首页> 外文期刊>Applied and Computational Harmonic Analysis >Wavelets on graphs via spectral graph theory
【24h】

Wavelets on graphs via spectral graph theory

机译:通过谱图理论在图上的小波

获取原文
获取原文并翻译 | 示例

摘要

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian C. Given a wavelet generating kernel g and a scale parameter t, we define the scaled wavelet operator T'g = g(tC). The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on g, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing C. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains.
机译:我们提出了一种新颖的方法来构造在任意有限加权图的顶点上定义的函数的小波变换。我们的方法基于使用傅立叶域的图类似物定义缩放比例,即离散图拉普拉斯C的频谱分解。给定一个生成内核g和比例参数t的小波,我们定义了缩放的小波算子T'g = g (tC)。然后通过将这个算子定位到一个指标函数上来对其局部化,从而形成频谱图小波。根据g的可容许性条件,此过程定义了一个可逆变换。我们探索小波在精细尺度范围内的定位特性。此外,我们提出了一种快速的Chebyshev多项式逼近算法来计算变换,从而避免了对角C的需要。我们通过对应于各种不同问题域的图上的小波示例,突出了变换的潜在应用。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号