Jaume Gibert

Graph embedding in vector spaces by node attribute statistics

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. Graph embedding into vector spaces 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 node attributes 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.

Dimensionality reduction for graph of words embedding

The Graph of Words Embedding consists in mapping every graph of a given dataset to a feature vector by counting unary and binary relations between node attributes of the graph. While it shows good properties in classification problems, it suffers from high dimensionality and sparsity. These two issues are addressed in this article. Two well-known techniques for dimensionality reduction, kernel principal component analysis (kPCA) and independent component analysis (ICA), are applied to the embedded graphs. We discuss their performance compared to the classification of the original vectors on three different public databases of graphs.

EMBEDDING OF GRAPHS WITH DISCRETE ATTRIBUTES VIA LABEL FREQUENCIES

Graph-based representations of patterns are very flexible and powerful, but they are not easily processed due to the lack of learning algorithms in the domain of graphs. Embedding a graph into a vector space solves this problem since graphs are turned into feature vectors and thus all the statistical learning machinery becomes available for graph input patterns. In this work we present a new way of embedding discrete attributed graphs into vector spaces using node and edge label frequencies. The methodology is experimentally tested on graph classification problems, using patterns of different nature, and it is shown to be competitive to state-of-the-art classification algorithms for graphs, while being computationally much more efficient.

Feature selection on node statistics based embedding of graphs

Representing a graph with a feature vector is a common way of making statistical machine learning algorithms applicable to the domain of graphs. Such a transition from graphs to vectors is known as graph embedding. A key issue in graph embedding is to select a proper set of features in order to make the vectorial representation of graphs as strong and discriminative as possible. In this article, we propose features that are constructed out of frequencies of node label representatives. We first build a large set of features and then select the most discriminative ones according to different ranking criteria and feature transformation algorithms. On different classification tasks, we experimentally show that only a small significant subset of these features is needed to achieve the same classification rates as competing to state-of-the-art methods.

Graph of words embedding for molecular structure-activity relationship analysis

Structure-Activity relationship analysis aims at discovering chemical activity of molecular compounds based on their structure. In this article we make use of a particular graph representation of molecules and propose a new graph embedding procedure to solve the problem of structure-activity relationship analysis. The embedding is essentially an arrangement of a molecule in the form of a vector by considering frequencies of appearing atoms and frequencies of covalent bonds between them. Results on two benchmark databases show the effectiveness of the proposed technique in terms of recognition accuracy while avoiding high operational costs in the transformation.

A kernel-based approach to document retrieval

In this paper we tackle the problem of document image retrieval by combining a similarity measure between documents and the probability that a given document belongs to a certain class. The membership probability to a specific class is computed using Support Vector Machines in conjunction with similarity measure based kernel applied to structural document representations. In the presented experiments, we use different document representations, both visual and structural, and we apply them to a database of historical documents. We show how our method based on similarity kernels outperforms the usual distance-based retrieval.

Vocabulary selection for graph of words embedding

The Graph of Words Embedding consists in mapping every graph in a given dataset to a feature vector by counting unary and binary relations between node attributes of the graph. It has been shown to perform well for graphs with discrete label alphabets. In this paper we extend the methodology to graphs with n-dimensional continuous attributes by selecting node representatives. We propose three different discretization procedures for the attribute space and experimentally evaluate the dependence on both the selector and the number of node representatives. In the context of graph classification, the experimental results reveal that on two out of three public databases the proposed extension achieves superior performance over a standard reference system.

On the correlation of graph edit distance and L 1 distance in the attribute statistics embedding space

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.

Multiple classifiers for graph of words embedding

During the last years, there has been an increasing interest in applying the multiple classifier framework to the domain of structural pattern recognition. Constructing base classifiers when the input patterns are graph based representations is not an easy problem. In this work, we make use of the graph embedding methodology in order to construct different feature vector representations for graphs. The graph of words embedding assigns a feature vector to every graph by counting unary and binary relations between node representatives and combining these pieces of information into a single vector. Selecting different node representatives leads to different vectorial representations and therefore to different base classifiers that can be combined. We experimentally show how this methodology significantly improves the classification of graphs with respect to single base classifiers.

Graph embedding based on nodes attributes representatives and a graph of words representation

Although graph embedding has recently been used to extend statistical pattern recognition techniques to the graph domain, some existing embeddings are usually computationally expensive as they rely on classical graph-based operations. In this paper we present a new way to embed graphs into vector spaces by first encapsulating the information stored in the original graph under another graph representation by clustering the attributes of the graphs to be processed. This new representation makes the association of graphs to vectors an easy step by just arranging both node attributes and the adjacency matrix in the form of vectors. To test our method, we use two different databases of graphs whose nodes attributes are of different nature. A comparison with a reference method permits to show that this new embedding is better in terms of classification rates, while being much more faster.