A Cheeger Cut for Uniform Hypergraphs

The graph Cheeger constant and Cheeger inequalities are generalized to the case of hypergraphs whose edges have the same cardinality. In particular, it is shown that the second largest eigenvalue of the generalized normalized Laplacian is bounded both above and below by the generalized Cheeger constant, and the corresponding eigenfunctions can be used to approximate the Cheeger cut.

Cheeger Cut Model for the Balanced Data Classification Problem

In this paper we propose a numerical method based on the splitting strategy to solve the Cheeger cut model. In order to improve the classification results, we propose a new self-tuning strategy to choose a robust scaling parameter. Some numerical examples are arranged to illustrate the efficiency of our proposed method.