Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Linear discriminant analysis (LDA) is extended for higher-order data classification as multilinear discriminant analysis (MDA).
• Existing MDA methods like general tensor discriminant analysis (GTDA) and discriminant analysis with tensor representation (DATER) use iterative approximations to handle tensor mode dependency.
• GTDA offers convergence but requires parameter tuning, while DATER shows better performance but lacks convergence and is sensitive to iteration count.

Purpose of the Study:

• To develop more efficient and accurate MDA methods.
• To address the limitations of parameter tuning in GTDA and convergence issues in DATER.
• To introduce novel MDA techniques with improved performance and stability.

Main Methods:

• Proposed direct GTDA (DGTDA), a closed-form solution for the GTDA scatter difference objective, eliminating parameter tuning.
• Introduced constrained multilinear discriminant analysis (CMDA) to learn optimal tensor subspaces by maximizing the scatter ratio criterion iteratively.
• Provided theoretical and experimental validation for both DGTDA and CMDA.

Main Results:

• DGTDA demonstrated superior efficiency and accuracy compared to GTDA.
• CMDA showed improved and more stable performance than DATER.
• CMDA's scatter ratio criterion was proven to approach its extreme value with bounded error.

Conclusions:

• DGTDA offers a parameter-free, efficient, and accurate alternative for MDA.
• CMDA provides a robust and stable approach for tensor subspace learning in classification.
• The proposed methods advance the field of higher-order data classification.