scholarly journals SECOND-ORDER RANDOM GRAPHS FOR MODELING SETS OF ATTRIBUTED GRAPHS AND THEIR APPLICATION TO OBJECT LEARNING AND RECOGNITION

2004 ◽  
Vol 18 (03) ◽  
pp. 375-396 ◽  
Author(s):  
ALBERTO SANFELIU ◽  
FRANCESC SERRATOSA ◽  
RENÉ ALQUÉZAR
Keyword(s):  
Random Graphs ◽  
Distance Measure ◽  
Graph Matching ◽  
Joint Probability ◽  
Second Order ◽  
Graph Representation ◽  
Expected Improvement ◽  
Probability Functions ◽  
Object Learning ◽  
Attributed Graphs

The aim of this article is to present a random graph representation, that is based on second-order relations between graph elements, for modeling sets of attributed graphs (AGs). We refer to these models as Second-Order Random Graphs (SORGs). The basic feature of SORGs is that they include both marginal probability functions of graph elements and second-order joint probability functions. This allows a more precise description of both the structural and semantic information contents in a set of AGs and, consequently, an expected improvement in graph matching and object recognition. The article presents a probabilistic formulation of SORGs that includes as particular cases the two previously proposed approaches based on random graphs, namely the First-Order Random Graphs (FORGs) and the Function-Described Graphs (FDGs). We then propose a distance measure derived from the probability of instantiating a SORG into an AG and an incremental procedure to synthesize SORGs from sequences of AGs. Finally, SORGs are shown to improve the performance of FORGs, FDGs and direct AG-to-AG matching in three experimental recognition tasks: one in which AGs are randomly generated and the other two in which AGs represent multiple views of 3D objects (either synthetic or real) that have been extracted from color images. In the last case, object learning is achieved through the synthesis of SORG models.

Learning Graph Matching Substitution Weights Based on the Ground Truth Node Correspondence

2016 ◽  
Vol 30 (02) ◽  
pp. 1650005 ◽  
Author(s):  
Xavier Cortés ◽  
Francesc Serratosa
Keyword(s):  
Pattern Recognition ◽  
Distance Measure ◽  
Graph Matching ◽  
Ground Truth ◽  
Local Characteristic ◽  
Attributed Graphs ◽  
Structured Objects

In pattern recognition, it is usual to compare structured objects through attributed graphs in which nodes represent local parts and edges relations between them. Thus, each characteristic in the local parts is represented by different attributes on the nodes or edges. In this framework, the comparison between structured objects is performed through a distance between attributed graphs. If we want to correctly tune the distance and node correspondence between graphs, we need to add some weights on the node and edge attributes to gauge the importance of each local characteristic while defining the distance measure between graphs. In this paper, we present a method to learn the weights of each node and edge attribute such that the distance between the ground truth correspondence between graphs and the automatically obtained correspondence is minimized.

scholarly journals SYNTHESIS OF FUNCTION-DESCRIBED GRAPHS AND CLUSTERING OF ATTRIBUTED GRAPHS

2002 ◽  
Vol 16 (06) ◽  
pp. 621-655 ◽  
Author(s):  
FRANCESC SERRATOSA ◽  
RENÉ ALQUÉZAR ◽  
ALBERTO SANFELIU
Keyword(s):  
Pattern Recognition ◽  
Distance Measure ◽  
Graph Matching ◽  
Synthetic Data ◽  
Matching Method ◽  
Structural Pattern ◽  
Matching Algorithm ◽  
First Order ◽  
Structural Pattern Recognition ◽  
Attributed Graphs

Function-Described Graphs (FDGs) have been introduced by the authors as a representation of an ensemble of Attributed Graphs (AGs) for structural pattern recognition alternative to first-order random graphs. Both optimal and approximate algorithms for error-tolerant graph matching, which use a distance measure between AGs and FDGs, have been reported elsewhere. In this paper, both the supervised and the unsupervised synthesis of FDGs from a set of graphs is addressed. First, two procedures are described to synthesize an FDG from a set of commonly labeled AGs or FDGs, respectively. Then, the unsupervised synthesis of FDGs is studied in he context of clustering a set of AGs and obtaining an FDG model for each cluster. Two algorithms based on incremental and hierarchical clustering, respectively, are proposed, which are parameterized by a graph matching method. Some experimental results both on synthetic data and a real 3D-object recognition application show that the proposed algorithms are effective for clustering a set of AGs and synthesizing the FDGs that describe the classes. Moreover, the synthesized FDGs are shown to be useful for pattern recognition thanks to the distance measure and matching algorithm previously reported.

scholarly journals Hierarchical and Unsupervised Graph Representation Learning with Loukas’s Coarsening

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 206
Author(s):  
Louis Béthune ◽  
Yacouba Kaloga ◽  
Pierre Borgnat ◽  
Aurélien Garivier ◽  
Amaury Habrard
Keyword(s):  
State Of The Art ◽  
Back Propagation ◽  
Representation Learning ◽  
Graph Representation ◽  
High Quality ◽  
Attributed Graphs ◽  
Information Maximization ◽  
Classification Tasks ◽  
Micro Structures ◽  
Mutual Information Maximization

We propose a novel algorithm for unsupervised graph representation learning with attributed graphs. It combines three advantages addressing some current limitations of the literature: (i) The model is inductive: it can embed new graphs without re-training in the presence of new data; (ii) The method takes into account both micro-structures and macro-structures by looking at the attributed graphs at different scales; (iii) The model is end-to-end differentiable: it is a building block that can be plugged into deep learning pipelines and allows for back-propagation. We show that combining a coarsening method having strong theoretical guarantees with mutual information maximization suffices to produce high quality embeddings. We evaluate them on classification tasks with common benchmarks of the literature. We show that our algorithm is competitive with state of the art among unsupervised graph representation learning methods.

scholarly journals Long-Term Loop Closure Detection through Visual-Spatial Information Preserving Multi-Order Graph Matching

2020 ◽  
Vol 34 (06) ◽  
pp. 10369-10376
Author(s):  
Peng Gao ◽  
Hao Zhang
Keyword(s):  
Spatial Information ◽  
Graph Matching ◽  
Fundamental Problem ◽  
Graph Representation ◽  
Spatial Relationships ◽  
Matching Problem ◽  
Loop Closure ◽  
Loop Closure Detection ◽  
Visual Spatial

Loop closure detection is a fundamental problem for simultaneous localization and mapping (SLAM) in robotics. Most of the previous methods only consider one type of information, based on either visual appearances or spatial relationships of landmarks. In this paper, we introduce a novel visual-spatial information preserving multi-order graph matching approach for long-term loop closure detection. Our approach constructs a graph representation of a place from an input image to integrate visual-spatial information, including visual appearances of the landmarks and the background environment, as well as the second and third-order spatial relationships between two and three landmarks, respectively. Furthermore, we introduce a new formulation that formulates loop closure detection as a multi-order graph matching problem to compute a similarity score directly from the graph representations of the query and template images, instead of performing conventional vector-based image matching. We evaluate the proposed multi-order graph matching approach based on two public long-term loop closure detection benchmark datasets, including the St. Lucia and CMU-VL datasets. Experimental results have shown that our approach is effective for long-term loop closure detection and it outperforms the previous state-of-the-art methods.

scholarly journals Second-order differentiability of probability functions

2016 ◽  
Vol 11 (1) ◽  
pp. 179-194 ◽  
Author(s):  
Wim van Ackooij ◽  
Jérôme Malick
Keyword(s):  
Second Order ◽  
Probability Functions

scholarly journals Ferromagnetic and spin-glass like transition in the q-neighbor Ising model on random graphs

2021 ◽  
Vol 94 (3) ◽  
Author(s):  
A. Krawiecki
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Spin Glass ◽  
Phase Diagrams ◽  
Random Graphs ◽  
Second Order ◽  
Ferromagnetic Phase ◽  
Ferromagnetic Transition ◽  
Antiferromagnetic Exchange

Abstract The q-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model for the opinion formation in which the agents, represented by two-state spins, change their opinions according to a Metropolis-like algorithm taking into account interactions with only a randomly chosen subset of their q neighbors. Depending on the model parameters in Monte Carlo simulations, phase diagrams are observed with first-order ferromagnetic transition, both first- and second-order ferromagnetic transitions and second-order ferromagnetic and spin-glass-like transitions as the temperature and fraction of antiferromagnetic exchange integrals are varied; in the latter case, the obtained phase diagrams qualitatively resemble those for the dilute spin-glass model. Homogeneous mean-field and pair approximations are extended to take into account the effect of the antiferromagnetic exchange interactions on the ferromagnetic phase transition in the model. For a broad range of parameters, critical temperatures for the first- or second-order ferromagnetic transition predicted by the homogeneous pair approximation show quantitative agreement with those obtained from Monte Carlo simulations; significant differences occur mainly in the vicinity of the tricritical point in which the critical lines for the second-order ferromagnetic and spin-glass-like transitions meet. Graphic abstract

BRIDGING STRUCTURE AND FEATURE REPRESENTATIONS IN GRAPH MATCHING

2012 ◽  
Vol 26 (05) ◽  
pp. 1260005 ◽  
Author(s):  
WAN-JUI LEE ◽  
VERONIKA CHEPLYGINA ◽  
DAVID M. J. TAX ◽  
MARCO LOOG ◽  
ROBERT P. W. DUIN
Keyword(s):  
Graph Matching ◽  
Structural Description ◽  
Dissimilarity Representation ◽  
Feature Representations ◽  
Bag Of Features ◽  
Attributed Graphs ◽  
Feature Based ◽  
Types Of Information ◽  
Essential Problem ◽  
Better Than

Structures and features are opposite approaches in building representations for object recognition. Bridging the two is an essential problem in pattern recognition as the two opposite types of information are fundamentally different. As dissimilarities can be computed for both the dissimilarity representation can be used to combine the two. Attributed graphs contain structural as well as feature-based information. Neglecting the attributes yields a pure structural description. Isolating the features and neglecting the structure represents objects by a bag of features. In this paper we will show that weighted combinations of dissimilarities may perform better than these two extremes, indicating that these two types of information are essentially different and strengthen each other. In addition we present two more advanced integrations than weighted combining and show that these may improve the classification performances even further.

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