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Miquel Ferrer, Ernest Valveny, & F. Serratosa. (2006). Spectral Median Graphs Applied to Graphical Symbol Recognition. In 11th Iberoamerican Congress on Pattern Recognition (CIARP´06), J.P. Martinez–Trinidad et al. (Eds.), LNCS 4225: 774–783.
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Miquel Ferrer, Ernest Valveny, & F. Serratosa. (2007). Bounding the Size Of the Median Graph. In 3rd Iberian Conference on Pattern Recognition and Image Analysis (IbPRIA 2007), J. Marti et al. (Eds.) LNCS 4478(2):491–498.
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Miquel Ferrer, Ernest Valveny, & F. Serratosa. (2007). Comparison Between two Spectral-based Methods for Median Graph Computation. In 3rd Iberian Conference on Pattern Recognition and Image Analysis (IbPRIA 2007), J. Marti et al. (Eds.) LNCS 4478(2):580–587.
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Miquel Ferrer, Ernest Valveny, & F. Serratosa. (2007). A New Optimal Algorithm for the Generalized Median Graph Computation Based on the Maximum Common Subgraph.
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Miquel Ferrer, Ernest Valveny, & F. Serratosa. (2009). Median graph: A new exact algorithm using a distance based on the maximum common subgraph. PRL - Pattern Recognition Letters, 30(5), 579–588.
Abstract: Median graphs have been presented as a useful tool for capturing the essential information of a set of graphs. Nevertheless, computation of optimal solutions is a very hard problem. In this work we present a new and more efficient optimal algorithm for the median graph computation. With the use of a particular cost function that permits the definition of the graph edit distance in terms of the maximum common subgraph, and a prediction function in the backtracking algorithm, we reduce the size of the search space, avoiding the evaluation of a great amount of states and still obtaining the exact median. We present a set of experiments comparing our new algorithm against the previous existing exact algorithm using synthetic data. In addition, we present the first application of the exact median graph computation to real data and we compare the results against an approximate algorithm based on genetic search. These experimental results show that our algorithm outperforms the previous existing exact algorithm and in addition show the potential applicability of the exact solutions to real problems.
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Miquel Ferrer, Ernest Valveny, & F. Serratosa. (2009). Median Graphs: A Genetic Approach based on New Theoretical Properties. PR - Pattern Recognition, 42(9), 2003–2012.
Abstract: Given a set of graphs, the median graph has been theoretically presented as a useful concept to infer a representative of the set. However, the computation of the median graph is a highly complex task and its practical application has been very limited up to now. In this work we present two major contributions. On one side, and from a theoretical point of view, we show new theoretical properties of the median graph. On the other side, using these new properties, we present a new approximate algorithm based on the genetic search, that improves the computation of the median graph. Finally, we perform a set of experiments on real data, where none of the existing algorithms for the median graph computation could be applied up to now due to their computational complexity. With these results, we show how the concept of the median graph can be used in real applications and leaves the box of the only-theoretical concepts, demonstrating, from a practical point of view, that can be a useful tool to represent a set of graphs.
Keywords: Median graph; Genetic search; Maximum common subgraph; Graph matching; Structural pattern recognition
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Miquel Ferrer, Ernest Valveny, & F. Serratosa. (2009). Median Graph Computation by means of a Genetic Approach Based on Minimum Common Supergraph and Maximum Common Subraph. In 4th Iberian Conference on Pattern Recognition and Image Analysis (Vol. 5524, 346–353). LNCS. Springer Berlin Heidelberg.
Abstract: Given a set of graphs, the median graph has been theoretically presented as a useful concept to infer a representative of the set. However, the computation of the median graph is a highly complex task and its practical application has been very limited up to now. In this work we present a new genetic algorithm for the median graph computation. A set of experiments on real data, where none of the existing algorithms for the median graph computation could be applied up to now due to their computational complexity, show that we obtain good approximations of the median graph. Finally, we use the median graph in a real nearest neighbour classification showing that it leaves the box of the only-theoretical concepts and demonstrating, from a practical point of view, that can be a useful tool to represent a set of graphs.
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