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Yuichi Tanaka  One of the best experts on this subject based on the ideXlab platform.

oversampled graph Laplacian Matrix for graph filter banks
IEEE Transactions on Signal Processing, 2014CoAuthors: Akie Sakiyama, Yuichi TanakaAbstract:We describe a method of oversampling signals defined on a weighted graph by using an oversampled graph Laplacian Matrix. The conventional method of using critically sampled graph filter banks has to decompose the original graph into bipartite subgraphs, and a transform has to be performed on each subgraph because of the spectral folding phenomenon caused by downsampling of graph signals. Therefore, the conventional method cannot always utilize all edges of the original graph in a single stage transformation. Our method is based on oversampling of the underlying graph itself, and it can append nodes and edges to the graph somewhat arbitrarily. We use this approach to make one oversampled bipartite graph that includes all edges of the original nonbipartite graph. We apply the oversampled graph with the critically sampled graph filter bank or the oversampled one for decomposing graph signals and show the performances on some experiments.

edge aware image graph expansion methods for oversampled graph Laplacian Matrix
International Conference on Image Processing, 2014CoAuthors: Akie Sakiyama, Yuichi TanakaAbstract:Graph signals can represent highdimensional data effectively and images can also be viewed as signals on weighted graphs by connecting the pixels with their neighboring ones. Recently, we proposed the graph oversampling methods for signal processing on graphs that appends nodes and links to the original graph to obtain an oversampled graph Laplacian Matrix. In this paper, we consider new oversampling methods of image graphs. By using the graph oversampling, we can make a bipartite graph that considers rectangular and diagonal connections simultaneously, while it cannot be realized by conventional critically sampled bipartite graphs. Furthermore, expanding the graphs according to the edge information enables us to decompose the image with the edgepreserving property. We perform the critically sampled graph filter bank on the oversampled graph and show that the proposed method outperforms other transforms, including the critically sampled graph filter banks and the graph Laplacian pyramid, in nonlinear approximation and denoising experiments.

ICIP  Edgeaware image graph expansion methods for oversampled graph Laplacian Matrix
2014 IEEE International Conference on Image Processing (ICIP), 2014CoAuthors: Akie Sakiyama, Yuichi TanakaAbstract:Graph signals can represent highdimensional data effectively and images can also be viewed as signals on weighted graphs by connecting the pixels with their neighboring ones. Recently, we proposed the graph oversampling methods for signal processing on graphs that appends nodes and links to the original graph to obtain an oversampled graph Laplacian Matrix. In this paper, we consider new oversampling methods of image graphs. By using the graph oversampling, we can make a bipartite graph that considers rectangular and diagonal connections simultaneously, while it cannot be realized by conventional critically sampled bipartite graphs. Furthermore, expanding the graphs according to the edge information enables us to decompose the image with the edgepreserving property. We perform the critically sampled graph filter bank on the oversampled graph and show that the proposed method outperforms other transforms, including the critically sampled graph filter banks and the graph Laplacian pyramid, in nonlinear approximation and denoising experiments.
Akie Sakiyama  One of the best experts on this subject based on the ideXlab platform.

oversampled graph Laplacian Matrix for graph filter banks
IEEE Transactions on Signal Processing, 2014CoAuthors: Akie Sakiyama, Yuichi TanakaAbstract:We describe a method of oversampling signals defined on a weighted graph by using an oversampled graph Laplacian Matrix. The conventional method of using critically sampled graph filter banks has to decompose the original graph into bipartite subgraphs, and a transform has to be performed on each subgraph because of the spectral folding phenomenon caused by downsampling of graph signals. Therefore, the conventional method cannot always utilize all edges of the original graph in a single stage transformation. Our method is based on oversampling of the underlying graph itself, and it can append nodes and edges to the graph somewhat arbitrarily. We use this approach to make one oversampled bipartite graph that includes all edges of the original nonbipartite graph. We apply the oversampled graph with the critically sampled graph filter bank or the oversampled one for decomposing graph signals and show the performances on some experiments.

edge aware image graph expansion methods for oversampled graph Laplacian Matrix
International Conference on Image Processing, 2014CoAuthors: Akie Sakiyama, Yuichi TanakaAbstract:Graph signals can represent highdimensional data effectively and images can also be viewed as signals on weighted graphs by connecting the pixels with their neighboring ones. Recently, we proposed the graph oversampling methods for signal processing on graphs that appends nodes and links to the original graph to obtain an oversampled graph Laplacian Matrix. In this paper, we consider new oversampling methods of image graphs. By using the graph oversampling, we can make a bipartite graph that considers rectangular and diagonal connections simultaneously, while it cannot be realized by conventional critically sampled bipartite graphs. Furthermore, expanding the graphs according to the edge information enables us to decompose the image with the edgepreserving property. We perform the critically sampled graph filter bank on the oversampled graph and show that the proposed method outperforms other transforms, including the critically sampled graph filter banks and the graph Laplacian pyramid, in nonlinear approximation and denoising experiments.

ICIP  Edgeaware image graph expansion methods for oversampled graph Laplacian Matrix
2014 IEEE International Conference on Image Processing (ICIP), 2014CoAuthors: Akie Sakiyama, Yuichi TanakaAbstract:Graph signals can represent highdimensional data effectively and images can also be viewed as signals on weighted graphs by connecting the pixels with their neighboring ones. Recently, we proposed the graph oversampling methods for signal processing on graphs that appends nodes and links to the original graph to obtain an oversampled graph Laplacian Matrix. In this paper, we consider new oversampling methods of image graphs. By using the graph oversampling, we can make a bipartite graph that considers rectangular and diagonal connections simultaneously, while it cannot be realized by conventional critically sampled bipartite graphs. Furthermore, expanding the graphs according to the edge information enables us to decompose the image with the edgepreserving property. We perform the critically sampled graph filter bank on the oversampled graph and show that the proposed method outperforms other transforms, including the critically sampled graph filter banks and the graph Laplacian pyramid, in nonlinear approximation and denoising experiments.
Masaki Aida  One of the best experts on this subject based on the ideXlab platform.

method for estimating the eigenvectors of a scaled Laplacian Matrix using the resonance of oscillation dynamics on networks
Advances in Social Networks Analysis and Mining, 2017CoAuthors: Satoshi Furutani, Chisa Takano, Masaki AidaAbstract:Spectral graph theory gives a useful approach to analyzing network structure based on the adjacency Matrix or the Laplacian Matrix that represents the network topology and link weights. However, in large scale and complex social networks, since it is difficult to know the network topology and link weights, we cannot determine the components of these matrices directly. To solve this problem, we consider a method for indirectly determining a Laplacian Matrix from its eigenvalues and eigenvectors. As the first step, our prior study proposed a method for estimating eigenvalues of a Laplacian Matrix by using the resonance of oscillation dynamics on networks with no a priori information about the network structure, and showed the effectiveness of this method. In this paper, we propose a method for estimating the eigenvectors of a Laplacian Matrix by once again using the resonance of oscillation dynamics on networks.

ASONAM  Method for Estimating the Eigenvectors of a Scaled Laplacian Matrix Using the Resonance of Oscillation Dynamics on Networks
Proceedings of the 2017 IEEE ACM International Conference on Advances in Social Networks Analysis and Mining 2017  ASONAM '17, 2017CoAuthors: Satoshi Furutani, Chisa Takano, Masaki AidaAbstract:Spectral graph theory gives a useful approach to analyzing network structure based on the adjacency Matrix or the Laplacian Matrix that represents the network topology and link weights. However, in large scale and complex social networks, since it is difficult to know the network topology and link weights, we cannot determine the components of these matrices directly. To solve this problem, we consider a method for indirectly determining a Laplacian Matrix from its eigenvalues and eigenvectors. As the first step, our prior study proposed a method for estimating eigenvalues of a Laplacian Matrix by using the resonance of oscillation dynamics on networks with no a priori information about the network structure, and showed the effectiveness of this method. In this paper, we propose a method for estimating the eigenvectors of a Laplacian Matrix by once again using the resonance of oscillation dynamics on networks.

proposal of the network resonance method for estimating eigenvalues of the scaled Laplacian Matrix
Intelligent Networking and Collaborative Systems, 2016CoAuthors: Satoshi Furutani, Chisa Takano, Masaki AidaAbstract:Eigenvalues of the Laplacian Matrix play an important role in characterizing structural and dynamical properties of networks. In the procedure for calculating eigenvalues of the Laplacian Matrix, we need to get the Laplacian Matrix that represents structures of the network. Since the actual structure of networks and the strength of links are difficult to know, it is difficult to determine elements of the Laplacian Matrix. To solve this problem, our previous study proposed a concept of the network resonance method, which is for estimating eigenvalues of the scaled Laplacian Matrix using resonance of oscillation dynamics on networks. This method does not need a priori information about the network structure. In this research, we investigate feasibility of the network resonance method, and show that the method can estimate eigenvalues of the scaled Laplacian Matrix of the entire network through observations of oscillation dynamics even if observable nodes are restricted to a part of network.

INCoS  Proposal of the Network Resonance Method for Estimating Eigenvalues of the Scaled Laplacian Matrix
2016 International Conference on Intelligent Networking and Collaborative Systems (INCoS), 2016CoAuthors: Satoshi Furutani, Chisa Takano, Masaki AidaAbstract:Eigenvalues of the Laplacian Matrix play an important role in characterizing structural and dynamical properties of networks. In the procedure for calculating eigenvalues of the Laplacian Matrix, we need to get the Laplacian Matrix that represents structures of the network. Since the actual structure of networks and the strength of links are difficult to know, it is difficult to determine elements of the Laplacian Matrix. To solve this problem, our previous study proposed a concept of the network resonance method, which is for estimating eigenvalues of the scaled Laplacian Matrix using resonance of oscillation dynamics on networks. This method does not need a priori information about the network structure. In this research, we investigate feasibility of the network resonance method, and show that the method can estimate eigenvalues of the scaled Laplacian Matrix of the entire network through observations of oscillation dynamics even if observable nodes are restricted to a part of network.
Dragan Nesic  One of the best experts on this subject based on the ideXlab platform.

corrigendum to on eigenvalues of Laplacian Matrix for a class of directed signed graphs linear algebra appl 523 2017 281 306
Linear Algebra and its Applications, 2017CoAuthors: Saeed Ahmadizadeh, Iman Shames, Samuel Martin, Dragan NesicAbstract:Abstract This note corrects an error in the results of Subsection 3.1 in authors' paper “On Eigenvalues of Laplacian Matrix for a Class of Directed Signed Graphs”, which appeared in Linear Algebra and its Applications 523 (2017), 281–306.

Corrigendum to “On eigenvalues of Laplacian Matrix for a class of directed signed graphs” [Linear Algebra Appl. 523 (2017) 281–306]
Linear Algebra and its Applications, 2017CoAuthors: Saeed Ahmadizadeh, Iman Shames, Samuel Martin, Dragan NesicAbstract:Abstract This note corrects an error in the results of Subsection 3.1 in authors' paper “On Eigenvalues of Laplacian Matrix for a Class of Directed Signed Graphs”, which appeared in Linear Algebra and its Applications 523 (2017), 281–306.

on eigenvalues of Laplacian Matrix for a class of directed signed graphs
Linear Algebra and its Applications, 2017CoAuthors: Saeed Ahmadizadeh, Iman Shames, Samuel Martin, Dragan NesicAbstract:Abstract The eigenvalues of the Laplacian Matrix for a class of directed graphs with both positive and negative weights are studied. The Laplacian Matrix naturally arises in a wide range of applications involving networks. First, a class of directed signed graphs is studied in which one pair of nodes (either connected or not) is perturbed with negative weights. A necessary and sufficient condition is proposed to attain the following objective for the perturbed graph: the real parts of the nonzero eigenvalues of its Laplacian Matrix are positive. Under certain assumption on the unperturbed graph, it is established that the objective is achieved if and only if the magnitudes of the added negative weights are smaller than an easily computable upper bound. This upper bound is shown to depend on the topology of the unperturbed graph. It is also pointed out that the obtained condition can be applied in a recursive manner to deal with multiple edges with negative weights. Secondly, for directed graphs, a subset of pairs of nodes are identified where if any of the pairs is connected by an edge with infinitesimal negative weight, the resulting Laplacian Matrix will have at least one eigenvalue with negative real part. Illustrative examples are presented to show the applicability of our results.

on eigenvalues of Laplacian Matrix for a class of directed signed graphs
arXiv: Optimization and Control, 2017CoAuthors: Saeed Ahmadizadeh, Iman Shames, Samuel Martin, Dragan NesicAbstract:The eigenvalues of the Laplacian Matrix for a class of directed graphs with both positive and negative weights are studied. First, a class of directed signed graphs is investigated in which one pair of nodes (either connected or not) is perturbed with negative weights. A necessary condition is proposed to attain the following objective for the perturbed graph: the real parts of the nonzero eigenvalues of its Laplacian Matrix are positive. A sufficient condition is also presented that ensures the aforementioned objective for the unperturbed graph. It is then highlighted the case where the condition becomes necessary and sufficient. Secondly, for directed graphs, a subset of pairs of nodes are identified where if any of the pairs is connected by an edge with infinitesimal negative weight, the resulting Laplacian Matrix will have at least one eigenvalue with negative real part. Illustrative examples are presented to show the applicability of our results.
Satoshi Furutani  One of the best experts on this subject based on the ideXlab platform.

method for estimating the eigenvectors of a scaled Laplacian Matrix using the resonance of oscillation dynamics on networks
Advances in Social Networks Analysis and Mining, 2017CoAuthors: Satoshi Furutani, Chisa Takano, Masaki AidaAbstract:Spectral graph theory gives a useful approach to analyzing network structure based on the adjacency Matrix or the Laplacian Matrix that represents the network topology and link weights. However, in large scale and complex social networks, since it is difficult to know the network topology and link weights, we cannot determine the components of these matrices directly. To solve this problem, we consider a method for indirectly determining a Laplacian Matrix from its eigenvalues and eigenvectors. As the first step, our prior study proposed a method for estimating eigenvalues of a Laplacian Matrix by using the resonance of oscillation dynamics on networks with no a priori information about the network structure, and showed the effectiveness of this method. In this paper, we propose a method for estimating the eigenvectors of a Laplacian Matrix by once again using the resonance of oscillation dynamics on networks.

ASONAM  Method for Estimating the Eigenvectors of a Scaled Laplacian Matrix Using the Resonance of Oscillation Dynamics on Networks
Proceedings of the 2017 IEEE ACM International Conference on Advances in Social Networks Analysis and Mining 2017  ASONAM '17, 2017CoAuthors: Satoshi Furutani, Chisa Takano, Masaki AidaAbstract:Spectral graph theory gives a useful approach to analyzing network structure based on the adjacency Matrix or the Laplacian Matrix that represents the network topology and link weights. However, in large scale and complex social networks, since it is difficult to know the network topology and link weights, we cannot determine the components of these matrices directly. To solve this problem, we consider a method for indirectly determining a Laplacian Matrix from its eigenvalues and eigenvectors. As the first step, our prior study proposed a method for estimating eigenvalues of a Laplacian Matrix by using the resonance of oscillation dynamics on networks with no a priori information about the network structure, and showed the effectiveness of this method. In this paper, we propose a method for estimating the eigenvectors of a Laplacian Matrix by once again using the resonance of oscillation dynamics on networks.

proposal of the network resonance method for estimating eigenvalues of the scaled Laplacian Matrix
Intelligent Networking and Collaborative Systems, 2016CoAuthors: Satoshi Furutani, Chisa Takano, Masaki AidaAbstract:Eigenvalues of the Laplacian Matrix play an important role in characterizing structural and dynamical properties of networks. In the procedure for calculating eigenvalues of the Laplacian Matrix, we need to get the Laplacian Matrix that represents structures of the network. Since the actual structure of networks and the strength of links are difficult to know, it is difficult to determine elements of the Laplacian Matrix. To solve this problem, our previous study proposed a concept of the network resonance method, which is for estimating eigenvalues of the scaled Laplacian Matrix using resonance of oscillation dynamics on networks. This method does not need a priori information about the network structure. In this research, we investigate feasibility of the network resonance method, and show that the method can estimate eigenvalues of the scaled Laplacian Matrix of the entire network through observations of oscillation dynamics even if observable nodes are restricted to a part of network.

INCoS  Proposal of the Network Resonance Method for Estimating Eigenvalues of the Scaled Laplacian Matrix
2016 International Conference on Intelligent Networking and Collaborative Systems (INCoS), 2016CoAuthors: Satoshi Furutani, Chisa Takano, Masaki AidaAbstract:Eigenvalues of the Laplacian Matrix play an important role in characterizing structural and dynamical properties of networks. In the procedure for calculating eigenvalues of the Laplacian Matrix, we need to get the Laplacian Matrix that represents structures of the network. Since the actual structure of networks and the strength of links are difficult to know, it is difficult to determine elements of the Laplacian Matrix. To solve this problem, our previous study proposed a concept of the network resonance method, which is for estimating eigenvalues of the scaled Laplacian Matrix using resonance of oscillation dynamics on networks. This method does not need a priori information about the network structure. In this research, we investigate feasibility of the network resonance method, and show that the method can estimate eigenvalues of the scaled Laplacian Matrix of the entire network through observations of oscillation dynamics even if observable nodes are restricted to a part of network.