Technical Report: Using Laplacian Methods, RKHS Smoothing Splines and Bayesian Estimation as a framework for Regression on Graph and Graph Related Domains
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چکیده
1 Laplacian Methods: An Overview 2 1.1 De nition: The Laplacian operator of a Graph . . . . . . . . . . 2 1.2 Properties of the Laplacian and its Spectrum . . . . . . . . . . . 4 1.2.1 Spectrum of L and e L: Graph eigenvalues and eigenvectors: 4 1.2.2 Other interesting / useful properties of the normalized Laplacian (Chung): . . . . . . . . . . . . . . . . . . . . . 6 1.2.3 Laplacians of Weighted Graphs and Generalized Laplacians as Elliptic Operators . . . . . . . . . . . . . . . . . . 7 1.3 Other operators / Basis . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Calculus on Graphs: . . . . . . . . . . . . . . . . . . . . . . . . . 8
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