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http://hdl.handle.net/10985/15022
Classification des Signaux sur Graphes par Mesures Spectrales Algébriques
BAY-AHMED, Hadj-Ahmed; BOUDRAA, Abdel; DARE-EMZIVAT, Delphine; PREAUX, Yves
La notion de mesure de similarité est très importante dans de nombreux domaines tels que l’apprentissage statistique, la fouille de données ou les sciences cognitives. Dans cet article, nous nous intéressons à la similarité des signaux sur graphes et nous proposons deux nouvelles mesures de similarité spectrales, compactes et efficaces, basées sur la comparaison des spectres propres des graphes, appelées Covariance Spectrale (CS) et Similarité Spectrale Conjointe (SSC). Combinées à un noyau de diffusion sur graphe, ces nouvelles mesures ont permis d’obtenir des performances de classification excellentes sur des données moléculaires réelles, montrant ainsi la pertinence des valeurs propres pour la classification des signaux sur graphes. Les résultats sont comparés à ceux obtenus par les algorithmes k-NN et SVM appliqués sur des graphes projetés dans un espace vectoriel.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/150222017-01-01T00:00:00ZBAY-AHMED, Hadj-AhmedBOUDRAA, AbdelDARE-EMZIVAT, DelphinePREAUX, YvesLa notion de mesure de similarité est très importante dans de nombreux domaines tels que l’apprentissage statistique, la fouille de données ou les sciences cognitives. Dans cet article, nous nous intéressons à la similarité des signaux sur graphes et nous proposons deux nouvelles mesures de similarité spectrales, compactes et efficaces, basées sur la comparaison des spectres propres des graphes, appelées Covariance Spectrale (CS) et Similarité Spectrale Conjointe (SSC). Combinées à un noyau de diffusion sur graphe, ces nouvelles mesures ont permis d’obtenir des performances de classification excellentes sur des données moléculaires réelles, montrant ainsi la pertinence des valeurs propres pour la classification des signaux sur graphes. Les résultats sont comparés à ceux obtenus par les algorithmes k-NN et SVM appliqués sur des graphes projetés dans un espace vectoriel.Graph Signals Classification Using Total Variation and Graph Energy Informations
http://hdl.handle.net/10985/15078
Graph Signals Classification Using Total Variation and Graph Energy Informations
BAY-AHMED, Hadj-Ahmed; DARE-EMZIVAT, Delphine; BOUDRAA, Abdel
In this work, we consider the problem of graph signals classification. We investigate the relevance of two attributes, namely the total variation (TV) and the graph energy (GE) for graph signals classification. The TV is a compact and informative attribute for efficient graph discrimination. The GE information is used to quantify the complexity of the graph structure which is a pertinent information. Based on these two attributes, three similarity measures are introduced. Key of these measures is their low complexity. The effectiveness of these similarity measures are illustrated on five data sets and the results compared to those of five kernel-based methods of the literature. We report results on computation runtime and classification accuracy on graph benchmark data sets. The obtained results confirm the effectiveness of the proposed methods in terms of CPU runtime and of classification accuracy. These findings also show the potential of TV and GE informations for graph signals classification.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/150782017-01-01T00:00:00ZBAY-AHMED, Hadj-AhmedDARE-EMZIVAT, DelphineBOUDRAA, AbdelIn this work, we consider the problem of graph signals classification. We investigate the relevance of two attributes, namely the total variation (TV) and the graph energy (GE) for graph signals classification. The TV is a compact and informative attribute for efficient graph discrimination. The GE information is used to quantify the complexity of the graph structure which is a pertinent information. Based on these two attributes, three similarity measures are introduced. Key of these measures is their low complexity. The effectiveness of these similarity measures are illustrated on five data sets and the results compared to those of five kernel-based methods of the literature. We report results on computation runtime and classification accuracy on graph benchmark data sets. The obtained results confirm the effectiveness of the proposed methods in terms of CPU runtime and of classification accuracy. These findings also show the potential of TV and GE informations for graph signals classification.A Joint Spectral Similarity Measure for Graphs Classification
http://hdl.handle.net/10985/15019
A Joint Spectral Similarity Measure for Graphs Classification
BAY-AHMED, Hadj-Ahmed; BOUDRAA, Abdel; DARE-EMZIVAT, Delphine
In spite of the simple linear relationship between the adjacency A and the Laplacian L matrices, L=D-A where D is the degrees matrix, these matrices seem to reveal informations about the graph in different ways, where it appears that some details are detected only by one of them, as in the case of cospectral graphs. Based on this observation, a new graphs similarity measure, referred to as joint spectral similarity (JSS) incorporating both spectral information from A and L is introduced. A weighting parameter to control the relative influence of each matrix is used. Furthermore, to highlight the overlapping and the unequal contributions of these matrices for graph representation, they are compared in terms of the so called Von Neumann entropy (VN), connectivity and complexity measures. The graph is viewed as a quantum system and thus, the calculated VN entropy of its perturbed density matrix emphasizes the overlapping in terms of information quantity of A and L matrices. The impact of matrix representation is strongly illustrated by classification findings on real and conceptual graphs based on JSS measure. The obtained results show the effectiveness of the JSS measure in terms of graph classification accuracies and also highlight varying information overlapping rates of A and L, and point out their different ways in recovering structural information of the graph.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/150192019-01-01T00:00:00ZBAY-AHMED, Hadj-AhmedBOUDRAA, AbdelDARE-EMZIVAT, DelphineIn spite of the simple linear relationship between the adjacency A and the Laplacian L matrices, L=D-A where D is the degrees matrix, these matrices seem to reveal informations about the graph in different ways, where it appears that some details are detected only by one of them, as in the case of cospectral graphs. Based on this observation, a new graphs similarity measure, referred to as joint spectral similarity (JSS) incorporating both spectral information from A and L is introduced. A weighting parameter to control the relative influence of each matrix is used. Furthermore, to highlight the overlapping and the unequal contributions of these matrices for graph representation, they are compared in terms of the so called Von Neumann entropy (VN), connectivity and complexity measures. The graph is viewed as a quantum system and thus, the calculated VN entropy of its perturbed density matrix emphasizes the overlapping in terms of information quantity of A and L matrices. The impact of matrix representation is strongly illustrated by classification findings on real and conceptual graphs based on JSS measure. The obtained results show the effectiveness of the JSS measure in terms of graph classification accuracies and also highlight varying information overlapping rates of A and L, and point out their different ways in recovering structural information of the graph.On signal denoising by EMD in the frequency domain
http://hdl.handle.net/10985/10293
On signal denoising by EMD in the frequency domain
BAY-AHMED, Hadj-Ahmed; KOMATY, Ali; DARE, Delphine; BOUDRAA, Abdel-Ouahab
In this work a new denoising scheme based on the empirical mode decomposition associated with a frequency analysis is introduced. Compared to classical approaches where the extracted modes are thresholded in time domain, in the proposed strategy the thresholding is done in the frequency domain. Each mode is divided into blocks of equal length where the frequency content of each one is analyzed. Relevant modes are identified using an energy and a frequency thresholds obtained by training. The denoised signal is obtained by the superposition of the thresholded modes. The effectiveness of the proposed scheme is illustrated on synthetic and real signals and the results compared to those of methods reported recently.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/102932015-01-01T00:00:00ZBAY-AHMED, Hadj-AhmedKOMATY, AliDARE, DelphineBOUDRAA, Abdel-OuahabIn this work a new denoising scheme based on the empirical mode decomposition associated with a frequency analysis is introduced. Compared to classical approaches where the extracted modes are thresholded in time domain, in the proposed strategy the thresholding is done in the frequency domain. Each mode is divided into blocks of equal length where the frequency content of each one is analyzed. Relevant modes are identified using an energy and a frequency thresholds obtained by training. The denoised signal is obtained by the superposition of the thresholded modes. The effectiveness of the proposed scheme is illustrated on synthetic and real signals and the results compared to those of methods reported recently.Analyse de la vulnérabilité d’un réseau via la mesure de l’entropie de Von Neumann.
http://hdl.handle.net/10985/23425
Analyse de la vulnérabilité d’un réseau via la mesure de l’entropie de Von Neumann.
BAY-AHMED, Hadj-Ahmed; DARE-EMZIVAT, Delphine; BOUDRAA, Abdel-Ouahab
In this work, we present a new strategy for measuring the vulnerability of network connections, modeled by a graph, via the
variations of the Von Neumann entropy of the density matrix associated to this graph, this one being seen as a quantum system. We show that the change of the weight of an edge impacts the resulting Von Neumann entropy, which includes not only the intensity of the perturbation induced but also a quantity related to the degrees of the nodes adjacent to the perturbed edge. An algorithm based on this strategy has been developed. The obtained results confirm the relevance of this new measure. Our algorithm highlights the discontinuities that could appear in the structure by proposing a hierarchical decomposition into subgraphs relative to the degrees of vulnerability of the edges. The obtained map guarantees a better network security.
Sun, 01 Sep 2019 00:00:00 GMThttp://hdl.handle.net/10985/234252019-09-01T00:00:00ZBAY-AHMED, Hadj-AhmedDARE-EMZIVAT, DelphineBOUDRAA, Abdel-OuahabIn this work, we present a new strategy for measuring the vulnerability of network connections, modeled by a graph, via the
variations of the Von Neumann entropy of the density matrix associated to this graph, this one being seen as a quantum system. We show that the change of the weight of an edge impacts the resulting Von Neumann entropy, which includes not only the intensity of the perturbation induced but also a quantity related to the degrees of the nodes adjacent to the perturbed edge. An algorithm based on this strategy has been developed. The obtained results confirm the relevance of this new measure. Our algorithm highlights the discontinuities that could appear in the structure by proposing a hierarchical decomposition into subgraphs relative to the degrees of vulnerability of the edges. The obtained map guarantees a better network security.