The existing multi-view subspace clustering algorithms based on tensor singular value decomposition(t-SVD)predominantly utilize tensor nuclear norm to explore the intra view correlation between views of the same sampl...The existing multi-view subspace clustering algorithms based on tensor singular value decomposition(t-SVD)predominantly utilize tensor nuclear norm to explore the intra view correlation between views of the same samples,while neglecting the correlation among the samples within different views.Moreover,the tensor nuclear norm is not fully considered as a convex approximation of the tensor rank function.Treating different singular values equally may result in suboptimal tensor representation.A hypergraph regularized multi-view subspace clustering algorithm with dual tensor log-determinant(HRMSC-DTL)was proposed.The algorithm used subspace learning in each view to learn a specific set of affinity matrices,and introduced a non-convex tensor log-determinant function to replace the tensor nuclear norm to better improve global low-rankness.It also introduced hyper-Laplacian regularization to preserve the local geometric structure embedded in the high-dimensional space.Furthermore,it rotated the original tensor and incorporated a dual tensor mechanism to fully exploit the intra view correlation of the original tensor and the inter view correlation of the rotated tensor.At the same time,an alternating direction of multipliers method(ADMM)was also designed to solve non-convex optimization model.Experimental evaluations on seven widely used datasets,along with comparisons to several state-of-the-art algorithms,demonstrated the superiority and effectiveness of the HRMSC-DTL algorithm in terms of clustering performance.展开更多
We study the asymptotic behavior for log-determinants of two unitary but non-Hermitian random matrices： the spherical ensembles A-1B, where A and B are independent complex Ginibre ensembles and the truncation of circ...We study the asymptotic behavior for log-determinants of two unitary but non-Hermitian random matrices： the spherical ensembles A-1B, where A and B are independent complex Ginibre ensembles and the truncation of circular unitary ensembles. The corresponding Berry-Esseen bounds and Cram6r type moderate deviations are established. Our method is based on the estimates of corresponding cumulants. Numerical simulations are also presented to illustrate the theoretical results.展开更多
基金supported by National Natural Science Foundation of China(No.61806006)Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘The existing multi-view subspace clustering algorithms based on tensor singular value decomposition(t-SVD)predominantly utilize tensor nuclear norm to explore the intra view correlation between views of the same samples,while neglecting the correlation among the samples within different views.Moreover,the tensor nuclear norm is not fully considered as a convex approximation of the tensor rank function.Treating different singular values equally may result in suboptimal tensor representation.A hypergraph regularized multi-view subspace clustering algorithm with dual tensor log-determinant(HRMSC-DTL)was proposed.The algorithm used subspace learning in each view to learn a specific set of affinity matrices,and introduced a non-convex tensor log-determinant function to replace the tensor nuclear norm to better improve global low-rankness.It also introduced hyper-Laplacian regularization to preserve the local geometric structure embedded in the high-dimensional space.Furthermore,it rotated the original tensor and incorporated a dual tensor mechanism to fully exploit the intra view correlation of the original tensor and the inter view correlation of the rotated tensor.At the same time,an alternating direction of multipliers method(ADMM)was also designed to solve non-convex optimization model.Experimental evaluations on seven widely used datasets,along with comparisons to several state-of-the-art algorithms,demonstrated the superiority and effectiveness of the HRMSC-DTL algorithm in terms of clustering performance.
文摘We study the asymptotic behavior for log-determinants of two unitary but non-Hermitian random matrices： the spherical ensembles A-1B, where A and B are independent complex Ginibre ensembles and the truncation of circular unitary ensembles. The corresponding Berry-Esseen bounds and Cram6r type moderate deviations are established. Our method is based on the estimates of corresponding cumulants. Numerical simulations are also presented to illustrate the theoretical results.
