to create graph filters
for undirected graphs. The two major approaches that will be focused on will be developing filters in the
vertex domain and spectral domains. Filter design in the vertex domain aims to act on the laplacian or
adjacency matrices directly, while design in the spectral domain looks at acting on the spectral properties
of the graph. Some polynomial and rational filters are proposed in this thesis, and are applied to sample
graphs to demonstrate their effectiveness. Further study could be conducted with regard to directed graphs,
looking at a different variety of families of polynomials, or analyzing the efficiency of computing these filters
on larger graphs.