Graph Matching Process Research Articles

A fuzzy structure processing mechanism for graph grammar

Abstract A strict graph-matching mechanism brings normativeness to graph grammar but leads to graph grammar insufficiency when processing fuzzy grammatical structures. To address this issue, the current paper proposes an improved formal framework for graph grammar that enables it to effectively specify the ambiguity of graph models while maintaining normativeness and intuition. First, the improved framework defines the connection probability for edges and classifies the edges based on the connection probability, which is used as the quantitative and qualitative description of the graph grammar structure’s ambiguity. Second, the concepts of credibility threshold, credible subgraphs and candidate subgraphs are defined, and the constraints on the redex are adjusted to increase the fault tolerance of the graph-matching process. Finally, the grammatical operation is redesigned, with a matching weight defined for each redex based on the connection probability and the credibility threshold, thereby providing a theoretical basis and practical guidance for the selection of multiple redexes.

Learning resource recommendation via knowledge graphs and learning style clustering

An e-learning system should recommend learners appropriate learning resources according to their actual needs and cognitive status for improving their learning performance. To overcome the deficiencies of existing approaches (e.g., poor interpretability, limited efficiency and accuracy of recommendation), we propose a new recommendation approach to learning resources via knowledge graphs and learning style clustering. In this approach, the knowledge graphs of an online learning environment are constructed based on a generic ontology model, and the graph embedding algorithm and graph matching process are applied to optimize the efficiency of graph computation for identifying similar learning resources. By introducing learning style theory, learners are clustered based on their learning styles. Based on the clustering results, the learners’ degrees of interest in similar learning resources are measured, and the recommendation results are obtained according to the degrees of interest. Finally, the experiments demonstrate that the proposed approach significantly enhances the computational efficiency and the quality of learning resource recommendation compared with the existing approaches in large-scale graph data scenarios.

Learning for Graph Matching based Multi-object Tracking in Auto Driving

Multi-object tracking in autonomous driving aims to represent trajectories of moving objects for planning system of the vehicle. In this paper, we propose a new tracking-bydetection scheme based on deep neural networks for multi-object detection and tracking in autonomous driving scene. We first introduce a light-weight neural network branch for fast object detection, and based on the detection results on each frame, we build two object graphs for consecutive frames separately, where the vertices of the graph represent the objects in the image, and the edges of the graph represent the spatial relations between the objects. We then formulate the multi-object tracking problem as the graph matching process by learning the relevance between objects from another object association network branch. Experiments results on the MOT multi-object tracking dataset show that the proposed object detection and tracking approach achieves comparable results with state-of-the-art deep learning based multi-object tracking methods, and outperforms them in tracking efficiency, which ensures real-time multiobject tracking for autonomous driving.

A bipartite matching-based feature selection for multi-label learning

Many real-world data have multiple class labels known as multi-label data, where the labels are correlated with each other, and as such, they are not independent. Since these data are usually high-dimensional, and the current multi-label feature selection methods have not been precise enough, then a new feature selection method is necessary. In this paper, for the first time, we have modeled the problem of multi-label feature selection to a bipartite graph matching process. The proposed method constructs a bipartite graph of features (as the left vertices) and labels (as the right vertices), called Feature-Label Graph (FLG), where each feature is connected to the set of labels, where the weight of the edge between each feature and label is equal to their correlation. Then, the Hungarian algorithm estimates the best matching in FLG. The selected features in each matching are sorted by weighted correlation distance and added to the ranking vector. To select the discriminative features, the proposed method considers both the redundancy of features and the relevancy of each feature to the class labels. The results indicate the superiority of the proposed method against the other methods in classification measures.

Second- and High-Order Graph Matching for Correspondence Problems

Correspondence problems are challenging due to the complexity of real-world scenes. One way to solve this problem is to improve the graph matching (GM) process, which is flexible for matching non-rigid objects. GM can be classified into three categories that correspond with the variety of object functions: first-order, second-order, and high-order matching. Graph and hypergraph matching have been proposed separately in previous works. The former is equivalent to the second-order GM, and the latter is equivalent to high-order GM, but we use the terms second- and high-order GM to unify the terminology in this paper. Second- and high-order GM fit well with different types of problems; the key goal for these processes is to find better-optimized algorithms. Because the optimal problems for second- and high-order GM are different, we propose two novel optimized algorithms for them in this paper. (1) For the second-order GM, we first introduce a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -nearest-neighbor-pooling matching method that integrates feature pooling into GM and reduces the complexity. Meanwhile, we evaluate each matching candidate using discriminative weights on its <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -nearest neighbors by taking locality as well as sparsity into consideration. (2) High-order GM introduces numerous outliers, because precision is rarely considered in related methods. Therefore, we propose a sub-pattern structure to construct a robust high-order GM method that better integrates geometric information. To narrow the search space and solve the optimization problem, a new prior strategy and a cell-algorithm-based Markov Chain Monte Carlo framework are proposed. In addition, experiments demonstrate the robustness and improvements of these algorithms with respect to matching accuracy compared with other state-of-the-art algorithms.

Embedding the node-to-node mappings to learn the Graph edit distance parameters

This paper presents a learning method to automatically deduce the insertion, deletion and substitution costs of the Graph edit distance. The method is based on embedding the ground-truth node-to-node mappings into a Euclidean space and learning the edit costs through the hyperplane that splits the nodes into mapped ones and non-mapped ones in this new space. In this way, the algorithm does not need to compute any graph matching process, which is the main drawback of other methods due to its intrinsic exponential computational complexity. Nevertheless, our learning method has two main restrictions: 1) the insertion and deletion edit costs have to be constants; 2) the substitution edit costs have to be represented as inner products of two vectors. One vector represents certain weights and the other vector represents the distances between attributes. Experimental validation shows that the matching accuracy of this method outperforms the current methods. Furthermore, there is a significant reduction in the runtime in the learning process.

Gracker: A Graph-Based Planar Object Tracker.

Matching-based algorithms have been commonly used in planar object tracking. They often model a planar object as a set of keypoints, and then find correspondences between keypoint sets via descriptor matching. In previous work, unary constraints on appearances or locations are usually used to guide the matching. However, these approaches rarely utilize structure information of the object, and are thus suffering from various perturbation factors. In this paper, we proposed a graph-based tracker, named Gracker, which is able to fully explore the structure information of the object to enhance tracking performance. We model a planar object as a graph, instead of a simple collection of keypoints, to represent its structure. Then, we reformulate tracking as a sequential graph matching process, which establishes keypoint correspondence in a geometric graph matching manner. For evaluation, we compare the proposed Gracker with state-of-the-art planar object trackers on three benchmark datasets: two public ones and a newly collected one. Experimental results show that Gracker achieves robust tracking results against various environmental variations, and outperforms other algorithms in general on the datasets.

A Graph-Based Approach for 3D Building Model Reconstruction from Airborne LiDAR Point Clouds

3D building model reconstruction is of great importance for environmental and urban applications. Airborne light detection and ranging (LiDAR) is a very useful data source for acquiring detailed geometric and topological information of building objects. In this study, we employed a graph-based method based on hierarchical structure analysis of building contours derived from LiDAR data to reconstruct urban building models. The proposed approach first uses a graph theory-based localized contour tree method to represent the topological structure of buildings, then separates the buildings into different parts by analyzing their topological relationships, and finally reconstructs the building model by integrating all the individual models established through the bipartite graph matching process. Our approach provides a more complete topological and geometrical description of building contours than existing approaches. We evaluated the proposed method by applying it to the Lujiazui region in Shanghai, China, a complex and large urban scene with various types of buildings. The results revealed that complex buildings could be reconstructed successfully with a mean modeling error of 0.32 m. Our proposed method offers a promising solution for 3D building model reconstruction from airborne LiDAR point clouds.

Similarity matching for integrating spatial information extracted from place descriptions

ABSTRACTPlace descriptions are used in everyday communication as a common way to convey spatial information. Processing the information from place descriptions poses multiple significant challenges because these descriptions are written in natural language. In particular, corpora of place descriptions provide a plethora of human spatial knowledge beyond geographical information system, even if these descriptions refer to the same places in various ways. This article focuses on resolving ambiguous or synonymous place names from place descriptions by exploring the given relationships with other spatial features. It matches place names from multiple descriptions by developing a novel labelled graph matching process that relies solely on the comparison of string, linguistic and spatial similarities between identified places. This process uses unstructured place descriptions as an input, and produces a composite place graph with qualitative spatial relations from the descriptions. The performance of this novel process exceeds current toponym resolution by coping with non-gazetteered places.

Inexact graph matching using a hierarchy of matching processes

Inexact graph matching algorithms have proved to be useful in many applications, such as character recognition, shape analysis, and image analysis. Inexact graph matching is, however, inherently an NP-hard problem with exponential computational complexity. Much of the previous research has focused on solving this problem using heuristics or estimations. Unfortunately, many of these techniques do not guarantee that an optimal solution will be found. It is the aim of the proposed algorithm to reduce the complexity of the inexact graph matching process, while still producing an optimal solution for a known application. This is achieved by greatly simplifying each individual matching process, and compensating for lost robustness by producing a hierarchy of matching processes. The creation of each matching process in the hierarchy is driven by an application-specific criterion that operates at the subgraph scale. To our knowledge, this problem has never before been approached in this manner. Results show that the proposed algorithm is faster than two existing methods based on graph edit operations. The proposed algorithm produces accurate results in terms of matching graphs, and shows promise for the application of shape matching. The proposed algorithm can easily be extended to produce a sub-optimal solution if required.

Approximate Subgraph Matching-Based Literature Mining for Biomedical Events and Relations

The biomedical text mining community has focused on developing techniques to automatically extract important relations between biological components and semantic events involving genes or proteins from literature. In this paper, we propose a novel approach for mining relations and events in the biomedical literature using approximate subgraph matching. Extraction of such knowledge is performed by searching for an approximate subgraph isomorphism between key contextual dependencies and input sentence graphs. Our approach significantly increases the chance of retrieving relations or events encoded within complex dependency contexts by introducing error tolerance into the graph matching process, while maintaining the extraction precision at a high level. When evaluated on practical tasks, it achieves a 51.12% F-score in extracting nine types of biological events on the GE task of the BioNLP-ST 2011 and an 84.22% F-score in detecting protein-residue associations. The performance is comparable to the reported systems across these tasks, and thus demonstrates the generalizability of our proposed approach.

Topological simultaneous localization and mapping (SLAM): toward exact localization without explicit localization

This paper presents a new method for simultaneous localization and mapping that exploits the topology of the robot's free space to localize the robot on a partially constructed map. The topology of the environment is encoded in a topological map; the particular topological map used in this paper is the generalized Voronoi graph (GVG), which also encodes some metric information about the robot's environment, as well. In this paper, we present the low-level control laws that generate the GVG edges and nodes, thereby allowing for exploration of an unknown space. With these prescribed control laws, the GVG can be viewed as an arbitrator for a hybrid control system that determines when to invoke a particular low-level controller from a set of controllers all working toward the high-level capability of mobile robot exploration. The main contribution, however, is using the graph structure of the GVG, via a graph matching process, to localize the robot. Experimental results verify the described work.

Multiple graph matching with Bayesian inference

This paper describes the development of a Bayesian framework for multiple graph matching. The study is motivated by the plethora of multi-sensor fusion problems which can be abstracted as multiple graph matching tasks. The study uses as its starting point the Bayesian consistency measure recently developed by Wilson and Hancock. Hitherto, the consistency measure has been used exclusively in the matching of graph-pairs. In the multiple graph matching study reported in this paper, we use the Bayesian framework to construct an inference matrix which can be used to gauge the mutual consistency of multiple graph-matches. The multiple graph-matching process is realised as an iterative discrete relaxation process which aims to maximise the elements of the inference matrix. We experiment with our multiple graph matching process using an application vehicle furnished by the matching of aerial imagery. Here we are concerned with the simultaneous fusion of optical, infra-red and synthetic aperture radar images in the presence of digital map data.

Face recognition by elastic bunch graph matching

We present a system for recognizing human faces from single images out of a large database containing one image per person. Faces are represented by labeled graphs, based on a Gabor wavelet transform. Image graphs of new faces are extracted by an elastic graph matching process and can be compared by a simple similarity function. The system differs from the preceding one (Lades et al., 1993) in three respects. Phase information is used for accurate node positioning. Object-adapted graphs are used to handle large rotations in depth. Image graph extraction is based on a novel data structure, the bunch graph, which is constructed from a small get of sample image graphs.