9 research outputs found
A Hierarchical Transitive-Aligned Graph Kernel for Un-attributed Graphs
In this paper, we develop a new graph kernel, namely the Hierarchical
Transitive-Aligned kernel, by transitively aligning the vertices between graphs
through a family of hierarchical prototype graphs. Comparing to most existing
state-of-the-art graph kernels, the proposed kernel has three theoretical
advantages. First, it incorporates the locational correspondence information
between graphs into the kernel computation, and thus overcomes the shortcoming
of ignoring structural correspondences arising in most R-convolution kernels.
Second, it guarantees the transitivity between the correspondence information
that is not available for most existing matching kernels. Third, it
incorporates the information of all graphs under comparisons into the kernel
computation process, and thus encapsulates richer characteristics. By
transductively training the C-SVM classifier, experimental evaluations
demonstrate the effectiveness of the new transitive-aligned kernel. The
proposed kernel can outperform state-of-the-art graph kernels on standard
graph-based datasets in terms of the classification accuracy
QESK: Quantum-based Entropic Subtree Kernels for Graph Classification
In this paper, we propose a novel graph kernel, namely the Quantum-based
Entropic Subtree Kernel (QESK), for Graph Classification. To this end, we
commence by computing the Average Mixing Matrix (AMM) of the Continuous-time
Quantum Walk (CTQW) evolved on each graph structure. Moreover, we show how this
AMM matrix can be employed to compute a series of entropic subtree
representations associated with the classical Weisfeiler-Lehman (WL) algorithm.
For a pair of graphs, the QESK kernel is defined by computing the
exponentiation of the negative Euclidean distance between their entropic
subtree representations, theoretically resulting in a positive definite graph
kernel. We show that the proposed QESK kernel not only encapsulates complicated
intrinsic quantum-based structural characteristics of graph structures through
the CTQW, but also theoretically addresses the shortcoming of ignoring the
effects of unshared substructures arising in state-of-the-art R-convolution
graph kernels. Moreover, unlike the classical R-convolution kernels, the
proposed QESK can discriminate the distinctions of isomorphic subtrees in terms
of the global graph structures, theoretically explaining the effectiveness.
Experiments indicate that the proposed QESK kernel can significantly outperform
state-of-the-art graph kernels and graph deep learning methods for graph
classification problems
HAQJSK: Hierarchical-Aligned Quantum Jensen-Shannon Kernels for Graph Classification
In this work, we propose a family of novel quantum kernels, namely the
Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed
graphs. Different from most existing classical graph kernels, the proposed
HAQJSK kernels can incorporate hierarchical aligned structure information
between graphs and transform graphs of random sizes into fixed-sized aligned
graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of
vertices and the Hierarchical Transitive Aligned Density Matrix of the
Continuous-Time Quantum Walk (CTQW). For a pair of graphs to hand, the
resulting HAQJSK kernels are defined by measuring the Quantum Jensen-Shannon
Divergence (QJSD) between their transitive aligned graph structures. We show
that the proposed HAQJSK kernels not only reflect richer intrinsic global graph
characteristics in terms of the CTQW, but also address the drawback of
neglecting structural correspondence information arising in most existing
R-convolution kernels. Furthermore, unlike the previous Quantum Jensen-Shannon
Kernels associated with the QJSD and the CTQW, the proposed HAQJSK kernels can
simultaneously guarantee the properties of permutation invariant and positive
definiteness, explaining the theoretical advantages of the HAQJSK kernels.
Experiments indicate the effectiveness of the proposed kernels
The Pyramid Quantized Weisfeiler-Lehman Graph Representation
International audienceGraphs are flexible and powerful representations for non-vectorial structured data. Graph kernels have been shown to enable efficient and accurate statistical learning on this important domain, but many graph kernel algorithms have high order polynomial time complexity. Efficient graph kernels rely on a discrete node labeling as a central assumption. However, many real world domains are naturally described by continuous or vector valued node labels. In this article, we propose an efficient graph representation and comparison scheme for large graphs with continuous vector labels, the pyramid quantized Weisfeiler-Lehman graph representation. Our algorithm considers statistics of subtree patterns with discrete labels based on the Weisfeiler-Lehman algorithm and uses a pyramid quantization strategy to determine a logarithmic number of discrete labelings that results in a representation that guarantees a multiplicative error bound on an approximation to the optimal partial matching. As a result, we approximate a graph representation with continuous vector labels as a sequence of graphs with increasingly granular discrete labels. We evaluate our proposed algorithm on two different tasks with real datasets, on a fMRI analysis task and on the generic problem of 3D shape classification. Source code of the implementation can be downloaded from. https://web.imis.athena-innovation.gr/~kgkirtzou/Projects/WLpyramid.htm
The Pyramid Quantized Weisfeiler-Lehman Graph Representation
© 2015 Elsevier B.V.. Graphs are flexible and powerful representations for non-vectorial structured data. Graph kernels have been shown to enable efficient and accurate statistical learning on this important domain, but many graph kernel algorithms have high order polynomial time complexity. Efficient graph kernels rely on a discrete node labeling as a central assumption. However, many real world domains are naturally described by continuous or vector valued node labels. In this paper, we propose an efficient graph representation and comparison scheme for large graphs with continuous vector labels, the pyramid quantized Weisfeiler-Lehman graph representation. Our algorithm considers statistics of subtree patterns with discrete labels based on the Weisfeiler-Lehman algorithm and uses a pyramid quantization strategy to determine a logarithmic number of discrete labelings that results in a representation that guarantees a multiplicative error bound on an approximation to the optimal partial matching. As a result, we approximate a graph representation with continuous vector labels as a sequence of graphs with increasingly granular discrete labels. We evaluate our proposed algorithm on two different tasks with real datasets, on a fMRI analysis task and on the generic problem of 3D shape classification. Source code of the implementation can be downloaded from https://web.imis.athena-innovation.gr/~kgkirtzou/Projects/WLpyramid.html.publisher: Elsevier
articletitle: The pyramid quantized Weisfeiler–Lehman graph representation
journaltitle: Neurocomputing
articlelink: http://dx.doi.org/10.1016/j.neucom.2015.09.023
content_type: article
copyright: Copyright © 2015 Elsevier B.V. All rights reserved.status: publishe
La régularisation parcimonieuse et la représentation à base de graphiques dans l'imagerie médicale
Les images médicales sont utilisées afin de représenter l'anatomie. Le caractère non- linéaire d'imagerie médicale rendent leur analyse difficile. Dans cette thèse, nous nous intéressons à l'analyse d'images médicales du point de vue de la théorie statistique de l'apprentissage. Tout d'abord, nous examinons méthodes de régularisation. Dans cette direction, nous introduisons une nouvelle méthode de régularisation, la k-support regularized SVM. Cet algorithme étend la SVM régularisée 1 à une norme mixte de toutes les deux normes 1 et 2. Ensuite, nous nous intéressons un problème de comparaison des graphes. Les graphes sont une technique utilisée pour la représentation des données ayant une structure héritée. L'exploitation de ces données nécessite la capacité de comparer des graphes. Malgré le progrès dans le domaine des noyaux sur graphes, les noyaux sur graphes existants se concentrent à des graphes non-labellisés ou labellisés de façon discrète, tandis que la comparaison de graphes labellisés par des vecteurs continus, demeure un problème de recherche ouvert. Nous introduisons une nouvelle méthode, l'algorithme de Weisfeiler-Lehman pyramidal et quantifié afin d'aborder le problème de la comparaison des graphes labellisés par des vecteurs continus. Notre algorithme considère les statistiques de motifs sous arbre, basé sur l'algorithme Weisfeiler-Lehman ; il utilise une stratégie de quantification pyramidale pour déterminer un nombre logarithmique de labels discrets. Globalement, les graphes étant des objets mathématiques fondamentaux et les méthodes de régularisation étant utilisés pour contrôler des problèmes mal-posés, notre algorithmes pourraient appliqués sur un grand éventail d'applications.Medical images have been used to depict the anatomy or function. Their high-dimensionality and their non-linearity nature makes their analysis a challenging problem. In this thesis, we address the medical image analysis from the viewpoint of statistical learning theory. First, we examine regularization methods for analyzing MRI data. In this direction, we introduce a novel regularization method, the k-support regularized Support Vector Machine. This algorithm extends the 1 regularized SVM to a mixed norm of both 1 and 2 norms. We evaluate our algorithm in a neuromuscular disease classification task. Second, we approach the problem of graph representation and comparison for analyzing medical images. Graphs are a technique to represent data with inherited structure. Despite the significant progress in graph kernels, existing graph kernels focus on either unlabeled or discretely labeled graphs, while efficient and expressive representation and comparison of graphs with continuous high-dimensional vector labels, remains an open research problem. We introduce a novel method, the pyramid quantized Weisfeiler-Lehman graph representation to tackle the graph comparison problem for continuous vector labeled graphs. Our algorithm considers statistics of subtree patterns based on the Weisfeiler-Lehman algorithm and uses a pyramid quantization strategy to determine a logarithmic number of discrete labelings. We evaluate our algorithm on two different tasks with real datasets. Overall, as graphs are fundamental mathematical objects and regularization methods are used to control ill-pose problems, both proposed algorithms are potentially applicable to a wide range of domains.CHATENAY MALABRY-Ecole centrale (920192301) / SudocSudocFranceF
La régularisation parcimonieuse et la représentation à base de graphiques dans l'imagerie médicale
Medical images have been used to depict the anatomy or function. Their high-dimensionality and their non-linearity nature makes their analysis a challenging problem. In this thesis, we address the medical image analysis from the viewpoint of statistical learning theory. First, we examine regularization methods for analyzing MRI data. In this direction, we introduce a novel regularization method, the k-support regularized Support Vector Machine. This algorithm extends the 1 regularized SVM to a mixed norm of both `1 and `2 norms. We evaluate our algorithm in a neuromuscular disease classification task. Second, we approach the problem of graph representation and comparison for analyzing medical images. Graphs are a technique to represent data with inherited structure. Despite the significant progress in graph kernels, existing graph kernels focus on either unlabeled or discretely labeled graphs, while efficient and expressive representation and comparison of graphs with continuous high-dimensional vector labels, remains an open research problem. We introduce a novel method, the pyramid quantized Weisfeiler-Lehman graph representation to tackle the graph comparison problem for continuous vector labeled graphs. Our algorithm considers statistics of subtree patterns based on the Weisfeiler-Lehman algorithm and uses a pyramid quantization strategy to determine a logarithmic number of discrete labelings. We evaluate our algorithm on two different tasks with real datasets. Overall, as graphs are fundamental mathematical objects and regularization methods are used to control ill-pose problems, both proposed algorithms are potentially applicable to a wide range of domains.Les images médicales sont utilisées afin de représenter l'anatomie. Le caractère non- linéaire d'imagerie médicale rendent leur analyse difficile. Dans cette thèse, nous nous intéressons à l'analyse d'images médicales du point de vue de la théorie statistique de l'apprentissage. Tout d'abord, nous examinons méthodes de régularisation. Dans cette direction, nous introduisons une nouvelle méthode de régularisation, la k-support regularized SVM. Cet algorithme étend la SVM régularisée `1 à une norme mixte de toutes les deux normes `1 et `2. Ensuite, nous nous intéressons un problème de comparaison des graphes. Les graphes sont une technique utilisée pour la représentation des données ayant une structure héritée. L'exploitation de ces données nécessite la capacité de comparer des graphes. Malgré le progrès dans le domaine des noyaux sur graphes, les noyaux sur graphes existants se concentrent à des graphes non-labellisés ou labellisés de façon discrète, tandis que la comparaison de graphes labellisés par des vecteurs continus, demeure un problème de recherche ouvert. Nous introduisons une nouvelle méthode, l'algorithme de Weisfeiler-Lehman pyramidal et quantifié afin d'aborder le problème de la comparaison des graphes labellisés par des vecteurs continus. Notre algorithme considère les statistiques de motifs sous arbre, basé sur l'algorithme Weisfeiler-Lehman ; il utilise une stratégie de quantification pyramidale pour déterminer un nombre logarithmique de labels discrets. Globalement, les graphes étant des objets mathématiques fondamentaux et les méthodes de régularisation étant utilisés pour contrôler des problèmes mal-posés, notre algorithmes pourraient appliqués sur un grand éventail d'applications