Estimating Descriptors for Large Graphs

by   Zohair Raza Hassan, et al.

Embedding networks into a fixed dimensional Euclidean feature space, while preserving its essential structural properties is a fundamental task in graph analytics. These feature vectors, referred to as graph descriptors, are used to measure pairwise similarity between graphs. This enables applying data mining algorithms such as classification, clustering, anomaly detection on graph structured data which have numerous applications in multiple domains. State-of-the-art algorithms for computing descriptors require the entire graph to be in memory, entailing a huge memory footprint, and thus, do not scale well to increasing sizes of real world networks. In this work, we propose streaming algorithms to efficiently approximate graph descriptors by estimating counts of sub-graphs of order k≤ 4, and thereby devise extensions of two existing graph comparison paradigms: the Graphlet Kernel and NetSimile. Our algorithms require a single scan over the edge stream, have space complexity that is a fraction of the input size, and approximate embeddings via a simple sampling scheme. Our design exploits the trade-off between available memory and estimation accuracy to provide a method that works well for limited memory requirements. We perform extensive experiments on benchmark real-world networks and demonstrate that our algorithms scale well to massive graphs.


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