Product graph-based higher order contextual similarities for inexact subgraph matching

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record Many algorithms formulate graph matching as an optimization of an objective function of pairwise quantification of nodes and edges of two graphs to be matched. Pairwise measurements usually consider local attributes but disregard contextual information involved in graph structures. We address this issue by proposing contextual similarities between pairs of nodes. This is done by considering the tensor product graph (TPG) of two graphs to be matched, where each node is an ordered pair of nodes of the operand graphs. Contextual similarities between a pair of nodes are computed by accumulating weighted walks (normalized pairwise similarities) terminating at the corresponding paired node in TPG. Once the contextual similarities are obtained, we formulate subgraph matching as a node and edge selection problem in TPG. We use contextual similarities to construct an objective function and optimize it with a linear programming approach. Since random walk formulation through TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities and better discrimination among the nodes and edges. Experimental results shown on synthetic as well as real benchmarks illustrate that higher order contextual similarities increase discriminating power and allow one to find approximate solutions to the subgraph matching problem.European Union Horizon 202

Discriminative prototype selection methods for graph embedding

Graphs possess a strong representational power for many types of patterns. However, a main limitation in their use for pattern analysis derives from their difficult mathematical treatment. One way of circumventing this problem is that of transforming the graphs into a vector space by means of graph embedding. Such an embedding can be conveniently obtained by using a set of prototype graphs and a dissimilarity measure. However, when we apply this approach to a set of class-labelled graphs, it is challenging to select prototypes capturing both the salient structure within each class and inter-class separation. In this paper, we introduce a novel framework for selecting a set of prototypes from a labelled graph set taking their discriminative power into account. Experimental results showed that such a discriminative prototype selection framework can achieve superior results in classification compared to other well-established prototype selection approaches. © 2012 Elsevier Ltd

The Selberg trace formula for Dirac operators

We examine spectra of Dirac operators on compact hyperbolic surfaces. Particular attention is devoted to symmetry considerations, leading to non-trivial multiplicities of eigenvalues. The relation to spectra of Maass-Laplace operators is also exploited. Our main result is a Selberg trace formula for Dirac operators on hyperbolic surfaces

Graph Edit Distance Reward: Learning to Edit Scene Graph

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.Comment: 14 pages, 6 figures, ECCV camera ready versio

A Coboundary Morphism For The Grothendieck Spectral Sequence

Given an abelian category $\mathcal{A}$ with enough injectives we show that a short exact sequence of chain complexes of objects in $\mathcal{A}$ gives rise to a short exact sequence of Cartan-Eilenberg resolutions. Using this we construct coboundary morphisms between Grothendieck spectral sequences associated to objects in a short exact sequence. We show that the coboundary preserves the filtrations associated with the spectral sequences and give an application of these result to filtrations in sheaf cohomology.Comment: 18 page

Graph edit distance or graph edit pseudo-distance?

Graph Edit Distance has been intensively used since its appearance in 1983. This distance is very appropriate if we want to compare a pair of attributed graphs from any domain and obtain not only a distance, but also the best correspondence between nodes of the involved graphs. In this paper, we want to analyse if the Graph Edit Distance can be really considered a distance or a pseudo-distance, since some restrictions of the distance function are not fulfilled. Distinguishing between both cases is important because the use of a distance is a restriction in some methods to return exact instead of approximate results. This occurs, for instance, in some graph retrieval techniques. Experimental validation shows that in most of the cases, it is not appropriate to denominate the Graph Edit Distance as a distance, but a pseudo-distance instead, since the triangle inequality is not fulfilled. Therefore, in these cases, the graph retrieval techniques not always return the optimal graph

Influence of the Time Scale on the Construction of Financial Networks

BACKGROUND: In this paper we investigate the definition and formation of financial networks. Specifically, we study the influence of the time scale on their construction. METHODOLOGY/PRINCIPAL FINDINGS: For our analysis we use correlation-based networks obtained from the daily closing prices of stock market data. More precisely, we use the stocks that currently comprise the Dow Jones Industrial Average (DJIA) and estimate financial networks where nodes correspond to stocks and edges correspond to none vanishing correlation coefficients. That means only if a correlation coefficient is statistically significant different from zero, we include an edge in the network. This construction procedure results in unweighted, undirected networks. By separating the time series of stock prices in non-overlapping intervals, we obtain one network per interval. The length of these intervals corresponds to the time scale of the data, whose influence on the construction of the networks will be studied in this paper. CONCLUSIONS/SIGNIFICANCE: Numerical analysis of four different measures in dependence on the time scale for the construction of networks allows us to gain insights about the intrinsic time scale of the stock market with respect to a meaningful graph-theoretical analysis