Fuzzy multilevel graph embedding

A Comparison of Explicit and Implicit Graph Embedding Methods for Pattern Recognition

“…The node degree, numeric resemblance attributes, numeric node attributes and numeric edge attributes are embedded by fuzzy histograms whereas the symbolic resemblance attributes, symbolic node attributes and symbolic edge attributes are embedded by crisp histograms. FMGE learns the intervals, for constructing these histograms, during an unsupervised learning phase and employs the learned intervals during graph embedding phase [12].…”

“…Similarly to the previous study described in [6], in this paper we propose a comparison between two implicit graph embedding methods based on graph kernels ( [1,5]) and three methods of explicit graph embedding with comparable behavior ( [7,12,17]). The difference between these techniques will be illustrated on classification problems using chemoinformatic datasets, such as those from IAM [14], the predictive toxicology challenge (PTC) dataset [20] and the MAO dataset from GREYC [5].…”

Network Sampling Algorithms and Applications

“…Fuzzy multilevel graph embedding [29] defines a vectorial representation encoding both local characteristics, such as node degrees or node and edge labels, and simple global information such as number of nodes and edges of graphs. Vectorial representation provided by a fuzzy multilevel graph embedding includes thus different levels of analysis of the graph.…”

Graph pyramid embedding in vector space

“…The writers [4] have recently introduced a method for labeled graphs based on statistics of the node labels and the edges between them, based on their similarity to a representatives set. The introduced method in [5] is considered the graph information in several levels of topology, structural and attributes; also it is used fuzzy logic for embedding to reduce sensitivity of numerical data against noise. Spectral embedding of graph is another extensive family based on extract features from graph by eigen-decomposition of adjacency and Laplacian matrices [6].…”

“…By constructing graph pyramid with similar λ for each graphs , the resulted graphs from each level of for is supposed as a new graph domain of . So if be a training set with graphs from domain , training sets corresponding to are obtained for new domains as follows: (4) By selecting prototypes set for each graph domain (5) mapping is defined by function (6) It is important to note that graph edit distance is a powerful and flexible concept and using this concept in graph embedding makes embedding framework more powerful. Nevertheless the major problem in using this concept is its exponential time complexity for calculating distances.…”