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.

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.

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: Infographics communicate information using a combination of textual, graphical and visual elements. This work explores the automatic understanding of infographic images by using a Visual Question Answering technique. To this end, we present InfographicVQA, a new dataset comprising a diverse collection of infographics and question-answer annotations. The questions require methods that jointly reason over the document layout, textual content, graphical elements, and data visualizations. We curate the dataset with an emphasis on questions that require elementary reasoning and basic arithmetic skills. For VQA on the dataset, we evaluate two Transformer-based strong baselines. Both the baselines yield unsatisfactory results compared to near perfect human performance on the dataset. The results suggest that VQA on infographics--images that are designed to communicate information quickly and clearly to human brain--is ideal for benchmarking machine understanding of complex document images. The dataset is available for download at docvqa. org

Abstract: This work addresses the problem of Question Answering (QA) on handwritten document collections. Unlike typical QA and Visual Question Answering (VQA) formulations where the answer is a short text, we aim to locate a document snippet where the answer lies. The proposed approach works without recognizing the text in the documents. We argue that the recognition-free approach is suitable for handwritten documents and historical collections where robust text recognition is often difficult. At the same time, for human users, document image snippets containing answers act as a valid alternative to textual answers. The proposed approach uses an off-the-shelf deep embedding network which can project both textual words and word images into a common sub-space. This embedding bridges the textual and visual domains and helps us retrieve document snippets that potentially answer a question. We evaluate results of the proposed approach on two new datasets: (i) HW-SQuAD: a synthetic, handwritten document image counterpart of SQuAD1.0 dataset and (ii) BenthamQA: a smaller set of QA pairs defined on documents from the popular Bentham manuscripts collection. We also present a thorough analysis of the proposed recognition-free approach compared to a recognition-based approach which uses text recognized from the images using an OCR. Datasets presented in this work are available to download at docvqa.org.