Partial Tubal Nuclear Norm-Regularized Multiview Subspace Learning.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Multiview subspace learning (MVSC) tasks are often treated independently.
• Existing methods may not optimally capture correlations between projection learning and low-rank tensor representation.
• Minimizing the tensor nuclear norm can be suboptimal due to equal weighting of singular values.

Purpose of the Study:

• To propose a unified multiview subspace learning model (PTN2MSL) for unsupervised MVSC, semisupervised MVSC, and multiview dimension reduction.
• To integrate projection learning and low-rank tensor representation to leverage their correlations.
• To introduce a novel regularization technique, the partial tubal nuclear norm (PTNN), for improved performance.

Main Methods:

• Developed a unified model, PTN2MSL, integrating projection learning and low-rank tensor representation.
• Introduced the partial tubal nuclear norm (PTNN) by minimizing the partial sum of tubal singular values.
• Applied the PTN2MSL method to unsupervised MVSC, semisupervised MVSC, and multiview dimension reduction tasks.

Main Results:

• Demonstrated that the integrated tasks organically benefit each other within the PTN2MSL framework.
• PTN2MSL achieved superior performance compared to state-of-the-art methods across the evaluated tasks.
• The PTNN regularization proved to be a more effective alternative to the standard tensor nuclear norm.

Conclusions:

• The proposed PTN2MSL model effectively unifies and enhances performance for multiple multiview subspace learning tasks.
• The integration of projection learning and tensor representation, coupled with PTNN, offers significant advantages.
• PTN2MSL provides a robust and high-performing solution for complex multiview data analysis.