Implement core TFA optimization algorithm

[jeremymanning]

Summary

Implement the core Topographic Factor Analysis optimization algorithm based on the BrainIAK implementation.

Tasks

• Implement k-means based initialization for spatial factors
• Add non-linear least squares optimization for factor estimation
• Implement ridge regression and OLS weight estimation methods
• Add convergence checking and iteration control
• Implement proper factor matching using linear sum assignment
• Add trust region optimization methods

Dependencies

• NumPy for numerical computations
• SciPy for optimization algorithms
• scikit-learn for k-means clustering

References

• Manning et al. (2014) - original TFA paper
• BrainIAK TFA implementation: https://github.com/brainiak/brainiak/blob/master/src/brainiak/factoranalysis/tfa.py

Acceptance Criteria

• TFA class can fit realistic neuroimaging data
• Optimization converges within reasonable iterations
• Factors and weights are properly estimated
• 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 core TFA algorithm has been fully implemented with:

• Complete k-means initialization for spatial factors
• Non-linear optimization using scipy with L-BFGS and trust region methods
• Ridge regression and OLS weight estimation
• Convergence checking and iteration control
• Proper factor matching using linear sum assignment
• Integration with scikit-learn BaseEstimator interface

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