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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. (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: 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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Alicia Fornes, Josep Llados, Gemma Sanchez, & Dimosthenis Karatzas. (2010). Rotation Invariant Hand-Drawn Symbol Recognition based on a Dynamic Time Warping Model. IJDAR - International Journal on Document Analysis and Recognition, 13(3), 229–241.
Abstract: One of the major difficulties of handwriting symbol recognition is the high variability among symbols because of the different writer styles. In this paper, we introduce a robust approach for describing and recognizing hand-drawn symbols tolerant to these writer style differences. This method, which is invariant to scale and rotation, is based on the dynamic time warping (DTW) algorithm. The symbols are described by vector sequences, a variation of the DTW distance is used for computing the matching distance, and K-Nearest Neighbor is used to classify them. Our approach has been evaluated in two benchmarking scenarios consisting of hand-drawn symbols. Compared with state-of-the-art methods for symbol recognition, our method shows higher tolerance to the irregular deformations induced by hand-drawn strokes.
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Mathieu Nicolas Delalandre, Ernest Valveny, Tony Pridmore, & Dimosthenis Karatzas. (2010). Generation of Synthetic Documents for Performance Evaluation of Symbol Recognition & Spotting Systems. IJDAR - International Journal on Document Analysis and Recognition, 13(3), 187–207.
Abstract: This paper deals with the topic of performance evaluation of symbol recognition & spotting systems. We propose here a new approach to the generation of synthetic graphics documents containing non-isolated symbols in a real context. This approach is based on the definition of a set of constraints that permit us to place the symbols on a pre-defined background according to the properties of a particular domain (architecture, electronics, engineering, etc.). In this way, we can obtain a large amount of images resembling real documents by simply defining the set of constraints and providing a few pre-defined backgrounds. As documents are synthetically generated, the groundtruth (the location and the label of every symbol) becomes automatically available. We have applied this approach to the generation of a large database of architectural drawings and electronic diagrams, which shows the flexibility of the system. Performance evaluation experiments of a symbol localization system show that our approach permits to generate documents with different features that are reflected in variation of localization results.
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