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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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Jaume Gibert, Ernest Valveny, & Horst Bunke. (2011). Vocabulary Selection for Graph of Words Embedding. In J. Vitria, J. M. R. Sanches, & M. Hernández (Eds.), 5th Iberian Conference on Pattern Recognition and Image Analysis (Vol. 6669, pp. 216–223). LNCS. Berlin: Springer.
Abstract: The Graph of Words Embedding consists in mapping every graph in a given dataset to a feature vector by counting unary and binary relations between node attributes of the graph. It has been shown to perform well for graphs with discrete label alphabets. In this paper we extend the methodology to graphs with n-dimensional continuous attributes by selecting node representatives. We propose three different discretization procedures for the attribute space and experimentally evaluate the dependence on both the selector and the number of node representatives. In the context of graph classification, the experimental results reveal that on two out of three public databases the proposed extension achieves superior performance over a standard reference system.
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Jaume Gibert, Ernest Valveny, & Horst Bunke. (2011). Dimensionality Reduction for Graph of Words Embedding. In Xiaoyi Jiang, Miquel Ferrer, & Andrea Torsello (Eds.), 8th IAPR-TC-15 International Workshop. Graph-Based Representations in Pattern Recognition (Vol. 6658, pp. 22–31). LNCS.
Abstract: The Graph of Words Embedding consists in mapping every graph of a given dataset to a feature vector by counting unary and binary relations between node attributes of the graph. While it shows good properties in classification problems, it suffers from high dimensionality and sparsity. These two issues are addressed in this article. Two well-known techniques for dimensionality reduction, kernel principal component analysis (kPCA) and independent component analysis (ICA), are applied to the embedded graphs. We discuss their performance compared to the classification of the original vectors on three different public databases of graphs.
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Jaume Gibert, Ernest Valveny, & Horst Bunke. (2010). Graph of Words Embedding for Molecular Structure-Activity Relationship Analysis. In 15th Iberoamerican Congress on Pattern Recognition (Vol. 6419, 30–37). LNCS.
Abstract: Structure-Activity relationship analysis aims at discovering chemical activity of molecular compounds based on their structure. In this article we make use of a particular graph representation of molecules and propose a new graph embedding procedure to solve the problem of structure-activity relationship analysis. The embedding is essentially an arrangement of a molecule in the form of a vector by considering frequencies of appearing atoms and frequencies of covalent bonds between them. Results on two benchmark databases show the effectiveness of the proposed technique in terms of recognition accuracy while avoiding high operational costs in the transformation.
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