Topic
Spectral graph theory
About: Spectral graph theory is a research topic. Over the lifetime, 1334 publications have been published within this topic receiving 77373 citations.
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TL;DR: In this article , a neighborhood degree sum based matrix is proposed as a modification of classical adjacency matrix, and a graph energy and its Estrada index are introduced, and their role as a molecular structural descriptor in chemical graph theory is investigated.
3 citations
12 Nov 2007
TL;DR: This paper develops a classification algorithm in the framework of spectral graph theory where the underlying manifold of a high dimensional data set is described by a graph and interprets this approach as a regularized version of the Cheeger constant based classifier that was introduced recently.
Abstract: This paper develops a classification algorithm in the framework of spectral graph theory where the underlying manifold of a high dimensional data set is described by a graph. The classification on the data is performed on the graph. The classifier optimizes an objective functional that combines prior information with the Cheeger constant. We interpret this approach as a regularized version of the Cheeger constant based classifier that we introduced recently. Our derivation shows that Cheeger regularization removes noise like a Laplacian based classifier but preserves better sharp boundaries needed for class separation. Experimental results show good performance of our proposed approach for classification applications.
3 citations
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TL;DR: In this article, the connection of separating finctions with locally scalar representations of graphs and spectral graph theory is investigated, and the connection between spectral graph theories and locally scalars is discussed.
Abstract: In this article we consider the connection of separating finctions $\rho_r$ with locally scalar representations of graphs and with spectral graph theory.
3 citations
11 Apr 2005
TL;DR: The main advantage of the new graph representation based on the path-weighted adjacency matrix is that it both preserves partition consistency and shows improved stability to structural error.
Abstract: In this paper we develop a new graph representation based on the path-weighted adjacency matrix for characterising global graph structure. The representation is derived from the heat-kernel of the graph. We investigate whether the path-weighted adjacency matrix can be used for the problem of graph partitioning. Here we demonstrate that the method out-performs the use of the adjacency matrix. The main advantage of the new method is that it both preserves partition consistency and shows improved stability to structural error.
3 citations
01 Nov 2019
TL;DR: A bipartite graph learning framework lying at the integration of Gaussian graphical models (GGM) and spectral graph theory is introduced and numerical experiments demonstrate the effectiveness of the proposed algorithm over existing state-of-the-art methods.
Abstract: Learning a graph with a bipartite structure IS essential for interpretability and identification of the relationships among data in numerous applications including document clustering, network medicine, etc. To learn a bipartite structure is equivalent to a max-cut problem, which is an NP-hard problem. Existing methods employ a two-stage procedure and are computationally demanding as they require solving semi-definite programming. In this paper, we introduce a bipartite graph learning framework lying at the integration of Gaussian graphical models (GGM) and spectral graph theory. The proposed algorithms are provably convergent and practically amenable for large-scale unsupervised graph learning tasks. Numerical experiments demonstrate the effectiveness of the proposed algorithm over existing state-of-the-art methods. An R package containing code for all the experimental results is available at https://cran.r-project.org/package=spectralGraphTopology.
3 citations