Questions tagged [spectral-analysis]

For questions related to Spectral analysis or Spectrum analysis is a analysis in terms of a spectrum of frequencies or related quantities such as energies, eigenvalues, etc. In specific areas it may refer to: Spectroscopy in chemistry and physics, a method of analyzing the properties of matter from their electromagnetic interactions.

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How does graph Fourier transform work when multiple signals present on each node?

Context: I was reading the following set of notes (page 83): here and it says: Thus, the Fourier transform of signal (or function) $ \mathbf{f} \in R^{|V|} $ on a graph can be computed as $$ \mathbf{...
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How does Chebyshev approximation of spectral convolution work?

I was reading the following paper: here. In it, it talks about spectral graph convolutions and says: We consider spectral convolutions on graphs defined as the multiplication of a signal $x \in R^N$ (...
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Are spectral approaches to Graph Neural Networks still considered?

I've been reading several papers and reviews about Graph Neural Networks, and I still feel a bit confused about the difference between the two approaches, and also if the spatial approaches have ...
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What exactly is the eigenspace of a graph (in spectral clustering)?

When we find the eigenvectors of a graph (say in the context of spectral clustering), what exactly is the vector space involved here? Of what vector space (or eigenspace) are we finding the ...
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Understanding the node information score in the paper "Hierarchical Graph Pooling with Structure Learning"

The paper Hierarchical Graph Pooling with Structure Learning (2019) introduces a distance measure between: a graph's node-representation matrix $\text{H}$, and an approximation of this constructed ...