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Learning functional brain connectivity is essential to the understanding of neurodegenerative diseases. In this paper, we introduce a novel graph regression model (GRM) which regards the imaging data as signals defined on a graph and optimizes the fitness between the graph and the data, with a sparsity level regularization. The proposed framework features a nice interpretation in terms of low-pass...
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed. Just as the classical result provides a tradeoff between signal localization in time and frequency, this result provides a fundamental tradeoff between a signal's...
The classical uncertainty principle provides a fundamental tradeoff in the localization of a signal in the time and frequency domains. In this paper we describe a similar tradeoff for signals defined on graphs. We describe the notions of “spread” in the graph and spectral domains, using the eigenvectors of the graph Laplacian as a surrogate Fourier basis. We then describe how to find signals that,...
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