On Embedding Uncertain Graphs

Graph data are prevalent in communication networks, social media, and biological networks. These data, which are often noisy or inexact, can be represented by uncertain graphs, whose edges are associated with probabilities to indicate the chances that they exist. Recently, researchers have studied various algorithms (e.g., clustering, classification, and k-NN) for uncertain graphs. These solutions face two problems: (1) high dimensionality: uncertain graphs are often highly complex, which can affect the mining quality; and (2) low reusability, where an existing mining algorithm has to be redesigned to deal with uncertain graphs on different tasks. To tackle these problems, we propose a solution called URGE, or UnceRtain Graph Embedding. Given an uncertain graph g, URGE generates g's embedding, or a set of low-dimensional vectors, which carry the proximity information of nodes in g. This embedding enables the dimensionality of g to be reduced, without destroying node proximity information. Due to its simplicity, existing mining solutions can be used on the embedding. We investigate two low- and high-order node proximity measures in the embedding generation process, and develop novel algorithms to enable fast evaluation. To our best knowledge, there is no prior study on the use of embedding for uncertain graphs. We have further performed extensive experiments for clustering, classification, and k-NN on several uncertain graph datasets. Our results show that URGE attains better effectiveness than current uncertain data mining algorithms, as well as state-of-the-art embedding solutions. The embedding and mining performance is also highly efficient in our experiments.