Graph pyramid embedding in vector space

Graph-based representation has an effective and extensive usage in pattern recognition due to represent properties of entities and binary relations at the same time. But a major drawback of graphs is lack of basic and essential mathematical operations required in many algorithms of pattern recognition. To overcome this problem, graph embedding in vector space enables classical statistical learning algorithms to be used on graph-based input patterns by providing a feature vector for each graph. The aim of this paper is to propose a new generic framework of graph embedding based on ideas from multiresolution theory. The main idea is mapping image pyramid from field of image processing to graph pyramid in graph domain. To this end, we suggest a summarization algorithm that can be used on graphs with continuous node labels. Finally we use resulted graph pyramid for a hierarchical embedding. In an experimental evaluation, we will show the advantages of this new approach in the context of classification problems.