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An Analysis of the Convergence of Graph Laplacians
"... Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a wellbehaved 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 wellbehaved 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
"... Abstract. 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 ..."
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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 HEgraph Laplacian. We consider infinite connected networkgraphs 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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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 semisupervised learning. Previous research on graph Laplacians investigated their convergence properties to La ..."
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Cited by 2 (0 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 semisupervised 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 noncompact graphs the same characteristics 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 noncompact graphs the same characteristics are determined
SIGNED GRAPH LAPLACIANS
"... Abstract. This paper uses chain complexes of based, finitelygenerated Zmodules 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 ..."
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Abstract. This paper uses chain complexes of based, finitelygenerated Zmodules 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
Kernels of Directed Graph Laplacians
"... Abstract. Let G denote a directed graph with adjacency matrix Q and indegree 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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Abstract. Let G denote a directed graph with adjacency matrix Q and indegree 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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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
GRAPH LAPLACIAN FOR INTERACTIVE IMAGE RETRIEVAL
"... Interactive image search or relevance feedback is the process which helps a user refining his query and finding difficult target categories. This consists in a stepbystep labeling of a very small fraction of an image database and iteratively refining a decision rule using both the labeled and unla ..."
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Cited by 3 (2 self)
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and unlabeled data. Training of this decision rule is referred to as transductive learning. Our work is an original approach for relevance feedback based on Graph Laplacian. We introduce a new Graph Laplacian which makes it possible to robustly learn the embedding of the manifold enclosing the dataset via a
Results 1  10
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27,843