A new algorithm for inexact graph matching

Linkage of medical databases, including insurer claims and electronic health records (EHRs), is increasingly common. However, few studies have investigated the behavior and output of linkage software. To determine how linkage quality is affected by different algorithms, blocking variables, methods for string matching and weight determination, and decision rules, we compared the performance of 4 nonproprietary linkage software packages linking patient identifiers from noninteroperable inpatient and outpatient EHRs. We linked datasets using first and last name, gender, and date of birth (DOB). We evaluated DOB and year of birth (YOB) as blocking variables and used exact and inexact matching methods. We compared the weights assigned to record pairs and evaluated how matching weights corresponded to a gold standard, medical record number. Deduplicated datasets contained 69,523 inpatient and 176,154 outpatient records, respectively. Linkage runs blocking on DOB produced weights ranging in number from 8 for exact matching to 64,273 for inexact matching. Linkage runs blocking on YOB produced 8 to 916,806 weights. Exact matching matched record pairs with identical test characteristics (sensitivity 90.48%, specificity 99.78%) for the highest ranked group, but algorithms differentially prioritized certain variables. Inexact matching behaved more variably, leading to dramatic differences in sensitivity (range 0.04–93.36%) and positive predictive value (PPV) (range 86.67–97.35%), even for the most highly ranked record pairs. Blocking on DOB led to higher PPV of highly ranked record pairs. An ensemble approach based on averaging scaled matching weights led to modestly improved accuracy. In summary, we found few differences in the rankings of record pairs with the highest matching weights across 4 linkage packages. Performance was more consistent for exact string matching than for inexact string matching. Most methods and software packages performed similarly when comparing matching accuracy with the gold standard. In some settings, an ensemble matching approach may outperform individual linkage algorithms.

This paper addresses the multi-attributed graph matching problem considering multiple attributes jointly while preserving the characteristics of each attribute. Since most of conventional graph matching algorithms integrate multiple attributes to construct a single attribute in an oversimplified way, the information from multiple attributes are not often fully exploited. In order to solve this problem, we propose a novel multi-layer graph structure that can preserve the particularities of each attribute in separated layers. Then, we also propose a multi-attributed graph matching algorithm based on the random walk centrality for the proposed multi-layer graph structure. We compare the proposed algorithm with other state-of-the-art graph matching algorithms based on the single-layer structure using synthetic and real datasets, and prove the superior performance of the proposed multi-layer graph structure and matching algorithm.

Graph matching based on spectral embedding with missing value

Towards exact and inexact approximate matching of executable binaries

Graph and hypergraph matching are fundamental problems in computer vision, which have been receiving a steadily growing attention in the last two decades due to the recent modern algorithms and models that are both fast and accurate. Graph and hypergraph matching are successful in tackling many real-world tasks that require 2D and 3D feature matching and alignment. Matching is a general problem in vision and graphs have always been quintessential for modeling information that has both local and longer range connections. Therefore, graph matching will continue to influence computer vision and robotics research, crossing over many different mathematical and computational models, including Bayesian networks, conditional and Markov random fields, spectral graph models, and, more recently, deep neural networks. While graph matching is limited to using pairwise relationships, hypergraph matching permits the use of relationships between sets of features of any order. Consequently, it carries the promise to make matching more robust to changes in scale, deformations, and outliers. In this chapter, we present several key ideas, computational models, and optimization methods that introduced in the literature the possibility to learn graph and hypergraph matching in a semi-supervised or even completely unsupervised fashion. We start by describing two methods for solving graph and hypergraph matching based on spectral matching and integer projected fixed point methods, introduced in Chap. 1. Then, based on the same intuition (also discussed in Chap. 1) that correct assignments form a strong cluster of agreements, we follow up by introducing the main approach to learning as it applies to graph and hypergraph matching, as well as the more general Maximum A Posteriori (MAP) inference problem in probabilistic graphical models (MRFs and CRFs). In the last part of the chapter, we demonstrate experimentally the effectiveness of the algorithms presented and, whenever possible, provide extensive comparisons to other top published methods. Moreover, we show that our learning approach is general and can significantly boost the performance of different state-of-the-art matching algorithms in the literature.

Graph matching aims at establishing correspondences between graph elements, and is widely used in many computer vision tasks. Among recently proposed graph matching algorithms, those utilizing the path following strategy have attracted special research attentions due to their exhibition of state-of-the-art performances. However, the paths computed in these algorithms often contain singular points, which could hurt the matching performance if not dealt properly. To deal with this issue, we propose a novel path following strategy, named branching path following (BPF), to improve graph matching accuracy. In particular, we first propose a singular point detector by solving a KKT system, and then design a branch switching method to seek for better paths at singular points. Moreover, to reduce the computational burden of the BPF strategy, an adaptive path estimation (APE) strategy is integrated into BPF to accelerate the convergence of searching along each path. A new graph matching algorithm named ABPF-G is developed by applying APE and BPF to a recently proposed path following algorithm named GNCCP (Liu & Qiao 2014). Experimental results reveal how our approach consistently outperforms state-of-the-art algorithms for graph matching on five public benchmark datasets.

Frequent subgraph mining refers usually to graph matching and it is widely used when analyzing big data with large graphs. A lot of research works dealt with structural exact or inexact graph matching but a little attention is paid to semantic matching when graph vertices and/or edges are attributed and typed. Therefore, it seems very interesting to integrate background knowledge into the analysis and that extracted frequent subgraphs should become more pruned by applying a new semantic filter instead of using only structural similarity in graph matching process. Consequently, this paper focuses on developing a new hybrid approximate structural semantic graph matching to discover a set of frequent subgraphs. It uses both similarity measures. An approximate structural similarity function based on graph edit distance function and a semantic vertices similarity function based on possibilistic information affinity function. Both structural and semantic filters contribute together to prune extracted frequent sets. Indeed, new hybrid structural-semantic frequent subgraph mining approach will be suitable to be applied to several applications such as community detection and social network analysis.

In this paper, we propose to represent shapes by graphs. Based on graphic primitives extracted from the binary images, attributed relational graphs were generated. Thus, the nodes of the graph represent shape primitives like vectors and quadrilaterals while arcs describing the mutual primitives relations. To be invariant to transformations such as rotation and scaling, relative geometric features extracted from primitives are associated to nodes and edges as attributes. Concerning graph matching, due to the fact of NP-completeness of graph-subgraph isomorphism, a considerable attention is given to different strategies of inexact graph matching. We also present a new scoring function to compute a similarity score between two graphs, using the numerical values associated to the nodes and edges of the graphs. The adaptation of a greedy graph matching algorithm with the new scoring function demonstrates significant performance improvements over traditional exhaustive searches of graph matching.

A graph can be exactly specified by the spectrum and corresponding eigenvectors of its adjacency matrix. This provides a solid foundation for spectrum based graph matching. However, most previous methods ignore the spectral multiplicity, which may significantly affect the matching accuracy. In this paper, we address the problem of minimizing the matching error when graph spectral multiplicity is involved. We first model spectral multiplicity by the sub-eigenspace rotation matrix R, and integrate R into the spectrum based graph matching model. We then focus on the exact graph matching problem, and show how to establish the vertex-to-vertex correspondence by iteratively optimizing the sub-eigenspace rotation matrix R and the permutation matrix P. A reliable matching initialization method is proposed to make this process converge rapidly. Finally, we extend the approach to the inexact graph matching problem by optimally warping two graphs to the same size. The proposed approach is robust and efficient. We support our approach with numerical experiments and demonstrate its effectiveness in the practical application of uncalibrated stereo matching.

We consider how continuous-time quantum walks can be used for graph matching. We focus in detail on both exact and inexact graph matching, and consider in depth the problem of measuring graph similarity. We commence by constructing an auxiliary graph, in which the two graph to be matched are co-joined by a layer of indicator nodes (one for each potential correspondence between a pair of nodes). We simulate a continuous time quantum walk in parallel on the two graphs. The layer of connecting indicator nodes in the auxiliary graph allow quantum interference to take place between the two walks. The interference amplitudes on the indicator nodes are determined by differences in the two walks. We show how these interference amplitudes can be used to compute graph edit distances without explicitly determining node correspondences.

Many graph matching algorithms follow the approach of node-similarity measurement, that is, matching graphs by means of comparing the corresponding pairs of nodes of the graphs. Based on this idea, the authors propose a high-level schema for node-to-node graph matching, namely N2N graph matching algorithm schema. The chapter shows that such a N2N graph matching algorithm schema is versatile enough to subsume most of the representative node-to-node based graph matching algorithms. It is also shown that improved algorithms can be derived from this N2N graph matching schema, compared with various corresponding algorithms. In addition, the authors point out the limitation and constraints of the propose algorithm schema and suggest some possible treatments.

Software tools for Social Network Analysis (SNA) are being developed which support various types of analysis of social networks extracted from social media websites (e.g., Twitter). Once extracted and stored in a database such social networks are amenable to analysis by SNA software. This data analysis often involves searching for occurrences of various subgraph patterns (i.e., graphical representations of entities and relationships). The authors have developed the Graph Matching Toolkit (GMT) which provides an intuitive Graphical User Interface (GUI) for a heuristic graph matching algorithm called the Truncated Search Tree (TruST) algorithm. GMT is a visual interface for graph matching algorithms processing large social networks. GMT enables an analyst to draw a subgraph pattern by using a mouse to select categories and labels for nodes and links from drop-down menus. GMT then executes the TruST algorithm to find the top five occurrences of the subgraph pattern within the social network stored in the database. GMT was tested using a simulated counter-insurgency dataset consisting of cellular phone communications within a populated area of operations in Iraq. The results indicated GMT (when executing the TruST graph matching algorithm) is a time-efficient approach to searching large social networks. GMT’s visual interface to a graph matching algorithm enables intelligence analysts to quickly analyze and summarize the large amounts of data necessary to produce actionable intelligence.

Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.

Integrating coarse-grained reconfigurable architectures (CGRAs) into a System-on-a-Chip (SoC) presents many benefits as well as important challenges. One of the challenges is how to customize the architecture for the target applications efficiently and effectively without performing explicit design space exploration. In this article we present a novel methodology for incremental interconnect customization of CGRAs that can suggest a new interconnection architecture which is able to maximize the performance for a given set of application kernels while minimizing the hardware cost. In our methodology, we translate the problem of interconnect customization into that of inexact graph matching, and we devised a heuristic for A* search algorithm to efficiently solve the inexact graph matching problem. Our experimental results demonstrate that our customization method can quickly find application-optimized interconnections that exhibit 80% higher performance on average compared to the base architecture which has mesh interconnections, with little energy and hardware increase in interconnections and muxes.

Exact string matching in labeled graphs is the problem of searching paths of a graph G=(V, E) such that the concatenation of their node labels is equal to a given pattern string P [1. m ]. This basic problem can be found at the heart of more complex operations on variation graphs in computational biology, of query operations in graph databases, and of analysis operations in heterogeneous networks. We prove a conditional lower bound stating that, for any constant ε > 0, an O (| E | 1 - ε m ) time, or an O (| E | m 1 - ε )time algorithm for exact string matching in graphs, with node labels and pattern drawn from a binary alphabet, cannot be achieved unless the Strong Exponential Time Hypothesis ( SETH ) is false. This holds even if restricted to undirected graphs with maximum node degree 2—that is, to zig-zag matching in bidirectional strings , or to deterministic directed acyclic graphs whose nodes have maximum sum of indegree and outdegree 3. These restricted cases make the lower bound stricter than what can be directly derived from related bounds on regular expression matching (Backurs and Indyk, FOCS’16). In fact, our bounds are tight in the sense that lowering the degree or the alphabet size yields linear time solvable problems. An interesting corollary is that exact and approximate matching are equally hard (i.e., quadratic time) in graphs under SETH . In comparison, the same problems restricted to strings have linear time vs quadratic time solutions, respectively (approximate pattern matching having also a matching SETH lower bound (Backurs and Indyk, STOC’15)).