Journal
IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
Volume 11, Issue 6, Pages 796-811Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/JSTSP.2017.2726979
Keywords
Clustering; graph Fourier transform; graph signal processing; total variation
Categories
Funding
- TROPIC Project [ICT-318784]
- Fondazione Cassa di Risparmio di Perugia
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The analysis of signals defined over a graph is relevant in many applications, such as social and economic networks, big data or biological networks, and so on. A key tool for analyzing these signals is the so-called graph Fourier transform (GFT). Alternative definitions of GFT have been suggested in the literature, based on the eigen-decomposition of either the graph Laplacian or adjacency matrix. In this paper, we address the general case of directed graphs and we propose an alternative approach that builds the graph Fourier basis as the set of orthonormal vectors that minimize a continuous extension of the graph cut size, known as the Lovasz extension. To cope with the nonconvexity of the problem, we propose two alternative iterative optimization methods, properly devised for handling orthogonality constraints. Finally, we extend the method to minimize a continuous relaxation of the balanced cut size. The formulated problem is again nonconvex, and we propose an efficient solution method based on an explicit-implicit gradient algorithm.
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