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An Analysis of the Convergence of Graph Laplacians
"... Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs. We also i ..."
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Cited by 14 (0 self)
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Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs. We also
FRAMES AND FACTORIZATION OF GRAPH LAPLACIANS
, 2014
"... Using functions from electrical networks (graphs with resistors assigned to edges), we prove existence (with explicit formulas) of a canonical Parseval frame in the energy Hilbert space HE of a prescribed infinite (or finite) network. Outside degenerate cases, our Parseval frame is not an orthonorm ..."
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is not an orthonormal basis. We apply our frame to prove a number of explicit results: With our Parseval frame and related closable operators in HE we characterize the Friedrichs extension of the HE-graph Laplacian. We consider infinite connected network-graphs G = (V,E), V for vertices, and E for edges. To every
On the spectrum of the normalized graph Laplacian
, 2008
"... The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this spectrum under local and global operations like motif doubling, gra ..."
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Cited by 3 (0 self)
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The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this spectrum under local and global operations like motif doubling
A Combinatorial View of the Graph Laplacians
, 2005
"... Discussions about different graph Laplacian, mainly normalized and unnormalized versions of graph Laplacian, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on graph Laplacians investigated their convergence properties to La ..."
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Cited by 3 (1 self)
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Discussions about different graph Laplacian, mainly normalized and unnormalized versions of graph Laplacian, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on graph Laplacians investigated their convergence properties
Graph Laplacians and Topology
, 2008
"... Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same character-istics are determined by th ..."
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Cited by 15 (3 self)
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Laplace operators on metric graphs are considered. It is proven that for compact graphs the spectrum of the Laplace operator determines the total length, the number of connected components, and the Euler characteristic. For a class of non-compact graphs the same character-istics are determined
SIGNED GRAPH LAPLACIANS
, 2002
"... This paper uses chain complexes of based, finitely-generated Z-modules to study the Laplacians of signed plane graphs. We extend a theorem of Lien and Watkins [6] regarding the Goeritz equivalence of the signed Laplacians of a signed plane graph and its dual by showing that it is possible to use o ..."
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This paper uses chain complexes of based, finitely-generated Z-modules to study the Laplacians of signed plane graphs. We extend a theorem of Lien and Watkins [6] regarding the Goeritz equivalence of the signed Laplacians of a signed plane graph and its dual by showing that it is possible to use
Kernels of directed graph Laplacians
- The Electronic Journal of Combinatorics
"... Abstract. Let G denote a directed graph with adjacency matrix Q and in-degree matrix D. We consider the Kirchhoff matrix L = D−Q, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity of the eigenvalue 0 equals the numbe ..."
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Cited by 2 (0 self)
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Abstract. Let G denote a directed graph with adjacency matrix Q and in-degree matrix D. We consider the Kirchhoff matrix L = D−Q, sometimes referred to as the directed Laplacian. A classical result of Kirchhoff asserts that when G is undirected, the multiplicity of the eigenvalue 0 equals
Bayesian Regularization via Graph Laplacian
, 2010
"... Regularization plays a critical role in modern statistical research, especially in high dimensional variable selection problems. Existing Bayesian methods usually assume independence between variables a priori. In this article, we propose a novel Bayesian approach, which explicitly models the depend ..."
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Cited by 3 (0 self)
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the dependence structure through a graph Laplacian matrix. We also generalize the graph Laplacian to allow both positively and negatively correlated variables. A prior distribution for the graph Laplacian is then proposed, which allows conjugacy and thereby greatly simplifies the computation. We show
Results 1 - 10
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1,447
