A fast algorithm for vertex-frequency representations of signals on graphs

TL;DR: The results indicate that the proposed method can diagnose the bearing faults with different types and degrees effectively, and the vertex domain index TVHVG is superior to some classical time domain indexes in distinguishing the different states of rolling bearings.

TL;DR: Traditional signal processing often does not offer reliable tools and algorithms to analyze new data types, especially true for cases where networks (e.g., the strength of connections), or signals on vertices, have properties that change over the network.

TL;DR: A comprehensive account of the relation of general vertex- frequencies analysis with classical time-frequency analysis is presented, an important but missing link for more advanced applications of graph signal processing.

TL;DR: Local smoothness, an important parameter of vertex-varying graph signals, is introduced and defined in this paper and basic properties of this parameter are given.

TL;DR: Eigenvalues and the Laplacian of a graph Isoperimetric problems Diameters and eigenvalues Paths, flows, and routing Eigen values and quasi-randomness

TL;DR: The field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process high-dimensional data on graphs as discussed by the authors, which are the analogs to the classical frequency domain and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs.

TL;DR: The S transform is shown to have some desirable characteristics that are absent in the continuous wavelet transform, and provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum.