Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics systems, learning molecular fingerprints, predicting protein interface, and classifying diseases demand a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures (like the dependency trees of sentences and the scene graphs of images) is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are neural models that capture the dependence of graphs via message passing between the nodes of graphs. In recent years, variants of GNNs such as graph convolutional network (GCN), graph attention network (GAT), graph recurrent network (GRN) have demonstrated ground-breaking performances on many deep learning tasks. In this survey, we propose a general design pipeline for GNN models and discuss the variants of each component, systematically categorize the applications, and propose four open problems for future research.

Graph Neural Networks: A Review of Methods and Applications

Models that depict innovation as a smooth, well-behaved linear process badly misspecify the nature and direction of the causal factors at work. Innovation is complex, uncertain, somewhat disorderly, and subject to changes of many sorts. Innovation is also difficult to measure and demands close coordination of adequate technical knowledge and excellent market judgment in order to satisfy economic, technological, and other types of constraints—all simultaneously. The process of innovation must be viewed as a series of changes in a complete system not only of hardware, but also of market environment, production facilities and knowledge, and the social contexts of the innovation organization.

An Overview of Innovation

A recent paper posed the question: "Graph Matching: What are we really talking about?". Far from providing a definite answer to that question, in this paper we will try to characterize the role that graphs play within the Pattern Recognition field. To this aim two taxonomies are presented and discussed. The first includes almost all the graph matching algorithms proposed from the late seventies, and describes the different classes of algorithms. The second taxonomy considers the types of common applications of graph-based techniques in the Pattern Recognition and Machine Vision field.

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Thirty years of graph matching in pattern recognition

We present an algorithm for graph isomorphism and subgraph isomorphism suited for dealing with large graphs. A first version of the algorithm has been presented in a previous paper, where we examined its performance for the isomorphism of small and medium size graphs. The algorithm is improved here to reduce its spatial complexity and to achieve a better performance on large graphs; its features are analyzed in detail with special reference to time and memory requirements. The results of a testing performed on a publicly available database of synthetically generated graphs and on graphs relative to a real application dealing with technical drawings are presented, confirming the effectiveness of the approach, especially when working with large graphs.

A (sub)graph isomorphism algorithm for matching large graphs

We propose an error-tolerant subgraph isomorphism algorithm formulated in terms of region adjacency graphs (RAG). A set of edit operations to transform one RAG into another one are defined as regions are represented by polylines and string matching techniques are used to measure their similarity. The algorithm follows a branch and bound approach driven by the RAG edit operations. This formulation allows matching computing under distorted inputs and also reaching a solution in a near polynomial time. The algorithm has been used for recognizing symbols in hand drawn diagrams.

Symbol recognition by error-tolerant subgraph matching between region adjacency graphs

The recognition of symbols in graphic documents is an intensive research activity in the community of pattern recognition and document analysis. A key issue in the interpretation of maps, engineering drawings, diagrams, etc. is the recognition of domain dependent symbols according to a symbol database. In this work we first review the most outstanding symbol recognition methods from two different points of view: application domains and pattern recognition methods. In the second part of the paper, open and unaddressed problems involved in symbol recognition are described, analyzing their current state of art and discussing future research challenges. Thus, issues such as symbol representation, matching, segmentation, learning, scalability of recognition methods and performance evaluation are addressed in this work. Finally, we discuss the perspectives of symbol recognition concerning to new paradigms such as user interfaces in handheld computers or document database and WWW indexing by graphical content.

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Symbol Recognition: Current Advances and Perspectives

In this paper, we present a segmentation-free word spotting method that is able to deal with heterogeneous document image collections. We propose a patch-based framework where patches are represented by a bag-of-visual-words model powered by SIFT descriptors. A later refinement of the feature vectors is performed by applying the latent semantic indexing technique. The proposed method performs well on both handwritten and typewritten historical document images. We have also tested our method on documents written in non-Latin scripts.

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Browsing Heterogeneous Document Collections by a Segmentation-Free Word Spotting Method

Offline signature verification is one of the most challenging tasks in biometrics and document forensics. Unlike other verification problems, it needs to model minute but critical details between genuine and forged signatures, because a skilled falsification might often resembles the real signature with small deformation. This verification task is even harder in writer independent scenarios which is undeniably fiscal for realistic cases. In this paper, we model an offline writer independent signature verification task with a convolutional Siamese network. Siamese networks are twin networks with shared weights, which can be trained to learn a feature space where similar observations are placed in proximity. This is achieved by exposing the network to a pair of similar and dissimilar observations and minimizing the Euclidean distance between similar pairs while simultaneously maximizing it between dissimilar pairs. Experiments conducted on cross-domain datasets emphasize the capability of our network to model forgery in different languages (scripts) and handwriting styles. Moreover, our designed Siamese network, named SigNet, exceeds the state-of-the-art results on most of the benchmark signature datasets, which paves the way for further research in this direction.

Josep Lladós

Papers

Symbol recognition by error-tolerant subgraph matching between region adjacency graphs

Symbol Recognition: Current Advances and Perspectives

Browsing Heterogeneous Document Collections by a Segmentation-Free Word Spotting Method

SigNet: Convolutional Siamese Network for Writer Independent Offline Signature Verification

Efficient segmentation-free keyword spotting in historical document collections