Abstract—Most network-based machine learning methods are based on the assumption that the labels of two adjacent vertices in the network are likely to be the same. However, assuming the pairwise relationship between vertices is not complete. The information a group of vertices that show very similar patterns and tend to have similar labels is missed. The natural way overcoming the information loss of the above assumption is to represent the given data as the hypergraph. However, representing the dataset as the hypergraph will not lead to the perfection. The number of hyper-edges may be large; hence this will lead to high time complexity of the clustering methods or the classification methods when we try to apply the clustering/classification methods to this hypergraph dataset. Thus, there exists a need to develop the dimensional reduction methods for the hypergraph datasets. In this paper, the two un-normalized and random walk hypergraph Laplacian Eigenmaps are introduced. Experiment results show that the accuracy performance measures of these two hypergraph Laplacian Eigenmaps combined with graph based semi-supervised learning method are greater than the accuracy performance measure of graph based semi-supervised learning method alone (i.e. the baseline method of this paper) applied to the original hypergraph datasets.
Index Terms—Hypergraph, Laplacian, Eigenmaps, semi-supervised learning, graph.
Loc Tran is with University of Technology, Sydney (e-mail: firstname.lastname@example.org).
Linh Tran is with Portland State University, Portland (e-mail: email@example.com).
Hoang Trang is with Ho Chi Minh City University of Technology, Vietnam (e-mail: firstname.lastname@example.org).
Hieu Le is with the IC Design Lab, Ho Chi Minh City University of Technology, Vietnam (e-mail: email@example.com).
Cite: Loc Hoang Tran, Linh Hoang Tran, Hoang Trang, and Le Trung Hieu, "Combinatorial and Random Walk Hypergraph Laplacian Eigenmaps," International Journal of Machine Learning and Computing vol.5, no. 6, pp. 462-466, 2015.