Emerging methods for the spectral analysis of graphs are analyzed in this paper, as graphs are currently used to study interactions in many fields from neuroscience to social networks. There are two main approaches related to the spectral transformation of graphs. The first approach is based on the Laplacian matrix. The graph Fourier transform is defined as an expansion of a graph signal in terms of eigenfunctions of the graph Laplacian. The calculated eigenvalues carry the notion of frequency of graph signals. The second approach is based on the graph weighted adjacency matrix, as it expands the graph signal into a basis of eigenvectors of the adjacency matrix instead of the graph Laplacian. Here, the notion of frequency is then obtained from the eigenvalues of the adjacency matrix or its Jordan decomposition. In this paper, advantages and drawbacks of both approaches are examined. Potential challenges and improvements to graph spectral processing methods are considered as well as the generalization of graph processing techniques in the spectral domain. Its generalization to the time-frequency domain and other potential extensions of classical signal processing concepts to graph datasets are also considered. Lastly, it is given an overview of the compressive sensing on graphs concepts.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.