Hierarchical stochastic graphlet embedding for graph-based pattern recognition

This is the final version. Available on open access from Springer via the DOI in this recordDespite being very successful within the pattern recognition and machine learning community, graph-based methods are often unusable with many machine learning tools. This is because of the incompatibility of most of the mathematical operations in graph domain. Graph embedding has been proposed as a way to tackle these difficulties, which maps graphs to a vector space and makes the standard machine learning techniques applicable for them. However, it is well known that graph embedding techniques usually suffer from the loss of structural information. In this paper, given a graph, we consider its hierarchical structure for mapping it into a vector space. The hierarchical structure is constructed by topologically clustering the graph nodes, and considering each cluster as a node in the upper hierarchical level. Once this hierarchical structure of graph is constructed, we consider its various configurations of its parts, and use stochastic graphlet embedding (SGE) for mapping them into vector space. Broadly speaking, SGE produces a distribution of uniformly sampled low to high order graphlets as a way to embed graphs into the vector space. In what follows, the coarse-to-fine structure of a graph hierarchy and the statistics fetched through the distribution of low to high order stochastic graphlets complements each other and include important structural information with varied contexts. Altogether, these two techniques substantially cope with the usual information loss involved in graph embedding techniques, and it is not a surprise that we obtain more robust vector space embedding of graphs. This fact has been corroborated through a detailed experimental evaluation on various benchmark graph datasets, where we outperform the state-of-the-art methods.European Union Horizon 2020Ministerio de Educación, Cultura y Deporte, SpainGeneralitat de Cataluny

Relaxed Dissimilarity-based Symbolic Histogram Variants for Granular Graph Embedding

Graph embedding is an established and popular approach when designing graph-based pattern recognition systems. Amongst the several strategies, in the last ten years, Granular Computing emerged as a promising framework for structural pattern recognition. In the late 2000\u2019s, symbolic histograms have been proposed as the driving force in order to perform the graph embedding procedure by counting the number of times each granule of information appears in the graph to be embedded. Similarly to a bag-of-words representation of a text corpora, symbolic histograms have been originally conceived as integer-valued vectorial representation of the graphs. In this paper, we propose six \u2018relaxed\u2019 versions of symbolic histograms, where the proper dissimilarity values between the information granules and the constituent parts of the graph to be embedded are taken into account, information which is discarded in the original symbolic histogram formulation due to the hard-limited nature of the counting procedure. Experimental results on six open-access datasets of fully-labelled graphs show comparable performance in terms of classification accuracy with respect to the original symbolic histograms (average accuracy shift ranging from -7% to +2%), counterbalanced by a great improvement in terms of number of resulting information granules, hence number of features in the embedding space (up to 75% less features, on average)

Pyramidal Stochastic Graphlet Embedding for Document Pattern Classification

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this recordDocument pattern classification methods using graphs have received a lot of attention because of its robust representation paradigm and rich theoretical background. However, the way of preserving and the process for delineating documents with graphs introduce noise in the rendition of underlying data, which creates instability in the graph representation. To deal with such unreliability in representation, in this paper, we propose Pyramidal Stochastic Graphlet Embedding (PSGE). Given a graph representing a document pattern, our method first computes a graph pyramid by successively reducing the base graph. Once the graph pyramid is computed, we apply Stochastic Graphlet Embedding (SGE) for each level of the pyramid and combine their embedded representation to obtain a global delineation of the original graph. The consideration of pyramid of graphs rather than just a base graph extends the representational power of the graph embedding, which reduces the instability caused due to noise and distortion. When plugged with support vector machine, our proposed PSGE has outperformed the state-of-The-art results in recognition of handwritten words as well as graphical symbols.European Union Horizon 2020Ministerio de Educación, Cultura y Deporte, SpainRamon y Cajal FellowshipCERCA Program/Generalitat de Cataluny

Complexity vs. performance in granular embedding spaces for graph classification

The most distinctive trait in structural pattern recognition in graph domain is the ability to deal with the organization and relations between the constituent entities of the pattern. Even if this can be convenient and/or necessary in many contexts, most of the state-of the art classi\ufb01cation techniques can not be deployed directly in the graph domain without \ufb01rst embedding graph patterns towards a metric space. Granular Computing is a powerful information processing paradigm that can be employed in order to drive the synthesis of automatic embedding spaces from structured domains. In this paper we investigate several classi\ufb01cation techniques starting from Granular Computing-based embedding procedures and provide a thorough overview in terms of model complexity, embedding space complexity and performances on several open-access datasets for graph classi\ufb01cation. We witness that certain classi\ufb01cation techniques perform poorly both from the point of view of complexity and learning performances as the case of non-linear SVM, suggesting that high dimensionality of the synthesized embedding space can negatively affect the effectiveness of these approaches. On the other hand, linear support vector machines, neuro-fuzzy networks and nearest neighbour classi\ufb01ers have comparable performances in terms of accuracy, with second being the most competitive in terms of structural complexity and the latter being the most competitive in terms of embedding space dimensionality

Fuzzy Multilevel Graph Embedding for Recognition, Indexing and Retrieval of Graphic Document Images

This thesis addresses the problem of lack of efficient computational tools for graph based structural pattern recognition approaches and proposes to exploit computational strength of statistical pattern recognition. It has two fold contributions. The first contribution is a new method of explicit graph embedding. The proposed graph embedding method exploits multilevel analysis of graph for extracting graph level information, structural level information and elementary level information from graphs. It embeds this information into a numeric feature vector. The method employs fuzzy overlapping trapezoidal intervals for addressing the noise sensitivity of graph representations and for minimizing the information loss while mapping from continuous graph space to discrete vector space. The method has unsupervised learning abilities and is capable of automatically adapting its parameters to underlying graph dataset. The second contribution is a framework for automatic indexing of graph repositories for graph retrieval and subgraph spotting. This framework exploits explicit graph embedding for representing the cliques of order 2 by numeric feature vectors, together with classification and clustering tools for automatically indexing a graph repository. It does not require a labeled learning set and can be easily deployed to a range of application domains, offering ease of query by example (QBE) and granularity of focused retrieval

A comparison between two representatives of a set of graphs: median vs barycenter graph

Trabajo presentado al Joint IAPR International Workshop on Structural, Syntactic and Statistical Pattern Recognition (SSPR&SPR) celebrado en Esmirna (Turquía) del 18 al 20 de agosto de 2010.In this paper we consider two existing methods to generate a representative of a given set of graphs, that satisfy the following two conditions. On the one hand, that they are applicable to graphs with any kind of labels in nodes and edges and on the other hand, that they can handle relatively large amount of data. Namely, the approximated algorithms to compute the Median Graph via graph embedding and a new method to compute the Barycenter Graph. Our contribution is to give a new algorithm for the barycenter computation and to compare it to the median Graph. To compare these two representatives, we take into account algorithmic considerations and experimental results on the quality of the representative and its robustness, on several datasets.This work was supported by projects: 'CONSOLIDER-INGENIO 2010 Multimodal interaction in pattern recognition and computer vision' (V-00069), 'Robotica ubicua para entornos urbanos' (J-01225).Peer Reviewe

A discriminative prototype selection approach for graph embedding in human action recognition

This paper proposes a novel graph-based method for representing a human's shape during the performance of an action. Despite their strong representational power graphs are computationally cumbersome for pattern analysis. One way of circumventing this problem is that of transforming the graphs into a vector space by means of graph embedding. Such an embedding can be conveniently obtained by way of a set of prototype graphs and a dissimilarity measure: yet the critical step in this approach is the selection of a suitable set of prototypes which can capture both the salient structure within each action class as well as the intra-class variation. This paper proposes a new discriminative approach for the selection of prototypes which maximizes a function of the inter-and intra-class distances. Experiments on an action recognition dataset reported in the paper show that such a discriminative approach outperforms well-established prototype selection methods such as center border and random prototype selection. © 2011 IEEE

Recognize multi-touch gestures by graph modeling and matching

International audienceExtract the features for a multi-touch gesture is difficult due to the complex temporal and motion relations between multiple trajectories. In this paper we present a new generic graph model to quantify the shape, temporal and motion information from multi-touch gesture. To make a comparison between graph, we also propose a specific graph matching method based on graph edit distance. Results prove that our graph model can be fruitfully used for multi-touch gesture pattern recognition purpose with the classifier of graph embedding and SVM