Multilinear Spatial Discriminant Analysis for Dimensionality Reduction.

Area of Science:

• Multilinear algebra and tensor analysis
• Machine learning and pattern recognition
• Data science and dimensionality reduction

Background:

• Linear projection techniques (LPT) vectorize data, potentially losing spatial information.
• Multilinear projection techniques (MPT) extend LPT for multidimensional tensor data.
• Existing MPTs like MPCA and TLPP focus on global or local structures, respectively.

Purpose of the Study:

• To propose a novel multilinear projection technique, Multilinear Spatial Discriminant Analysis (MSDA).
• To identify the underlying manifold of high-order tensor data.
• To develop a method that balances nonlocal and local data structures for improved discriminant analysis.

Main Methods:

• MSDA learns projection matrices from all tensor directions.
• It simultaneously maximizes nonlocal structure and minimizes local structure.
• The method considers both nonlocal and local data structures in the transform domain.

Main Results:

• MSDA demonstrates superior manifold preservation compared to TLPP and MPCA.
• Theoretical analysis shows MSDA encompasses other MPTs (e.g., MLDA, TLPP, MPCA, TM3C).
• Experiments on face and action databases validate MSDA's effectiveness.

Conclusions:

• MSDA offers a powerful approach for analyzing high-order tensor data by balancing global and local structures.
• The method provides a unified framework for various MPTs.
• MSDA shows significant potential for applications in pattern recognition and computer vision.