  For the high dimensional data representation, nonnegative tensor ring (NTR)
decomposition equipped with manifold learning has become a promising model to
exploit the multi-dimensional structure and extract the feature from tensor
data. However, the existing methods such as graph regularized tensor ring
decomposition (GNTR) only models the pair-wise similarities of objects. For
tensor data with complex manifold structure, the graph can not exactly
construct similarity relationships. In this paper, in order to effectively
utilize the higher-dimensional and complicated similarities among objects, we
introduce hypergraph to the framework of NTR to further enhance the feature
extraction, upon which a hypergraph regularized nonnegative tensor ring
decomposition (HGNTR) method is developed. To reduce the computational
complexity and suppress the noise, we apply the low-rank approximation trick to
accelerate HGNTR (called LraHGNTR). Our experimental results show that compared
with other state-of-the-art algorithms, the proposed HGNTR and LraHGNTR can
achieve higher performance in clustering tasks, in addition, LraHGNTR can
greatly reduce running time without decreasing accuracy.
