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112
Algorithmics and Applications of Tree and Graph Searching
 In Symposium on Principles of Database Systems
, 2002
"... Modern search engines answer keywordbased queries extremely efficiently. The impressive speed is due to clever inverted index structures, caching, a domainindependent knowledge of strings, and thousands of machines. Several research efforts have attempted to generalize keyword search to keytree an ..."
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Cited by 109 (8 self)
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Modern search engines answer keywordbased queries extremely efficiently. The impressive speed is due to clever inverted index structures, caching, a domainindependent knowledge of strings, and thousands of machines. Several research efforts have attempted to generalize keyword search to keytree and keygraph searching, because trees and graphs have many applications in nextgeneration database systems. This paper surveys both algorithms and applications, giving some emphasis to our own work.
Structural matching by discrete relaxation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... Abstract—This paper describes a Bayesian framework for performing relational graph matching by discrete relaxation. Our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching. Broadly speaking there are two main aspects ..."
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Cited by 106 (29 self)
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Abstract—This paper describes a Bayesian framework for performing relational graph matching by discrete relaxation. Our basic aim is to draw on this framework to provide a comparative evaluation of a number of contrasting approaches to relational matching. Broadly speaking there are two main aspects to this study. Firstly we focus on the issue of how relational inexactness may be quantified. We illustrate that several popular relational distance measures can be recovered as specific limiting cases of the Bayesian consistency measure. The second aspect of our comparison concerns the way in which structural inexactness is controlled. We investigate three different realizations of the matching process which draw on contrasting control models. The main conclusion of our study is that the active process of graphediting outperforms the alternatives in terms of its ability to effectively control a large population of contaminating clutter.
Structural graph matching using the em algorithm and singular value decomposition
 IEEE Trans. PAMI
, 2001
"... AbstractÐThis paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is to say, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions. Commencing from a probability distri ..."
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Cited by 66 (8 self)
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AbstractÐThis paper describes an efficient algorithm for inexact graph matching. The method is purely structural, that is to say, it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions. Commencing from a probability distribution for matching errors, we show how the problem of graph matching can be posed as maximumlikelihood estimation using the apparatus of the EM algorithm. Our second contribution is to cast the recovery of correspondence matches between the graph nodes in a matrix framework. This allows us to efficiently recover correspondence matches using singular value decomposition. We experiment with the method on both realworld and synthetic data. Here, we demonstrate that the method offers comparable performance to more computationally demanding methods. Index TermsÐInexact graph matching, EM algorithm, matrix factorization, mixture models, Delaunay triangulations. 1
Bayesian graph edit distance
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2000
"... AbstractÐThis paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of editdistance originally introduced for graphmatching by Sanfeliu and Fu [1]. We show how the Levenshtein distance can be used to model the probability distribution ..."
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Cited by 49 (5 self)
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AbstractÐThis paper describes a novel framework for comparing and matching corrupted relational graphs. The paper develops the idea of editdistance originally introduced for graphmatching by Sanfeliu and Fu [1]. We show how the Levenshtein distance can be used to model the probability distribution for structural errors in the graphmatching problem. This probability distribution is used to locate matches using MAP label updates. We compare the resulting graphmatching algorithm with that recently reported by Wilson and Hancock. The use of editdistance offers an elegant alternative to the exhaustive compilation of label dictionaries. Moreover, the method is polynomial rather than exponential in its worstcase complexity. We support our approach with an experimental study on synthetic data and illustrate its effectiveness on an uncalibrated stereo correspondence problem. This demonstrates experimentally that the gain in efficiency is not at the expense of quality of match.
RASCAL: Calculation of graph similarity using maximum common edge subgraphs
 The Computer Journal
, 2002
"... ..."
Indexing Hierarchical Structures Using Graph Spectra
, 2005
"... Hierarchical image structures are abundant in computer vision and have been used to encode part structure, scale spaces, and a variety of multiresolution features. In this paper, we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic g ..."
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Cited by 44 (10 self)
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Hierarchical image structures are abundant in computer vision and have been used to encode part structure, scale spaces, and a variety of multiresolution features. In this paper, we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph (DAG) into a lowdimensional vector space. Based on a novel spectral characterization of a DAG, this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearestneighbor search. We establish the insensitivity of the signature to minor perturbation of graph structure due to noise, occlusion, or node split/merge. To accommodate largescale occlusion, the DAG rooted at each nonleaf node of the query "votes" for model objects that share that "part," effectively accumulating local evidence in a model DAG's topological subspaces. We demonstrate the approach with a series of indexing experiments in the domain of viewbased 3D object recognition using shock graphs.
Graph edit distance from spectral seriation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Abstract—This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to st ..."
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Cited by 34 (6 self)
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Abstract—This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graphmatching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems. Index Terms—Graph edit distance, graph seriation, maximum a posteriori probability (MAP), graphspectral methods. 1
A shape analysis model with applications to a character recognition system
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 1994
"... A~s~Qc~A method for the recognition of multifont printed characters is proposed, giving emphasis to the identification of structural descriptions of character shapes using prototypes. Noise and shape variations are modeled as series of transformations from groups of features in the data to features ..."
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Cited by 32 (1 self)
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A~s~Qc~A method for the recognition of multifont printed characters is proposed, giving emphasis to the identification of structural descriptions of character shapes using prototypes. Noise and shape variations are modeled as series of transformations from groups of features in the data to features in each prototype. Thus, the method manages systematically the relative distortion between a candidate shape and its prototype, accomplishing robustness to noise with less than two prototypes per class, on average. Our method uses a flexible matching between components and a flexible grouping of the individual components to be matched. A number of shape transformations are defined, including filling of gaps, so that the method handles broken characters. Also, a measure of the amount of distortion that these transformations cause is given. Classification of character shapes is defined as a minimization problem among the possible transformations that map an input shape into prototypical shapes. Some tests with handprinted numerals confirmed the method’s high robustness level. Zndex TermsShape distance, graph matching, relative neighborhood graph, broken character recognition, subgraph homeomorphism. I.
Deriving Phylogenetic Trees From the Similarity Analysis of Metabolic Pathways
, 2002
"... Comparative analysis of metabolic pathways in different genomes can give insights into the understanding of evolutionary and organizational relationships among species. This type of analysis allows one to measure the evolution of complete processes (with different functional roles) rather than the ..."
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Cited by 26 (0 self)
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Comparative analysis of metabolic pathways in different genomes can give insights into the understanding of evolutionary and organizational relationships among species. This type of analysis allows one to measure the evolution of complete processes (with different functional roles) rather than the individual elements of a conventional analysis. We present a new technique for the phylogenetic analysis of metabolic pathways based on the topology of the underlying graphs. A distance measure between graphs is defined using the similarity between nodes of the graphs and the structural relationship between them.
Partial Least Squares Regression for Graph Mining
"... Attributed graphs are increasingly more common in many application domains such as chemistry, biology and text processing. A central issue in graph mining is how to collect informative subgraph patterns for a given learning task. We propose an iterative mining method based on partial least squares r ..."
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Cited by 26 (6 self)
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Attributed graphs are increasingly more common in many application domains such as chemistry, biology and text processing. A central issue in graph mining is how to collect informative subgraph patterns for a given learning task. We propose an iterative mining method based on partial least squares regression (PLS). To apply PLS to graph data, a sparse version of PLS is developed first and then it is combined with a weighted pattern mining algorithm. The mining algorithm is iteratively called with different weight vectors, creating one latent component per one mining call. Our method, graph PLS, is efficient and easy to implement, because the weight vector is updated with elementary matrix calculations. In experiments, our graph PLS algorithm showed competitive prediction accuracies in many chemical datasets and its efficiency was significantly superior to graph boosting (gBoost) and the naive method based on frequent graph mining.