When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum
When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum
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当斯莱皮安遇见费德勒：关注图谱
DOI：
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发表时间：
2017
影响因子：
3.9
通讯作者：
M. Preti
中科院分区：
文献类型：
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作者：
D. Ville;Robin Demesmaeker;M. Preti
复杂系统的研究极大地受益于图模型及其分析。特别是，图拉普拉斯算子的特征分解让全局组织的性质从局部相互作用中显现出来;例如，Fiedler向量具有最小的非零特征值，并且对于图聚类起关键作用。图形信号处理侧重于分析归因于图形节点的信号。同样，图拉普拉斯算子的特征分解对于定义图傅里叶变换和将传统的信号处理操作扩展到图是重要的。在这里，我们介绍了Slepian图信号的设计，通过最大限度地提高能量集中在一个预定义的子图给定的图形频谱带宽。我们建立了一个新的链接与经典的拉普拉斯嵌入和图聚类，这提供了一个意义本地化的图频率。
The study of complex systems greatly benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smallest nonzero eigenvalue and plays a key role for graph clustering. Graph signal processing focuses on the analysis of signals that are attributed to the graph nodes. Again, the eigendecomposition of the graph Laplacian is important to define the graph Fourier transform and extend conventional signal-processing operations to graphs. Here, we introduce the design of Slepian graph signals by maximizing energy concentration in a predefined subgraph given a graph spectral bandlimit. We establish a novel link with classical Laplacian embedding and graph clustering, which provides a meaning to localized graph frequencies.