|
|
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.
|
|
|
|
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
|
|
|
|
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.
|
|
|
|
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.
|
|
|
|
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
|
|
|
|
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.
|
|
|
|
Albert Gordo, Jaume Gibert, Ernest Valveny and Marçal Rusiñol. 2010. A Kernel-based Approach to Document Retrieval. 9th IAPR International Workshop on Document Analysis Systems.377–384.
Abstract: In this paper we tackle the problem of document image retrieval by combining a similarity measure between documents and the probability that a given document belongs to a certain class. The membership probability to a specific class is computed using Support Vector Machines in conjunction with similarity measure based kernel applied to structural document representations. In the presented experiments, we use different document representations, both visual and structural, and we apply them to a database of historical documents. We show how our method based on similarity kernels outperforms the usual distance-based retrieval.
|
|
|
|
Jaume Gibert and Ernest Valveny. 2010. Graph Embedding based on Nodes Attributes Representatives and a Graph of Words Representation. In In E.R. Hancock, R.C.W., T. Windeatt, I. Ulusoy and F. Escolano,, ed. 13th International worshop on structural and syntactic pattern recognition and 8th international worshop on statistical pattern recognition. Springer Berlin Heidelberg, 223–232. (LNCS.)
Abstract: Although graph embedding has recently been used to extend statistical pattern recognition techniques to the graph domain, some existing embeddings are usually computationally expensive as they rely on classical graph-based operations. In this paper we present a new way to embed graphs into vector spaces by first encapsulating the information stored in the original graph under another graph representation by clustering the attributes of the graphs to be processed. This new representation makes the association of graphs to vectors an easy step by just arranging both node attributes and the adjacency matrix in the form of vectors. To test our method, we use two different databases of graphs whose nodes attributes are of different nature. A comparison with a reference method permits to show that this new embedding is better in terms of classification rates, while being much more faster.
|
|
|
|
Albert Gordo and Ernest Valveny. 2009. A rotation invariant page layout descriptor for document classification and retrieval. 10th International Conference on Document Analysis and Recognition.481–485.
Abstract: Document classification usually requires of structural features such as the physical layout to obtain good accuracy rates on complex documents. This paper introduces a descriptor of the layout and a distance measure based on the cyclic dynamic time warping which can be computed in O(n2). This descriptor is translation invariant and can be easily modified to be scale and rotation invariant. Experiments with this descriptor and its rotation invariant modification are performed on the Girona archives database and compared against another common layout distance, the minimum weight edge cover. The experiments show that these methods outperform the MWEC both in accuracy and speed, particularly on rotated documents.
|
|
|
|
Albert Gordo and Ernest Valveny. 2009. The diagonal split: A pre-segmentation step for page layout analysis & classification. 4th Iberian Conference on Pattern Recognition and Image Analysis. Springer Berlin Heidelberg, 290–297. (LNCS.)
Abstract: Document classification is an important task in all the processes related to document storage and retrieval. In the case of complex documents, structural features are needed to achieve a correct classification. Unfortunately, physical layout analysis is error prone. In this paper we present a pre-segmentation step based on a divide & conquer strategy that can be used to improve the page segmentation results, independently of the segmentation algorithm used. This pre-segmentation step is evaluated in classification and retrieval using the selective CRLA algorithm for layout segmentation together with a clustering based on the voronoi area diagram, and tested on two different databases, MARG and Girona Archives.
|
|
