56,463 research outputs found
Pattern vectors from algebraic graph theory
Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs
A Survey on Graph Kernels
Graph kernels have become an established and widely-used technique for
solving classification tasks on graphs. This survey gives a comprehensive
overview of techniques for kernel-based graph classification developed in the
past 15 years. We describe and categorize graph kernels based on properties
inherent to their design, such as the nature of their extracted graph features,
their method of computation and their applicability to problems in practice. In
an extensive experimental evaluation, we study the classification accuracy of a
large suite of graph kernels on established benchmarks as well as new datasets.
We compare the performance of popular kernels with several baseline methods and
study the effect of applying a Gaussian RBF kernel to the metric induced by a
graph kernel. In doing so, we find that simple baselines become competitive
after this transformation on some datasets. Moreover, we study the extent to
which existing graph kernels agree in their predictions (and prediction errors)
and obtain a data-driven categorization of kernels as result. Finally, based on
our experimental results, we derive a practitioner's guide to kernel-based
graph classification
Structural Data Recognition with Graph Model Boosting
This paper presents a novel method for structural data recognition using a
large number of graph models. In general, prevalent methods for structural data
recognition have two shortcomings: 1) Only a single model is used to capture
structural variation. 2) Naive recognition methods are used, such as the
nearest neighbor method. In this paper, we propose strengthening the
recognition performance of these models as well as their ability to capture
structural variation. The proposed method constructs a large number of graph
models and trains decision trees using the models. This paper makes two main
contributions. The first is a novel graph model that can quickly perform
calculations, which allows us to construct several models in a feasible amount
of time. The second contribution is a novel approach to structural data
recognition: graph model boosting. Comprehensive structural variations can be
captured with a large number of graph models constructed in a boosting
framework, and a sophisticated classifier can be formed by aggregating the
decision trees. Consequently, we can carry out structural data recognition with
powerful recognition capability in the face of comprehensive structural
variation. The experiments shows that the proposed method achieves impressive
results and outperforms existing methods on datasets of IAM graph database
repository.Comment: 8 page
A Necessary and Sufficient Condition for Graph Matching to be equivalent to Clique Search
This paper formulates a necessary and sufficient condition for a generic graph matching problem to be equivalent to the maximum vertex and edge weight clique problem in a derived association graph. The consequences of this results are threefold: first, the condition is general enough to cover a broad range of practical graph matching problems; second, a proof to establish equivalence between graph matching and clique search reduces to showing that a given graph matching problem satisfies the proposed condition;\ud
and third, the result sets the scene for generic continuous solutions for a broad range of graph matching problems. To illustrate the mathematical framework, we apply it to a number of graph matching problems, including the problem of determining the graph edit distance
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