Rigorous optimisation of multilinear discriminant analysis with Tucker and PARAFAC structures

Area of Science:

• Multilinear data analysis
• Machine learning for neuroscience

Background:

• Existing Multilinear Discriminant Analysis (MDA) methods rely on heuristic optimization and ambiguous structures.
• Supervised feature extraction for multilinear data requires rigorous optimization techniques.

Purpose of the Study:

• To develop rigorously optimized supervised feature extraction methods for multilinear data using Multilinear Discriminant Analysis (MDA).
• To introduce MDA methods with PARAFAC structure and compare them with existing Tucker-based methods and unsupervised approaches.
• To apply and evaluate these methods on Electroencephalography (EEG) and simulated data.

Main Methods:

• Developed novel MDA methods using optimization on the cross-product of Stiefel manifolds.
• Introduced MDA methods incorporating the PARAFAC structure.
• Compared proposed methods against existing MDA techniques and unsupervised multilinear decompositions.

Main Results:

• Manifold optimization significantly enhanced MDA objective functions and classification performance on simulated data.
• Supervised MDA approaches substantially outperformed unsupervised multilinear methods.
• MDA applied to raw EEG data achieved competitive performance, extracting relevant discriminatory patterns without extensive preprocessing.
• PARAFAC-structured MDA models yielded meaningful activity patterns, comparable to Tucker structures.

Conclusions:

• The proposed manifold optimization offers the first rigorous, monotonous optimization for MDA and enables PARAFAC-structured MDA.
• Supervised MDA on raw EEG data effectively extracts discriminatory patterns, outperforming traditional unsupervised methods.
• PARAFAC-structured MDA models reveal meaningful patterns of brain activity relevant to EEG paradigms.