Fast and Robust Graph-based Transductive Learning via Minimum Tree Cut

Yan-Ming Zhang, Kaizhu Huang, Cheng-Lin Liu

Abstract: In this paper, we propose an efficient and robust algorithm for graph-based transductive classification. After approximating a graph with a spanning tree, we develop a linear-time algorithm to label the tree such that the cut size of the tree is minimized. This significantly improves typical graph-based methods, which either have a cubic time complexity (for a dense graph) or O(kn <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) (for a sparse graph with k denoting the node degree). Furthermore, our method shows great robustness to the graph construction both theoretically and empirically; this overcomes another big problem of traditional graph-based methods. In addition to its good scalability and robustness, the proposed algorithm demonstrates high accuracy. In particular, on a graph with 400,000 nodes (in which 10,000 nodes are labeled) and 10,455,545 edges, our algorithm achieves the highest accuracy of 99.6% but takes less than 10 seconds to label all the unlabeled data.