Automatic learning of cost functions for graph edit distance

Graph matching and graph edit distance have become important tools in structural pattern recognition. The graph edit distance concept allows us to measure the structural similarity of attributed graphs in an error-tolerant way. The key idea is to model graph variations by structural distortion operations. As one of its main constraints, however, the edit distance requires the adequate definition of edit cost functions, which eventually determine which graphs are considered similar. In the past, these cost functions were usually defined in a manual fashion, which is highly prone to errors. The present paper proposes a method to automatically learn cost functions from a labeled sample set of graphs. To this end, we formulate the graph edit process in a stochastic context and perform a maximum likelihood parameter estimation of the distribution of edit operations. The underlying distortion model is learned using an Expectation Maximization algorithm. From this model we finally derive the desired cost functions. In a series of experiments we demonstrate the learning effect of the proposed method and provide a performance comparison to other models.     

BIM 模型相似度计算方法

针对从业者不论是想从本地模型库还是线上共享网站获取所需的BIM 模型只能靠 逐个查找、人工识读的方法,而模型的数量越来越多,获取符合需求的模型需要花费大量的时 间和人力的问题,提出了一种构件级BIM 模型相似度计算方法。从模型的构件出发,以BIM 通用交互格式工业基础类(IFC)文件作数据源,以通用数据标准IFC 2×3 为数据基础,首先提取 模型中构件的几何信息、语义信息等,并利用改进的方向包围盒(OBB)碰撞检测算法查找相连 构件;然后以构件为顶点、构件间连接关系为边将BIM 模型构建为邻接图模型,并用图编辑距 离算法计算邻接图模型的编辑距离;最后即可计算出不同模型之间的相似度。该方法以构件级 BIM 模型的相似度为依据可以大大提升BIM 模型的检索速度与准确率。     

Efficient graph similarity join for information integration on graphs

Graphs have been widely used for complex data representation in many real applications, such as social network, bioinformatics, and computer vision. Therefore, graph similarity join has become imperative for integrating noisy and inconsistent data from multiple data sources. The edit distance is commonly used to measure the similarity between graphs. The graph similarity join problem studied in this paper is based on graph edit distance constraints. To accelerate the similarity join based on graph edit distance, in the paper, we make use of a preprocessing strategy to remove the mismatching graph pairs with significant differences. Then a novel method of building indexes for each graph is proposed by grouping the nodes which can be reached in k hops for each key node with structure conservation, which is the k-hop tree based indexing method. As for each candidate pair, we propose a similarity computation algorithm with boundary filtering, which can be applied with good efficiency and effectiveness. Experiments on real and synthetic graph databases also confirm that our method can achieve good join quality in graph similarity join. Besides, the join process can be finished in polynomial time.     

Graph edit distance from spectral seriation

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 graph-matching 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.     

基于变迁图编辑距离的流程相似性算法

为了提高从企业模型库中查询检索模型的效率,提出一种基于变迁图编辑距离的流程相似性算法。首先,给出了变迁图的概念及其生成方法;其次,提出边的长度概念,且删除和插入边的代价由该边的长度决定,基于此定义出图编辑操作及其代价,并用节点匹配算法计算最小图编辑距离;然后,给出两个过程模型的相似性概念和计算方法;最后,通过实验验证了算法的正确性且满足七条相似性性质,并验证了变迁图编辑距离满足四条距离性质。     

面向图相似性搜索的高效图编辑距离算法

在图相似性搜索问题中,图编辑距离是较为普遍的度量方法,其计算性能很大程度上决定了图相似性搜索算法的性能。针对传统图编辑距离算法中存在的因大量冗余映射和较大搜索空间导致的性能低下问题,提出了一种改进的图编辑距离算法。该算法首先对图中顶点进行等价划分,以此计算映射编码来判断等价映射;然后定义映射完整性更新等价映射优先级,选出主映射参与扩展;其次,设计高效的启发式函数,提出基于映射编码的下界计算方法,快速得到最优映射。最后,将改进的图编辑距离算法扩展应用于图相似性搜索。在不同数据集上的实验结果表明,该算法具有更好的搜索性能,在搜索空间上最大可降低49%,速度提升了约29%。     

Approximation of graph edit distance based on Hausdorff matching

Graph edit distance is a powerful and flexible method for error-tolerant graph matching. Yet it can only be calculated for small graphs in practice due to its exponential time complexity when considering unconstrained graphs. In this paper we propose a quadratic time approximation of graph edit distance based on Hausdorff matching. In a series of experiments we analyze the performance of the proposed Hausdorff edit distance in the context of graph classification and compare it with a cubic time algorithm based on the assignment problem. Investigated applications include nearest neighbor classification of graphs representing letter drawings, fingerprints, and molecular compounds as well as hidden Markov model classification of vector space embedded graphs representing handwriting. In many cases, a substantial speedup is achieved with only a minor loss in accuracy or, in one case, even with a gain in accuracy. Overall, the proposed Hausdorff edit distance shows a promising potential in terms of flexibility, efficiency, and accuracy.     

图编辑距离概述

图编辑距离是图模式匹配技术中常用的方法之一。基于图编辑距离的匹配方法能够处理多种类型的图数据,因而受到了学术界的广泛关注。首先介绍了图编辑距离的相关概念;然后简述了基于启发式搜索技术的精确图编辑距离算法,重点分析了基于二分图匹配的近似图编辑距离算法;最后对现存的一些图编辑问题进行了总结,并对未来的发展趋势进行了展望。     

On the Impact of Using Utilities Rather than Costs for Graph Matching

The concept of graph edit distance constitutes one of the most flexible graph matching paradigms available. The major drawback of graph edit distance, viz. the exponential time complexity, has been recently overcome by means of a reformulation of the edit distance problem to a linear sum assignment problem. However, the substantial speed up of the matching is also accompanied by an approximation error on the distances. Major contribution of this paper is the introduction of a transformation process in order to convert the underlying cost model into a utility model. The benefit of this transformation is that it enables the integration of additional information in the assignment process. We empirically confirm the positive effects of this transformation on five benchmark graph sets with respect to the accuracy and run time of a distance based classifier.     

Edit distance-based kernel functions for structural pattern classification

A common approach in structural pattern classification is to define a dissimilarity measure on patterns and apply a distance-based nearest-neighbor classifier. In this paper, we introduce an alternative method for classification using kernel functions based on edit distance. The proposed approach is applicable to both string and graph representations of patterns. By means of the kernel functions introduced in this paper, string and graph classification can be performed in an implicit vector space using powerful statistical algorithms. The validity of the kernel method cannot be established for edit distance in general. However, by evaluating theoretical criteria we show that the kernel functions are nevertheless suitable for classification, and experiments on various string and graph datasets clearly demonstrate that nearest-neighbor classifiers can be outperformed by support vector machines using the proposed kernel functions.     

基于树编辑距离的工作流距离度量方法

在工作流的发现和聚类等应用中,需要对两个工作流模型的距离进行度量。因此,提出一种计算两个不同结构化工作流的距离定量度量方法。首先介绍了结构化工作流,并将每一个结构化工作流转换为流程结构树;然后基于两个结构树之间的树编辑距离来计算工作流之间的距离及相应相似度。该距离度量方法满足距离度量的3个属性,即同实体不可区分性、对称性和三角不等式性质。这些属性使得该距离度量方法可以在工作流模型管理活动中作为定量分析工具。实验结果表明,基于树编辑距离的工作流度量方法是可行的。同时,与基于邻接矩阵的距离度量方法相比,该方法考虑了不同结构之间的语义距离,有效验证了此方法的合理性。     

Manipulation of CAD surface models with haptics based on shape control functions

With traditional two-dimensional based interfaces, many CAD surface models are difficult to design and edit due to their 3D nature. This paper discusses a technique for the deformation of CAD surface models with haptic interaction based on shape control functions. With the technique, designers can use a haptic interface to directly touch a native B-rep CAD model, and deform it in real-time by pushing, pulling and dragging its surfaces in a natural 3D environment. The deformation is governed by shape control functions. By using the shape functions, designers can specify the area of deformation, and also have greater controls on the shape of deformation. This technique is numerically efficient, and can deform complex surface models involving several thousand control points in real-time. The haptic-based deforming approach gives designers greater flexibility for the manipulation of complex CAD surfaces.     

3D CAD model retrieval based on the softassign quadratic assignment algorithm

A retrieval method for 3D CAD models based on the softassign quadratic assignment algorithm is presented in this paper. Firstly, retrieval models and target models are expressed as face adjacency graphs (FAGs) and thus 3D CAD model retrieval is turned to a graph matching problem. Secondly, vertex and edge compatibility matrices between the FAGs of a retrieval model and a target model are calculated. Then, an optimization objective function is created from compatibility matrices of a retrieval model and a target model, which serves as the similar metric for choosing vertex mapping matrix M of two models. Finally, the softassign quadratic assignment algorithm is introduced to find the optimal vertex mapping matrix M. Experimental results have shown that the proposed method supports 3D CAD model retrieval, and it is promising to meet the requirement of engineering applications.     

Meshing complexity: predicting meshing difficulty for single part CAD models

This paper proposes a method for predicting the complexity of meshing computer aided design (CAD) geometries with unstructured, hexahedral, finite elements. Meshing complexity refers to the relative level of effort required to generate a valid finite element mesh on a given CAD geometry. A function is proposed to approximate the meshing complexity for single part CAD models. The function is dependent on a user defined element size as well as on data extracted from the geometry and topology of the CAD part. Several geometry and topology measures are proposed, which both characterize the shape of the CAD part and detect configurations that complicate mesh generation. Based on a test suite of CAD models, the function is demonstrated to be accurate within a certain range of error. The solution proposed here is intended to provide managers and users of meshing software a method of predicting the difficulty in meshing a CAD model. This will enable them to make decisions about model simplification and analysis approaches prior to mesh generation.     

AutoCAD与Word之间的数据交换

Auto CAD具有很强的绘图和编辑功能 ,但文字编辑功能差 ;Word的文字功能十分强大 ,但绘图功能较差。介绍了一种 Auto CAD与 Word间数据交换的方法 ,利用 Windows剪贴板和对象链接与嵌入 (OLE) ,可将两个软件的功能结合在一起 ,形成图文复合文件     

A novel edge-centric approach for graph edit similarity computation

Graph similarity is an important notion with many applications. Graph edit distance is one of the most flexible graph similarity measures available. The main problem with this measure is that in practice it can only be computed for small graphs due to its exponential time complexity. This paper addresses the high complexity of graph edit distance computations. Specifically, we present CSI_GED, a novel edge-centric approach for computing graph edit distance through common sub-structure isomorphisms enumeration. CSI_GED utilizes backtracking search combined with a number of heuristics to reduce memory requirements and quickly prune away a large portion of the mapping search space. Experiments show that CSI_GED is highly efficient for computing graph edit distance; it outperforms the state-of-the-art methods by over three orders of magnitude. It also shows that CSI_GED scales the computation gracefully to larger and distant graphs on which current methods fail to run. Moreover, we evaluated CSI_GED as a stand-alone graph edit similarity search query method. The experiments show that CSI_GED is effective and scalable, and outperforms the state-of-the-art indexing-based methods by over two orders of magnitude.     

基于图像数据挖掘的有向图模型检索方法

为充分挖掘图像数据信息,提出了一种有向图模型检索方法,结合距离测度初次检索和有向图距离二次检索提高图像检索性能。首先,采用传统的纹理、边缘和颜色特征以及特征之间的欧氏距离测度来进行初次检索,得到一个查询排序列表;在此基础上,结合距离测度与余弦测度设计图像之间的相关测度,在不同的相关测度阈值下构建图像数据集的有向图模型集合;最后,计算有向图距离,据此进行二次检索,降低误检现象。在COREL和ImageCLEF两个数据集上的图像检索实验结果表明,该方法的平均精确度和平均召回率指标高。     

Topology based 2D engineering drawing and 3D model matching for process plant

Process plant models mainly include 3D models and 2D engineering drawings. Matching calculation between these CAD models has wide applicability in model consistency check and retrieval. In process plant, engineering design standards make 2D engineering drawing and 3D model differ in geometry, proportion and structure, leading to the inapplicability of current shape-feature based matching approaches. Since connection relationships between components are the core of a process plant, a topology based algorithm is proposed. Firstly, by exploiting components as vertices and relationships as edges, both 2D engineering drawing and 3D model are preprocessed into graph structures. Then each model’s relationship types are extracted from the graph. Finally, regarding the extracted relationship types as primary feature, feature similarity is calculated to measure the matching degree between their corresponding models. The proposed algorithm is geometric deformation invariant. Experiments with industrial applications are presented, which demonstrates the effectiveness and feasibility of the proposed algorithm.