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We design a critically sampled compact-support biorthogonal transform for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets so as to remove one every two nodes in the filterbank downsampling operations, the design is based on a partition of the graph in connected subgraphs. Coarsening is achieved by defining one “supernode” for each subgraph and the edges for this...
We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first k eigenvectors of the similarity matrix' Laplacian, whose computation cost, even for sparse matrices, becomes prohibitive for large datasets. We show that we can estimate the spectral clustering distance matrix without...
Joint filtering of signals indexed on a graph consists in filtering not only the signal, but also the graph by an appropriate downsampling. Existing methods for filtering and downsampling graph signals approximate graphs as sums of bipartite graphs or use nodal domains of the Laplacian. Here, a different method is introduced, and is based on the partitioning in meaningful subgraphs of the graph itself,...
An extension of Empirical Mode Decomposition (EMD) is defined for graph signals. EMD is an algorithm that decomposes a signal in an addition of modes, in a local and data-driven manner. The proposed Graph EMD (GEMD) for graph signals is based on careful considerations on key points of EMD: defining the extrema, interpolation procedure, and the sifting process stopping criterion. Examples of GEMD are...
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