Research and implement advanced HTFA variants

[jeremymanning]

Summary

Research and implement advanced variants and extensions of the HTFA algorithm.

Tasks

Algorithm Research

• Review recent literature on factor analysis improvements
• Investigate variational inference approaches
• Research non-negative matrix factorization variants
• Explore regularization techniques (L1, L2, elastic net)
• Study automatic relevance determination (ARD) priors

Advanced Features

• Implement sparse HTFA variants
• Add support for non-Gaussian data distributions
• Implement temporal dynamics modeling
• Add hierarchical Bayesian extensions
• Support for multi-modal data integration

Modern ML Techniques

• Investigate neural network-based factor analysis
• Research attention mechanisms for spatial factors
• Explore transformer architectures for temporal modeling
• Study graph neural networks for spatial relationships
• Investigate federated learning approaches

Evaluation Methods

• Implement advanced model selection criteria
• Add cross-validation frameworks
• Create benchmark datasets for comparison
• Develop interpretability metrics
• Add statistical significance testing

Research Timeline

• Phase 1: Literature review and feasibility analysis
• Phase 2: Prototype implementation of promising approaches
• Phase 3: Validation and performance comparison
• Phase 4: Integration with main codebase

Acceptance Criteria

• At least 2 advanced variants implemented
• Comprehensive evaluation against baseline HTFA
• Published research findings or preprint
• Integration maintains existing API compatibility

[jeremymanning]

Status Update: Core HTFA complete, advanced variants possible 🔬

Current Implementation:

• ✅ Standard TFA (Topographic Factor Analysis)
• ✅ Hierarchical TFA (multi-subject)
• ✅ Multiple optimization strategies (Adam, ALS, mini-batch)
• ✅ Ridge regression for regularization

Potential Advanced Variants:

• Sparse HTFA with L1 regularization
• Online/streaming HTFA for real-time analysis
• Non-negative HTFA for interpretability
• Probabilistic HTFA with uncertainty quantification
• Multi-modal HTFA for combining fMRI with other data

The core algorithm is solid and extensible. Advanced variants could be built on the existing foundation.