Graph Embedding in Vector Spaces by Means of Prototype Selection

Graph Embedding Using Constant Shift Embedding

“…Then, since the classification in the graph domain can be performed by only the k-NN classifiers, hence, it is used as reference system in the graph domain. Whereas in vector space the k-NN and the SVM 1 classifiers [24] are used to compare the embedding quality of the vectors resulting from our algorithm and the vectors resulting from the graph embedding approach recently proposed by Bunke et al [2,19,20]. This method was originally developed for the embedding of feature vectors in a dissimilarity space [16,17] and is based on the selection of some prototypes and the computation of the graph edit distance between the graph and the set of prototypes.…”

“…Moreover, Hancock et al [7,27,14,21] use spectral theory to convert graphs into vectors by means of spectral decomposition into eigenvalues and eigenvectors of the adjacency (or Laplacian) matrix of a graph. Besides, a new category of graph embedding techniques was introduced by Bunke et al [2,20,19], their method is based on the selection of some prototypes and the computation of the graph edit distance between the graph and the set of prototypes. This method was originally developed for the embedding of feature vectors in a dissimilarity space [16,17].…”

Graph-Based k-Means Clustering: A Comparison of the Set Median versus the Generalized Median Graph

“…In this work we will use another class of graph embedding procedures based on the selection of some prototypes and graph edit distance computation. This approach, which we explain in more detail in the next section, was first presented in [10], and it is based on the work proposed in [19]. The basic intuition is that the description of the regularities in observations of classes and objects is the basis to perform pattern classification.…”

“…In a first step, graphs are embedded into a vector space using a variation of the novel approach proposed in [10]. In that work, a set T of prototypes is used to embed each graph in a vector space.…”

“…To deal with the high time and space complexity of the median graph computation, a new approximate method based on graph embedding in vector spaces is also proposed. First, we map each graph into a vector space using an approach similar to [10]. The median of the set of vectors obtained with this mapping can be easily computed in the vector space.…”