Elastic Principal Component Regression

Warping Invariant PCR Regression using SRSF

moduleauthor:: J. Derek Tucker <jdtuck@sandia.gov>

class pcr_regression.elastic_lpcr_regression(f, y, time)

This class provides elastic logistic pcr regression for functional data using the SRVF framework accounting for warping

Usage: obj = elastic_lpcr_regression(f,y,time)

Parameters:

• f – (M,N) % matrix defining N functions of M samples

• y – response vector of length N (-1/1)

• warp_data – fdawarp object of alignment

• pca – class dependent on fPCA method used object of fPCA

• information –

• alpha – intercept

• b – coefficient vector

• Loss – logistic loss

• PC – probability of classification

• ylabels – predicted labels

Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov> Date : 18-Mar-2018

calc_model(pca_method='combined', no=5, smooth_data=False, sparam=25, parallel=False)

This function identifies a logistic regression model with phase-variability using elastic pca

Parameters:

• pca_method – string specifying pca method (options = “combined”, “vert”, or “horiz”, default = “combined”)

• no – scalar specify number of principal components (default=5)

• smooth_data – smooth data using box filter (default = F)

• sparam – number of times to apply box filter (default = 25)

• parallel – calculate in parallel (default = F)

predict(newdata=None)

This function performs prediction on regression model on new data if available or current stored data in object Usage: obj.predict(newdata)

Parameters:

• newdata (dict) – dict containing new data for prediction (needs the keys below, if None predicts on training data)

• f – (M,N) matrix of functions

• time – vector of time points

• y – truth if available

• smooth – smooth data if needed

• sparam – number of times to run filter

class pcr_regression.elastic_mlpcr_regression(f, y, time)

This class provides elastic multinomial logistic pcr regression for functional data using the SRVF framework accounting for warping

Usage: obj = elastic_mlpcr_regression(f,y,time)

Parameters:

• f – (M,N) % matrix defining N functions of M samples

• y – response vector of length N

• Y – coded label matrix

• warp_data – fdawarp object of alignment

• pca – class dependent on fPCA method used object of fPCA

• information –

• alpha – intercept

• b – coefficient vector

• Loss – logistic loss

• PC – probability of classification

• ylabels – predicted labels

Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov> Date : 18-Mar-2018

calc_model(pca_method='combined', no=5, smooth_data=False, sparam=25, parallel=False)

This function identifies a logistic regression model with phase-variability using elastic pca

Parameters:

• f (np.ndarray) – numpy ndarray of shape (M,N) of N functions with M samples

• y – numpy array of N responses

• time (np.ndarray) – vector of size M describing the sample points

• pca_method – string specifying pca method (options = “combined”, “vert”, or “horiz”, default = “combined”)

• no – scalar specify number of principal components (default=5)

• smooth_data – smooth data using box filter (default = F)

• sparam – number of times to apply box filter (default = 25)

• parallel – run model in parallel (default = F)

predict(newdata=None)

This function performs prediction on regression model on new data if available or current stored data in object Usage: obj.predict(newdata)

Parameters:

• newdata (dict) – dict containing new data for prediction (needs the keys below, if None predicts on training data)

• f – (M,N) matrix of functions

• time – vector of time points

• y – truth if available

• smooth – smooth data if needed

• sparam – number of times to run filter

class pcr_regression.elastic_pcr_regression(f, y, time)

This class provides elastic pcr regression for functional data using the SRVF framework accounting for warping

Usage: obj = elastic_pcr_regression(f,y,time)

Parameters:

• f – (M,N) % matrix defining N functions of M samples

• y – response vector of length N

• warp_data – fdawarp object of alignment

• pca – class dependent on fPCA method used object of fPCA

• alpha – intercept

• b – coefficient vector

• SSE – sum of squared errors

Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov> Date : 18-Mar-2018

calc_model(pca_method='combined', no=5, var_exp=None, smooth_data=False, sparam=25, parallel=False, C=None)

This function identifies a regression model with phase-variability using elastic pca

Parameters:

• pca_method – string specifying pca method (options = “combined”, “vert”, or “horiz”, default = “combined”)

• no – scalar specify number of principal components (default=5)

• var_exp – compute no based on value percent variance explained (example: 0.95)

• smooth_data – smooth data using box filter (default = F)

• sparam – number of times to apply box filter (default = 25)

• parallel – run in parallel (default = F)

• C – scale balance parameter for combined method (default = None)

predict(newdata=None, alpha=0.05)

This function performs prediction on regression model on new data if available or current stored data in object Usage: obj.predict(newdata)

Parameters:

• newdata (dict) – dict containing new data for prediction (needs the keys below, if None predicts on training data)

• f – (M,N) matrix of functions

• time – vector of time points

• y – truth if available

• smooth – smooth data if needed

• sparam – number of times to run filter