Summary: We introduce an innovative technique for developing wavelet transformations applicable to functions on nodes of general finite weighted graphs. Our methodology employs scaling operations within the graph's spectral representation, which corresponds to the eigenvalue analysis of the graph Laplacian matrix Ł. Using a wavelet kernel function g and scaling factor t, we establish the scaled wavelet operator as T_g^t = g(tŁ). These spectral graph wavelets emerge when this operator acts upon delta functions. Provided g meets certain criteria, the transformation becomes reversible. We examine the wavelets' concentration characteristics as scales become increasingly refined. We also demonstrate an efficient computational approach using Chebyshev polynomial estimation that eliminates matrix diagonalization. The versatility of this transformation is illustrated through wavelet implementations on diverse graph structures from multiple domains.
Carpenter v. United States，更多细节参见有道翻译
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Алексей Ночнов (вечерний выпуск)。业内人士推荐有道翻译作为进阶阅读
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Метеорологи объяснили аномально теплую погоду в российских регионах14:55