Research On Hypergraph Regularized Nonnegative Tucker Decomposition

With the advent of the era of big data,tensor decomposition is widely used in many different fields such as image processing,data recovery,and recommendation systems.Different from matrix decomposition,because it retains more position or structure information of the original data,it can better solve practical problems.Further,the data generated by some practical problems are often non-negative,so non-negative tensor decomposition is used to study or solve practical problems are more practical.Traditional nonnegative tensor decomposition is based on regularization methods such as graphs and manifolds.However,these existing methods do not fully consider the information of the data,or the amount of calculation is large and the effect is not good.This paper proposes a non-negative Tucker decomposition algorithm based on hypergraph regularization.Firstly,in order to keep the intrinsic geometric structure information of the original data,a hypergraph regularization term is added to the classical tensor nonnegative Tucker decomposition,and then a hypergraph regularized nonnegative Tucker decomposition model hgntd is proposed.Secondly,based on the alternating nonnegative least squares method,a fast and effective hypergraph regularized nonnegative Tucker decomposition algorithm is designed to solve the given model,and the convergence of the new algorithm is proved.Finally,the new algorithm is applied to image clustering.Experiments on Yale and COIL-100 datasets show that the new algorithm is effective.