p-Laplacian Regularization of Signals on Directed Graphs
Abstract: The graph Laplacian plays an important role in describing the structure of a graph signal from weights that measure the similarity between the vertices of the graph. In the literature, three definitions of the graph Laplacian have been considered for undirected graphs: the combinatorial, the normalized and the random-walk Laplacians. Moreover, a nonlinear extension of the Laplacian, called the p-Laplacian, has also been put forward for undirected graphs. In this paper, we propose several formulations for p-Laplacians on directed graphs directly inspired from the Laplacians on undirected graphs. Then, we consider the problem of p-Laplacian regularization of signals on directed graphs. Finally, we provide experimental results to illustrate the effect of the proposed p-laplacians on different types of graph signals.
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