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Register a new userFlexible graph matching and graph edit distance using answer set programming
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Added by
James Cheney
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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The graph isomorphism, subgraph isomorphism, and graph edit distance problems are combinatorial problems with many applications. Heuristic exact and approximate algorithms for each of these problems have been developed for different kinds of graphs: directed, undirected, labeled, etc. However, additional work is often needed to adapt such algorithms to different classes of graphs, for example to accommodate both labels and property annotations on nodes and edges. In this paper, we propose an approach based on answer set programming. We show how each of these problems can be defined for a general class of property graphs with directed edges, and labels and key-value properties annotating both nodes and edges. We evaluate this approach on a variety of synthetic and realistic graphs, demonstrating that it is feasible as a rapid prototyping approach.
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Scene Graph, as a vital tool to bridge the gap between language domain and image domain, has been widely adopted in the cross-modality task like VQA. In this paper, we propose a new method to edit the scene graph according to the user instructions, which has never been explored. To be specific, in order to learn editing scene graphs as the semantics given by texts, we propose a Graph Edit Distance Reward, which is based on the Policy Gradient and Graph Matching algorithm, to optimize neural symbolic model. In the context of text-editing image retrieval, we validate the effectiveness of our method in CSS and CRIR dataset. Besides, CRIR is a new synthetic dataset generated by us, which we will publish it soon for future use.
In this thesis, we introduce a novel formal framework to represent and reason about qualitative direction and distance relations between extended objects using Answer Set Programming (ASP). We take Cardinal Directional Calculus (CDC) as a starting point and extend CDC with new sorts of constraints which involve defaults, preferences and negation. We call this extended version as nCDC. Then we further extend nCDC by augmenting qualitative distance relation and name this extension as nCDC+. For CDC, nCDC, nCDC+, we introduce an ASP-based general framework to solve consistency checking problems, address composition and inversion of qualitative spatial relations, infer unknown or missing relations between objects, and find a suitable configuration of objects which fulfills a given inquiry.
Computing efficiently a robust measure of similarity or dissimilarity between graphs is a major challenge in Pattern Recognition. The Graph Edit Distance (GED) is a flexible measure of dissimilarity between graphs which arises in error-tolerant graph matching. It is defined from an optimal sequence of edit operations (edit path) transforming one graph into an other. Unfortunately, the exact computation of this measure is NP-hard. In the last decade, several approaches have been proposed to approximate the GED in polynomial time, mainly by solving linear programming problems. Among them, the bipartite GED has received much attention. It is deduced from a linear sum assignment of the nodes of the two graphs, which can be efficiently computed by Hungarian-type algorithms. However, edit operations on nodes and edges are not handled simultaneously, which limits the accuracy of the approximation. To overcome this limitation, we propose to extend the linear assignment model to a quadratic one, for directed or undirected graphs having labelized nodes and edges. This is realized through the definition of a family of edit paths induced by assignments between nodes. We formally show that the GED, restricted to the paths in this family, is equivalent to a quadratic assignment problem. Since this problem is NP-hard, we propose to compute an approximate solution by an adaptation of the Integer Projected Fixed Point method. Experiments show that the proposed approach is generally able to reach a more accurate approximation of the optimal GED than the bipartite GED, with a computational cost that is still affordable for graphs of non trivial sizes.
Given a hereditary property of graphs $mathcal{H}$ and a $pin [0,1]$, the edit distance function ${rm ed}_{mathcal{H}}(p)$ is asymptotically the maximum proportion of edge-additions plus edge-deletions applied to a graph of edge density $p$ sufficient to ensure that the resulting graph satisfies $mathcal{H}$. The edit distance function is directly related to other well-studied quantities such as the speed function for $mathcal{H}$ and the $mathcal{H}$-chromatic number of a random graph. Let $mathcal{H}$ be the property of forbidding an ErdH{o}s-R{e}nyi random graph $Fsim mathbb{G}(n_0,p_0)$, and let $varphi$ represent the golden ratio. In this paper, we show that if $p_0in [1-1/varphi,1/varphi]$, then a.a.s. as $n_0toinfty$, begin{align*} {rm ed}_{mathcal{H}}(p) = (1+o(1)),frac{2log n_0}{n_0} cdotminleft{ frac{p}{-log(1-p_0)}, frac{1-p}{-log p_0} right}. end{align*} Moreover, this holds for $pin [1/3,2/3]$ for any $p_0in (0,1)$.
Biometric authentication by means of handwritten signatures is a challenging pattern recognition task, which aims to infer a writer model from only a handful of genuine signatures. In order to make it more difficult for a forger to attack the verification system, a promising strategy is to combine different writer models. In this work, we propose to complement a recent structural approach to offline signature verification based on graph edit distance with a statistical approach based on metric learning with deep neural networks. On the MCYT and GPDS benchmark datasets, we demonstrate that combining the structural and statistical models leads to significant improvements in performance, profiting from their complementary properties.
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