Semi-supervised learning and clustering algorithms on hypergraph cutting are conducted a research;By discussing hy-pergraph cutting and hyperedge expansion methods as well as its cutting function,the total variation on hypergraph is introduced as a Lovasz extension of hypergraph cutting.Based on this,this paper puts forward a set of regularization functions related to the Lapla-cian regularization on the graph,presents a semi-supervised learning method based on regularization function family,and proposes a spectral clustering method based on balanced hypergraph cutting;In order to solve these two learning problems,they are transformed into solving the convex optimization problem,and a scalable algorithm whose main component is proximal mapping is proposed to real-ize the semi-supervised learning and clustering;Simulation results show that the proposed semi-supervised learning and clustering method based on hypergraph cutting has a better standard deviation and clustering error performance than the classical hyperedge ex-pansion and other graph cutting methods.
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