Research and implement advanced HTFA variants

## 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