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Miquel Ferrer, Ernest Valveny, F. Serratosa, K. Riesen, & Horst Bunke. (2008). An Approximate Algorith for Median Graph Computation using Graph Embedding. In 19th International Conference on Pattern Recognition..
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Miquel Ferrer, Ernest Valveny, F. Serratosa, K. Riesen, & Horst Bunke. (2010). Generalized Median Graph Computation by Means of Graph Embedding in Vector Spaces. PR - Pattern Recognition, 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, & Horst Bunke. (2009). Graph-based k-means clustering: A comparison of the set versus the generalized median graph. In 13th International Conference on Computer Analysis of Images and Patterns (Vol. 5702, 342–350). LNCS. Springer Berlin Heidelberg.
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, F. Serratosa, & Horst Bunke. (2008). Exact Median Graph Computation via Graph Embedding. In 12th International Workshop on Structural and Syntactic Pattern Recognition (Vol. 5324, 15–24). LNCS.
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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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Miquel Ferrer, & Ernest Valveny. (2007). Combination of OCR Engines for Page Segmentation based on Performance Evaluation. In 9th International Conference on Document Analysis and Recognition (Vol. 2, 784–788).
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Miquel Ferrer, Dimosthenis Karatzas, Ernest Valveny, I. Bardaji, & Horst Bunke. (2011). A Generic Framework for Median Graph Computation based on a Recursive Embedding Approach. CVIU - Computer Vision and Image Understanding, 115(7), 919–928.
Abstract: The median graph has been shown to be a good choice to obtain a represen- tative of a set of graphs. However, its computation is a complex problem. Recently, graph embedding into vector spaces has been proposed to obtain approximations of the median graph. The problem with such an approach is how to go from a point in the vector space back to a graph in the graph space. The main contribution of this paper is the generalization of this previ- ous method, proposing a generic recursive procedure that permits to recover the graph corresponding to a point in the vector space, introducing only the amount of approximation inherent to the use of graph matching algorithms. In order to evaluate the proposed method, we compare it with the set me- dian and with the other state-of-the-art embedding-based methods for the median graph computation. The experiments are carried out using four dif- ferent databases (one semi-artificial and three containing real-world data). Results show that with the proposed approach we can obtain better medi- ans, in terms of the sum of distances to the training graphs, than with the previous existing methods.
Keywords: Median Graph, Graph Embedding, Graph Matching, Structural Pattern Recognition
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Miquel Ferrer, Dimosthenis Karatzas, Ernest Valveny, & Horst Bunke. (2009). A Recursive Embedding Approach to Median Graph Computation. In 7th IAPR – TC–15 Workshop on Graph–Based Representations in Pattern Recognition (Vol. 5534, 113–123). LNCS. Springer Berlin Heidelberg.
Abstract: The median graph has been shown to be a good choice to infer a representative of a set of graphs. It has been successfully applied to graph-based classification and clustering. Nevertheless, its computation is extremely complex. Several approaches have been presented up to now based on different strategies. In this paper we present a new approximate recursive algorithm for median graph computation based on graph embedding into vector spaces. Preliminary experiments on three databases show that this new approach is able to obtain better medians than the previous existing approaches.
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Miquel Ferrer. (2006). Spectral Median Graphs and its Application to Graphical Symbol Recognition.
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