PCA computation speedup by switching to Eigen #2473
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Switch ParticleShapeStatistics::compute_modes() from VNL's vnl_symmetric_eigensystem to Eigen's BDCSVD algorithm. This provides: - Better numerical stability by computing SVD directly on the centered data matrix rather than forming the covariance matrix A^T*A first - Reduced dependency on legacy VNL library in favor of Eigen - Cleaner code using Eigen's built-in vector normalization The SVD singular values squared equal the eigenvalues, and the left singular vectors (U) correspond to the eigenvectors in particle space. Results are reversed to maintain ascending eigenvalue order for backward compatibility. Also add profiling instrumentation to compute_modes() and Studio main.
The switch from VNL's vnl_symmetric_eigensystem to Eigen's BDCSVD introduced test failures due to eigenvector sign ambiguity. In PCA, eigenvectors are only determined up to a sign (both v and -v are valid), and different libraries may return either arbitrarily. Add a consistent sign convention: make the first element of each eigenvector positive. This ensures deterministic results regardless of the underlying linear algebra implementation. Update test baselines to match the new consistent sign convention. This way if we switch to another implementation later, we can keep the results consistent.
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Replace VNL eigensystem with Eigen SVD for PCA computation
Switch ParticleShapeStatistics::compute_modes() from VNL's vnl_symmetric_eigensystem to Eigen's BDCSVD algorithm. This provides:
The SVD singular values squared equal the eigenvalues, and the left singular vectors (U) correspond to the eigenvectors in particle space. Results are reversed to maintain ascending eigenvalue order for backward compatibility.
Also add profiling instrumentation to compute_modes() and Studio main.
Profiling with a large dataset (1024 particles X 5,000 shapes) reduced PCA computation from 90 seconds to 19, about 4-5 times faster.