Abstract: Graph embeddings in vector spaces aim at assigning a pattern vector to every graph so that the problems of graph classification and clustering can be solved by using data processing algorithms originally developed for statistical feature vectors. An important requirement graph features should fulfil is that they reproduce as much as possible the properties among objects in the graph domain. In particular, it is usually desired that distances between pairs of graphs in the graph domain closely resemble those between their corresponding vectorial representations. In this work, we analyse relations between the edit distance in the graph domain and the L1 distance of the attribute statistics based embedding, for which good classification performance has been reported on various datasets. We show that there is actually a high correlation between the two kinds of distances provided that the corresponding parameter values that account for balancing the weight between node and edge based features are properly selected.

Abstract: Graph representation of graphical documents often suffers from noise viz. spurious nodes and spurios edges of graph and their discontinuity etc. In general these errors occur during the low-level image processing viz. binarization, skeletonization, vectorization etc. Hierarchical graph representation is a nice and efficient way to solve this kind of problem by hierarchically merging node-node and node-edge depending on the distance.
But the creation of hierarchical graph representing the graphical information often uses hard thresholds on the distance to create the hierarchical nodes (next state) of the lower nodes (or states) of a graph. As a result the representation often loses useful information. This paper introduces plausibilities to the nodes of hierarchical graph as a function of distance and proposes a modified algorithm for matching subgraphs of the hierarchical
graphs. The plausibility-annotated nodes help to improve the performance of the matching algorithm on two hierarchical structures. To show the potential of this approach, we conduct an experiment with the SESYD dataset.

Abstract: Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments,
etc.) and edges characterize the relationships between these primitives. However, these non-vectorial graph data cannot be straightforwardly plugged into off-the-shelf machine learning algorithms without a preliminary step of – explicit/implicit –graph vectorization and embedding. This embedding process
should be resilient to intra-class graph variations while being highly discriminant. In this paper, we propose a novel high-order stochastic graphlet embedding (SGE) that maps graphs into vector spaces. Our main contribution includes a new stochastic search procedure that efficiently parses a given graph and extracts/samples unlimitedly high-order graphlets. We consider
these graphlets, with increasing orders, to model local primitives as well as their increasingly complex interactions. In order to build our graph representation, we measure the distribution of these graphlets into a given graph, using particular hash functions that efficiently assign sampled graphlets into isomorphic sets with a very low probability of collision. When
combined with maximum margin classifiers, these graphlet-based representations have positive impact on the performance of pattern comparison and recognition as corroborated through extensive experiments using standard benchmark databases.

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 in terms of feature vectors. Retrieving a query graph from a large dataset of graphs has the drawback of the high computational complexity required to compare the query and the target graphs. The most important property for a large-scale retrieval is the search time complexity to be sub-linear in the number of database examples. In this paper we propose a fast indexation formalism for graph 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. Hence, each attribute counts the length of a walk of order k originated in a vertex with label l. 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 a handwritten word spotting scenario in images of historical documents.

Abstract: Graph-based representations are of broad use and applicability in pattern recognition. They exhibit, however, a major drawback with regards to the processing tools that are available in their domain. Graphembedding into vectorspaces is a growing field among the structural pattern recognition community which aims at providing a feature vector representation for every graph, and thus enables classical statistical learning machinery to be used on graph-based input patterns. In this work, we propose a novel embedding methodology for graphs with continuous nodeattributes and unattributed edges. The approach presented in this paper is based on statistics of the node labels and the edges between them, based on their similarity to a set of representatives. We specifically deal with an important issue of this methodology, namely, the selection of a suitable set of representatives. In an experimental evaluation, we empirically show the advantages of this novel approach in the context of different classification problems using several databases of graphs.