About: Diffusion wavelets

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Diffusion wavelets are a fast multiscale framework for the analysis of functions on discrete (or discretized continuous) structures like graphs, manifolds, and point clouds in Euclidean space. Diffusion wavelets are an extension of classical wavelet theory from harmonic analysis. Unlike classical wavelets whose basis functions are predetermined, diffusion wavelets are adapted to the geometry of a given diffusion operator (e.g., a heat kernel or a random walk). Moreover, the diffusion wavelet basis functions are constructed by dilation using the dyadic powers (powers of two) of . These dyadic powers of diffusion over the space and propagate local relationships in the function throughout the space until they become global. And if the rank of higher powers of decrease (i.e., its spectrum d

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  • Diffusion wavelets are a fast multiscale framework for the analysis of functions on discrete (or discretized continuous) structures like graphs, manifolds, and point clouds in Euclidean space. Diffusion wavelets are an extension of classical wavelet theory from harmonic analysis. Unlike classical wavelets whose basis functions are predetermined, diffusion wavelets are adapted to the geometry of a given diffusion operator (e.g., a heat kernel or a random walk). Moreover, the diffusion wavelet basis functions are constructed by dilation using the dyadic powers (powers of two) of . These dyadic powers of diffusion over the space and propagate local relationships in the function throughout the space until they become global. And if the rank of higher powers of decrease (i.e., its spectrum decays), then these higher powers become compressible. From these decaying dyadic powers of comes a chain of decreasing subspaces. These subspaces are the scaling function approximation subspaces, and the differences in the subspace chain are the wavelet subspaces. Diffusion wavelets were first introduced in 2004 by Ronald Coifman and Mauro Maggioni at Yale University. (en)
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  • Diffusion wavelets are a fast multiscale framework for the analysis of functions on discrete (or discretized continuous) structures like graphs, manifolds, and point clouds in Euclidean space. Diffusion wavelets are an extension of classical wavelet theory from harmonic analysis. Unlike classical wavelets whose basis functions are predetermined, diffusion wavelets are adapted to the geometry of a given diffusion operator (e.g., a heat kernel or a random walk). Moreover, the diffusion wavelet basis functions are constructed by dilation using the dyadic powers (powers of two) of . These dyadic powers of diffusion over the space and propagate local relationships in the function throughout the space until they become global. And if the rank of higher powers of decrease (i.e., its spectrum d (en)
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  • Diffusion wavelets (en)
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