Gene

Singular value

Algorithm

Physics

Pattern recognition (psychology)

Artificial intelligence

Tensor (intrinsic definition)

Eigenvalues and eigenvectors

Political science

Chemistry

Norm (philosophy)

Pure mathematics

Singular value decomposition

Subspace topology

Mathematics

Computer science

Biochemistry

Quantum mechanics

Robustness (evolution)

Cluster analysis

Matrix norm

Low-rank representation based on tensor-Singular Value Decomposition (t-SVD) has achieved impressive results for multi-view subspace clustering, but it does not well deal with noise and illumination changes embedded in multi-view data. The major reason is that all the singular values have the same contribution in tensor-nuclear norm based on t-SVD, which does not make sense in the existence of noise and illumination change. To improve the robustness and clustering performance, we study the weighted tensor-nuclear norm based on t-SVD and develop an efficient algorithm to optimize the weighted tensor-nuclear norm minimization (WTNNM) problem. We further apply the WTNNM algorithm to multi-view subspace clustering by exploiting the high order correlations embedded in different views. Extensive experimental results reveal that our WTNNM method is superior to several state-of-the-art multi-view subspace clustering methods in terms of performance.

Tensor-SVD Based Graph Learning for Multi-View Subspace Clustering