Functional Principal Component Analysis¶
Vertical and Horizontal Functional Principal Component Analysis using SRSF
moduleauthor:: J. Derek Tucker <jdtuck@sandia.gov>
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class
fPCA.
fdahpca
(fdawarp)[source]¶ This class provides horizontal fPCA using the SRVF framework
Usage: obj = fdahpca(warp_data)
Parameters: - warp_data – fdawarp class with alignment data
- gam_pca – warping functions principal directions
- psi_pca – srvf principal directions
- latent – latent values
- U – eigenvectors
- coef – coefficients
- vec – shooting vectors
- mu – Karcher Mean
- tau – principal directions
Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov> Date : 15-Mar-2018
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calc_fpca
(no=3, stds=array([-1, 0, 1]))[source]¶ This function calculates horizontal functional principal component analysis on aligned data
Parameters: - no (int) – number of components to extract (default = 3)
- stds – number of standard deviations along gedoesic to compute (default = -1,0,1)
Return type: fdahpca object of numpy ndarray
Return q_pca: srsf principal directions
Return f_pca: functional principal directions
Return latent: latent values
Return coef: coefficients
Return U: eigenvectors
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class
fPCA.
fdajpca
(fdawarp)[source]¶ This class provides joint fPCA using the SRVF framework
Usage: obj = fdajpca(warp_data)
Parameters: - warp_data – fdawarp class with alignment data
- q_pca – srvf principal directions
- f_pca – f principal directions
- latent – latent values
- coef – principal coefficients
- id – point used for f(0)
- mqn – mean srvf
- U – eigenvectors
- mu_psi – mean psi
- mu_g – mean g
- C – scaling value
- stds – geodesic directions
Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov> Date : 18-Mar-2018
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calc_fpca
(no=3, stds=array([-1., 0., 1.]), id=None, parallel=False, cores=-1)[source]¶ This function calculates joint functional principal component analysis on aligned data
Parameters: - no (int) – number of components to extract (default = 3)
- id (int) – point to use for f(0) (default = midpoint)
- stds – number of standard deviations along gedoesic to compute (default = -1,0,1)
- parallel (bool) – run in parallel (default = F)
- cores (int) – number of cores for parallel (default = -1 (all))
Return type: fdajpca object of numpy ndarray
Return q_pca: srsf principal directions
Return f_pca: functional principal directions
Return latent: latent values
Return coef: coefficients
Return U: eigenvectors
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class
fPCA.
fdavpca
(fdawarp)[source]¶ This class provides vertical fPCA using the SRVF framework
Usage: obj = fdavpca(warp_data)
Parameters: - warp_data – fdawarp class with alignment data
- q_pca – srvf principal directions
- f_pca – f principal directions
- latent – latent values
- coef – principal coefficients
- id – point used for f(0)
- mqn – mean srvf
- U – eigenvectors
- stds – geodesic directions
Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov> Date : 15-Mar-2018
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calc_fpca
(no=3, id=None, stds=array([-1, 0, 1]))[source]¶ This function calculates vertical functional principal component analysis on aligned data
Parameters: Return type: fdavpca object containing
Return q_pca: srsf principal directions
Return f_pca: functional principal directions
Return latent: latent values
Return coef: coefficients
Return U: eigenvectors