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用于周期图频率分析的随机游走拉普拉斯算子

Random-Walk Laplacian for Frequency Analysis in Periodic Graphs.

作者信息

Boukrab Rachid, Pagès-Zamora Alba

机构信息

SPCOM Group, Universitat Politècnica de Catalunya-Barcelona Tech, 08034 Barcelona, Spain.

出版信息

Sensors (Basel). 2021 Feb 11;21(4):1275. doi: 10.3390/s21041275.

DOI:10.3390/s21041275
PMID:33670095
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7916899/
Abstract

This paper presents the benefits of using the random-walk normalized Laplacian matrix as a graph-shift operator and defines the frequencies of a graph by the eigenvalues of this matrix. A criterion to order these frequencies is proposed based on the Euclidean distance between a graph signal and its shifted version with the transition matrix as shift operator. Further, the frequencies of a periodic graph built through the repeated concatenation of a basic graph are studied. We show that when a graph is replicated, the graph frequency domain is interpolated by an upsampling factor equal to the number of replicas of the basic graph, similarly to the effect of zero-padding in digital signal processing.

摘要

本文介绍了使用随机游走归一化拉普拉斯矩阵作为图移位算子的好处，并通过该矩阵的特征值定义图的频率。基于图信号与其以转移矩阵为移位算子的移位版本之间的欧几里得距离，提出了对这些频率进行排序的准则。此外，还研究了通过基本图的重复拼接构建的周期图的频率。我们表明，当一个图被复制时，图频域会通过一个等于基本图副本数量的上采样因子进行插值，这类似于数字信号处理中的零填充效果。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/ac2028535075/sensors-21-01275-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/c3e37729bbaa/sensors-21-01275-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/da5fb55f643b/sensors-21-01275-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/118cf9a78806/sensors-21-01275-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/ad1f07304d16/sensors-21-01275-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/377899c8c00f/sensors-21-01275-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/d468dbe86654/sensors-21-01275-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/ac2028535075/sensors-21-01275-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/c3e37729bbaa/sensors-21-01275-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/da5fb55f643b/sensors-21-01275-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/118cf9a78806/sensors-21-01275-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/ad1f07304d16/sensors-21-01275-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/377899c8c00f/sensors-21-01275-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/d468dbe86654/sensors-21-01275-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1f6/7916899/ac2028535075/sensors-21-01275-g007.jpg

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