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Gemma Sanchez, Josep Llados, & K. Tombre. (2002). A mean string algorithm to compute the average among a set of 2D shapes. PRL - Pattern Recognition Letters, 23(1-3), 203–214.
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Jaume Gibert, Ernest Valveny, & Horst Bunke. (2013). Embedding of Graphs with Discrete Attributes Via Label Frequencies. IJPRAI - International Journal of Pattern Recognition and Artificial Intelligence, 27(3), 1360002–1360029.
Abstract: Graph-based representations of patterns are very flexible and powerful, but they are not easily processed due to the lack of learning algorithms in the domain of graphs. Embedding a graph into a vector space solves this problem since graphs are turned into feature vectors and thus all the statistical learning machinery becomes available for graph input patterns. In this work we present a new way of embedding discrete attributed graphs into vector spaces using node and edge label frequencies. The methodology is experimentally tested on graph classification problems, using patterns of different nature, and it is shown to be competitive to state-of-the-art classification algorithms for graphs, while being computationally much more efficient.
Keywords: Discrete attributed graphs; graph embedding; graph classification
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Jaume Gibert, Ernest Valveny, & Horst Bunke. (2012). Graph Embedding in Vector Spaces by Node Attribute Statistics. PR - Pattern Recognition, 45(9), 3072–3083.
Abstract: Graph-based representations are of broad use and applicability in pattern recognition. They exhibit, however, a major drawback with regards to the processing tools that are available in their domain. Graphembedding into vectorspaces is a growing field among the structural pattern recognition community which aims at providing a feature vector representation for every graph, and thus enables classical statistical learning machinery to be used on graph-based input patterns. In this work, we propose a novel embedding methodology for graphs with continuous nodeattributes and unattributed edges. The approach presented in this paper is based on statistics of the node labels and the edges between them, based on their similarity to a set of representatives. We specifically deal with an important issue of this methodology, namely, the selection of a suitable set of representatives. In an experimental evaluation, we empirically show the advantages of this novel approach in the context of different classification problems using several databases of graphs.
Keywords: Structural pattern recognition; Graph embedding; Data clustering; Graph classification
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Jaume Gibert, Ernest Valveny, & Horst Bunke. (2012). Feature Selection on Node Statistics Based Embedding of Graphs. PRL - Pattern Recognition Letters, 33(15), 1980–1990.
Abstract: Representing a graph with a feature vector is a common way of making statistical machine learning algorithms applicable to the domain of graphs. Such a transition from graphs to vectors is known as graphembedding. A key issue in graphembedding is to select a proper set of features in order to make the vectorial representation of graphs as strong and discriminative as possible. In this article, we propose features that are constructed out of frequencies of node label representatives. We first build a large set of features and then select the most discriminative ones according to different ranking criteria and feature transformation algorithms. On different classification tasks, we experimentally show that only a small significant subset of these features is needed to achieve the same classification rates as competing to state-of-the-art methods.
Keywords: Structural pattern recognition; Graph embedding; Feature ranking; PCA; Graph classification
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Joan Mas, Josep Llados, Gemma Sanchez, & J.A. Jorge. (2010). A syntactic approach based on distortion-tolerant Adjacency Grammars and a spatial-directed parser to interpret sketched diagrams. PR - Pattern Recognition, 43(12), 4148–4164.
Abstract: This paper presents a syntactic approach based on Adjacency Grammars (AG) for sketch diagram modeling and understanding. Diagrams are a combination of graphical symbols arranged according to a set of spatial rules defined by a visual language. AG describe visual shapes by productions defined in terms of terminal and non-terminal symbols (graphical primitives and subshapes), and a set functions describing the spatial arrangements between symbols. Our approach to sketch diagram understanding provides three main contributions. First, since AG are linear grammars, there is a need to define shapes and relations inherently bidimensional using a sequential formalism. Second, our parsing approach uses an indexing structure based on a spatial tessellation. This serves to reduce the search space when finding candidates to produce a valid reduction. This allows order-free parsing of 2D visual sentences while keeping combinatorial explosion in check. Third, working with sketches requires a distortion model to cope with the natural variations of hand drawn strokes. To this end we extended the basic grammar with a distortion measure modeled on the allowable variation on spatial constraints associated with grammar productions. Finally, the paper reports on an experimental framework an interactive system for sketch analysis. User tests performed on two real scenarios show that our approach is usable in interactive settings.
Keywords: Syntactic Pattern Recognition; Symbol recognition; Diagram understanding; Sketched diagrams; Adjacency Grammars; Incremental parsing; Spatial directed parsing
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