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Albert Gordo, Alicia Fornes, Ernest Valveny and Josep Llados. 2010. A Bag of Notes Approach to Writer Identification in Old Handwritten Music Scores. 9th IAPR International Workshop on Document Analysis Systems.247–254.
Abstract: Determining the authorship of a document, namely writer identification, can be an important source of information for document categorization. Contrary to text documents, the identification of the writer of graphical documents is still a challenge. In this paper we present a robust approach for writer identification in a particular kind of graphical documents, old music scores. This approach adapts the bag of visual terms method for coping with graphic documents. The identification is performed only using the graphical music notation. For this purpose, we generate a graphic vocabulary without recognizing any music symbols, and consequently, avoiding the difficulties in the recognition of hand-drawn symbols in old and degraded documents. The proposed method has been tested on a database of old music scores from the 17th to 19th centuries, achieving very high identification rates.
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Miquel Ferrer, Ernest Valveny, F. Serratosa, K. Riesen and Horst Bunke. 2010. Generalized Median Graph Computation by Means of Graph Embedding in Vector Spaces. PR, 43(4), 1642–1655.
Abstract: The median graph has been presented as a useful tool to represent a set of graphs. Nevertheless its computation is very complex and the existing algorithms are restricted to use limited amount of data. In this paper we propose a new approach for the computation of the median graph based on graph embedding. Graphs are embedded into a vector space and the median is computed in the vector domain. We have designed a procedure based on the weighted mean of a pair of graphs to go from the vector domain back to the graph domain in order to obtain a final approximation of the median graph. Experiments on three different databases containing large graphs show that we succeed to compute good approximations of the median graph. We have also applied the median graph to perform some basic classification tasks achieving reasonable good results. These experiments on real data open the door to the application of the median graph to a number of more complex machine learning algorithms where a representative of a set of graphs is needed.
Keywords: Graph matching; Weighted mean of graphs; Median graph; Graph embedding; Vector spaces
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Miquel Ferrer, Ernest Valveny, F. Serratosa, I. Bardaji and Horst Bunke. 2009. Graph-based k-means clustering: A comparison of the set versus the generalized median graph. 13th International Conference on Computer Analysis of Images and Patterns. Springer Berlin Heidelberg, 342–350. (LNCS.)
Abstract: In this paper we propose the application of the generalized median graph in a graph-based k-means clustering algorithm. In the graph-based k-means algorithm, the centers of the clusters have been traditionally represented using the set median graph. We propose an approximate method for the generalized median graph computation that allows to use it to represent the centers of the clusters. Experiments on three databases show that using the generalized median graph as the clusters representative yields better results than the set median graph.
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Miquel Ferrer, Ernest Valveny and F. Serratosa. 2009. Median Graph Computation by means of a Genetic Approach Based on Minimum Common Supergraph and Maximum Common Subraph. 4th Iberian Conference on Pattern Recognition and Image Analysis. Springer Berlin Heidelberg, 346–353. (LNCS.)
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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Miquel Ferrer, Ernest Valveny and F. Serratosa. 2009. Median Graphs: A Genetic Approach based on New Theoretical Properties. PR, 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 and F. Serratosa. 2009. Median graph: A new exact algorithm using a distance based on the maximum common subgraph. PRL, 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 and Horst Bunke. 2008. Exact Median Graph Computation via Graph Embedding. 12th International Workshop on Structural and Syntactic Pattern Recognition.15–24. (LNCS.)
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Miquel Ferrer, Ernest Valveny, F. Serratosa, K. Riesen and Horst Bunke. 2008. An Approximate Algorith for Median Graph Computation using Graph Embedding. 19th International Conference on Pattern Recognition..
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Miquel Ferrer, Ernest Valveny and 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 and F. Serratosa. 2007. Comparison Between two Spectral-based Methods for Median Graph Computation. 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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