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.

Abstract: Sequence-to-sequence models have recently become very popular for tackling
handwritten word recognition problems. However, how to effectively integrate an external language model into such recognizer is still a challenging
problem. The main challenge faced when training a language model is to
deal with the language model corpus which is usually different to the one
used for training the handwritten word recognition system. Thus, the bias
between both word corpora leads to incorrectness on the transcriptions, providing similar or even worse performances on the recognition task. In this
work, we introduce Candidate Fusion, a novel way to integrate an external
language model to a sequence-to-sequence architecture. Moreover, it provides suggestions from an external language knowledge, as a new input to
the sequence-to-sequence recognizer. Hence, Candidate Fusion provides two
improvements. On the one hand, the sequence-to-sequence recognizer has
the flexibility not only to combine the information from itself and the language model, but also to choose the importance of the information provided
by the language model. On the other hand, the external language model
has the ability to adapt itself to the training corpus and even learn the
most commonly errors produced from the recognizer. Finally, by conducting
comprehensive experiments, the Candidate Fusion proves to outperform the
state-of-the-art language models for handwritten word recognition tasks.

Abstract: Graph-based representations are experiencing a growing usage in visual recognition and retrieval due to their representational power in front of classical appearance-based representations. However, retrieving a query graph from a large dataset of graphs implies a high computational complexity. The most important property for a large-scale retrieval is the search time complexity to be sub-linear in the number of database examples. With this aim, in this paper we propose a graph indexation formalism applied to visual retrieval. A binary embedding is defined as hashing keys for graph nodes. Given a database of labeled graphs, graph nodes are complemented with vectors of attributes representing their local context. Then, each attribute vector is converted to a binary code applying a binary-valued hash function. Therefore, graph retrieval is formulated in terms of finding target graphs in the database whose nodes have a small Hamming distance from the query nodes, easily computed with bitwise logical operators. As an application example, we validate the performance of the proposed methods in different real scenarios such as handwritten word spotting in images of historical documents or symbol spotting in architectural floor plans.