Implement HTFA hierarchical optimization

[jeremymanning]

Summary

Implement the hierarchical optimization algorithm that extends TFA to multi-subject analysis.

Tasks

• Implement global template computation across subjects
• Add iterative optimization with global and local iterations
• Implement MAP (Maximum A Posteriori) estimation
• Add factor matching across subjects using linear sum assignment
• Implement convergence checking for global template
• Add proper handling of variable subject/voxel counts

Algorithm Details

1. Initialize individual subject TFA models
2. Compute global template from subject factors
3. Iteratively:
   • Update subject models using global template information
   • Recompute global template
   • Check convergence
4. Extract final parameters

Dependencies

• Core TFA implementation (issue Implement core TFA optimization algorithm #60)
• SciPy for optimization
• Linear sum assignment algorithms

References

• BrainIAK HTFA implementation: https://github.com/brainiak/brainiak/blob/master/src/brainiak/factoranalysis/htfa.py

Acceptance Criteria

• HTFA can process multi-subject data
• Global template converges across iterations
• Subject-specific factors and weights are extracted
• All unit tests pass

[jeremymanning]

✅ Completed as part of Epic #68 initial-implementation

This issue was successfully completed during the initial HTFA implementation epic. The HTFA hierarchical optimization has been fully implemented with:

• Global template computation across subjects with proper convergence
• Iterative optimization with global and local iterations
• MAP (Maximum A Posteriori) estimation implementation
• Factor matching across subjects using linear sum assignment
• Convergence checking for global template
• Proper handling of variable subject/voxel counts
• Integration with core TFA foundation

All acceptance criteria met. Issue completed on 2025-09-04.