| In many problems in information retrieval,machine learning and pat-tern recognition,the data recorded from real-word applications is of very high dimension.Classical clustering methods don’t work well on high-dimensional arrays,so it is essential to explore low-dimensional represen-tations of these high-dimensional arrays.First,in order to simultaneously consider the geometric information of the data space and the smoothness of the low-dimensional representa-tion,the auto-weighted multiple graph regularizedsmooth non-negative matrix is proposed.This model automatically selects the weights of dif-ferent graphs and uses these weights as coefficients to form auto-weighted multiple graph regular term by linearly combining these graphs to more closely approximate the intrinsic geometry of the data.And this model also usessmooth constraints to obtain a smooth and more accurate solution.An algorithm obtained by using multiplicative update rules–Auto-weighted Multiple Graph RegularizedSmooth Non-negative Ma-trix Factorization Algorithm（AMGSNMF）.Applying the AMGSNMF to clustering,experiments on the COIL20 and ORL single-view data sets show that the AMGSNMF algorithm improves accuracy by 0.4%-11.44%and normalized mutual information by 0.53%-3.86%over the four classical non-negative matrix factorization algorithms.Experiments on three multi-view data sets show that the AMGSNMF algorithm improves accuracy by4.93%-12.24%and normalized mutual information by 1.32%-5.00%over the Parameter-free Auto-weighted Multiple Graph Learning.Then,in order to solve the problem that non-negative matrix fac-torization destroys the original structure of high-dimensional arrays,the auto-weighted multiple graph non-negative Tucker decomposition is pro-posed.This model combines the auto-weighted multiple graph regular term with the non-negative Tucker decomposition model to preserve the original structure of the data and to explore the internal geometric informa-tion of the data space.An algorithm obtained by using alternating updat-ing algorithm–Auto-weighted Multiple Graph Regularized Non-negative Tucker Decomposition Algorithm（AMGNTD）and the convergence of the algorithm is demonstrated.Applying the AMGNTD to clustering and the experimental results also illustrate the effectiveness of the algorithm. |
