Hierarchical graph embedding in vector space by graph pyramid

• We propose a hierarchical framework which extracts local and global features from different scales of given graph at the same time.
• Reducing the computational complexity with processing at higher levels of abstraction.
• Independent processing of different resolutions of graph based on application.
• Bridging the gap between elementary features and more descriptive ones.

Loss of information is the major challenge in graph embedding in vector space which reduces the impact of representational power of graphs in pattern recognition tasks. The objective of this article is to present a hierarchical framework which can decrease this loss in a reasonable computational time. Inspired by multi-resolution ideas in image processing, a graph pyramid is formed based on a selected graph summarization algorithm which can provide the required information for classification. All the pyramid levels or some of them are embedded into a vector through an available embedding method which constructs an informative description containing both local and global features. The experiments are conducted on graphs with numerical and categorical attributes. In the numerical case, a proposed summarization algorithm is applied while in the categorical case, k-SNAP graph summarization is applied. The results indicate that this new framework is efficient in terms of accuracy and time consumption in the context of classification problems. It is observed that this improvement is achieved regardless of selected embedding techniques.