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Modern Methods for Characterization of Social Networks through Network Models
Published in Natalie M. Scala, James P. Howard, Handbook of Military and Defense Operations Research, 2020
Christine M. Schubert Kabban, Fairul Mohd-Zaid, Richard F. Deckro
Graph matching methodology has developed over many decades and a comprehensive survey of methods and applications for graph matching over a span of three decades from the early 1970s to 2004 was conducted by Conte et al. (2004). In general, graph matching is categorized into two main groups: Exact Matching and Inexact Matching. Exact Matching methods consider edge preserving matches or edge mappings such as graph isomorphisms, graph homomorphisms, or maximum common subgraphs (MCS). Such methods are NP-complete with the exception of graph isomorphism which has not yet been shown to be NP-complete. Currently, MCS methods are only able to handle relatively small graphs due to their computational complexity. Exact Matching methods include other techniques such as Tree Searches which work to iteratively expand the set of paired matched nodes, group theory, subgraph decomposition, or decision trees on a library of known graphs.
Graph Edit Distance—Theory, Algorithms, and Applications
Published in Olivier Lézoray, Leo Grady, Image Processing and Analysis with Graphs, 2012
Graph matching is the specific process of evaluating the structural similarity of two graphs1,2. It can be split into two categories, namely exact and error-tolerant graph matching. In exact graph matching, the basic objective is to decide whether two graphs or parts of them are identical in terms of their structure and labels. Methods for exact graph matching include graph isomorphism, subgraph isomorphism [15], maximum common subgraph [16], and minimum common supergraph [17]. The main advantage of exact graph matching methods is their stringent definition and solid mathematical foundation. Nevertheless, it is still imperative for the underlying graphs to share isomorphic parts to be considered similar. This means that the two graphs under comparison must be identical to a large extent in terms of structure and labels to produce high similarity values. In practice, node and edge labels used to describe the properties of the underlying objects (represented by the graphs) are often of continuous nature. In this situation, at least two problems arise. First, it is not sufficient to check whether two labels are identical or not, but one has also to evaluate their similarity. In addition, under all the matching procedures mentioned so far, two labels will be considered different regardless of the degree of difference between them. This may lead to considering two graphs with similar, but not identical labels completely dissimilar even if they have identical structure. It is therefore clear that a more sophisticated method is needed to measure the dissimilarity between graphs, taking into account such limitations. This leads to the definition of inexact, or error-tolerant, graph matching.
Automatically inferring technology compatibility with an ontology and graph rewriting rules
Published in Journal of Engineering Design, 2021
The concept of graph matching is more formally explained using graph morphisms. Let G be the system graph that the rule r is to be applied to. When there is a match of the pattern L in G, there is a graph morphism . A graph morphism m consists of two functions and , such that and (Ehrig et al. 2015). Here V denotes the vertices of a graph and E its edges. Furthermore, s is a function that retrieves the source node of an edge, and t a function that retrieves the target node.
Grid graph-based large-scale point clouds registration
Published in International Journal of Digital Earth, 2023
Yi Han, Guangyun Zhang, Rongting Zhang
Affinity graph with candidate matches. The graph matching process between and can be represented as a ranking within the association graph . The attribute is encoded into the affinity matrix , which is utilized for calculating the graph matching. The affinity matrix element , denoting the affinity of , measures the mutual consistency of . is as defined as follows: Where , , . Non-diagonal element is pairwise similarity between and . The diagonal term denotes the unary similarity of a correspondence. The column-wise vectorized replica of , represented as , is used in graph matching to seek the optimal solution that maximizes the similarity function, which can be expressed as follows:
A comprehensive study on face recognition: methods and challenges
Published in The Imaging Science Journal, 2020
Parekh Payal, Mahesh M. Goyani
Konen and Malsburg [56] used Dynamic Link Architecture (DLA) to finding and mapping topological, feature preserving mappings between parts of the input image. Such mappings are systems of pairwise links that are neighbourhood preserving and that connect pairs of points with the same local properties in the input pattern. Wiskott et al. [57] introduced Elastic Bunch-graph Matching (EBGM) which produces label graph based on a Gabor wavelet transform and then performed similarity measure between the image graph which compared with dataset images. Lin et al. [58] used Probabilistic Decision-based Neural Network (PDBNN) for face detector, eye localizer determines the positions of both eyes in order to generate meaningful feature vectors. The facial region proposed contains eyebrows, eyes, and nose, but excluding mouth and face recognizer. Liu and Wechsler [59] used FR for genetic algorithms (GAs) in determining the optimal basis for encoding human faces. In analogy to the pursuit, methods are called Evolutionary Pursuit (EP). Yang [60] used Kernel Methods (KM) for learning low dimensional representation for FR. E.g. KPCA and KIDA. Srisuk et al. [61] used Trace Transform (TT) to the generalization of the Radon transform, which is a new tool for image processing which can be used for recognizing objects under transformations (linear distortions), e.g. rotation, translation, and scaling. Queirolo et al. [62] used Simulated Annealing for range image registration with the Surface Interpenetration Measure (SIM), as similarity measure, in order to match two face images of 3D-FR. Liu et al. [63], used Partial Least Squares (PLS) for learned on video and audio features to distinguish each class from the other confusing ones.