Re-Revisiting Learning on Hypergraphs: Confidence Interval, Subgradient Method, and Extension to Multiclass

Chenzi Zhang, Shuguang Hu, Zhihao Gavin Tang, T.-H. Hubert Chan

Abstract: We revisit semi-supervised learning on hypergraphs. Same as previous approaches, our method uses a convex program whose objective function is not everywhere differentiable. We exploit the non-uniqueness of the optimal solutions, and consider confidence intervals which give the exact ranges that unlabeled vertices take in any optimal solution. Moreover, we give a much simpler approach for solving the convex program based on the subgradient method. Our experiments on real-world datasets confirm that our confidence interval approach on hypergraphs outperforms existing methods, and our subgradient method gives faster running times when the number of vertices is much larger than the number of edges. Our experiments also support that using directed hypergraphs to capture causal relationships can improve the prediction accuracy. Furthermore, our model can be readily extended to capture multiclass learning.