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-Elastic Regression
-Warping Invariant Regression using SRSF
-moduleauthor:: J. Derek Tucker <jdtuck@sandia.gov>
-
--
-class regression.elastic_logistic(f, y, time)[source]
-This class provides elastic logistic regression for functional data using the
-SRVF framework accounting for warping
-Usage: obj = elastic_logistic(f,y,time)
-
-- 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
B – optional matrix describing Basis elements
alpha – alpha parameter of model
beta – beta(t) of model
fn – aligned functions - numpy ndarray of shape (M,N) of M functions with N samples
qn – aligned srvfs - similar structure to fn
gamma – calculated warping functions
q – original training SRSFs
b – basis coefficients
Loss – logistic loss
-
-Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov>
-Date : 29-Oct-2021
-
--
-calc_model(B=None, lam=0, df=20, max_itr=20, cores=- 1, smooth=False)[source]
-This function identifies a regression model with phase-variability
-using elastic pca
-
-- Parameters:
-
-B – optional matrix describing Basis elements
lam – regularization parameter (default 0)
df – number of degrees of freedom B-spline (default 20)
max_itr – maximum number of iterations (default 20)
cores – number of cores for parallel processing (default all)
-
-
-
-
--
-predict(newdata=None)[source]
-This function performs prediction on regression model on new data if available or current stored data in object
-Usage: obj.predict()
-
-
-
-- 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 regression.elastic_mlogistic(f, y, time)[source]
-This class provides elastic multinomial logistic regression for functional data using the
-SRVF framework accounting for warping
-Usage: obj = elastic_mlogistic(f,y,time)
-
-- 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
B – optional matrix describing Basis elements
alpha – alpha parameter of model
beta – beta(t) of model
fn – aligned functions - numpy ndarray of shape (M,N) of N functions with M samples
qn – aligned srvfs - similar structure to fn
gamma – calculated warping functions
q – original training SRSFs
b – basis coefficients
Loss – logistic loss
-
-Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov>
-Date : 29-Oct-2021
-
--
-calc_model(B=None, lam=0, df=20, max_itr=20, delta=0.01, cores=- 1, smooth=False)[source]
-This function identifies a regression model with phase-variability
-using elastic pca
-
-- Parameters:
-
-B – optional matrix describing Basis elements
lam – regularization parameter (default 0)
df – number of degrees of freedom B-spline (default 20)
max_itr – maximum number of iterations (default 20)
cores – number of cores for parallel processing (default all)
-
-
-
-
--
-predict(newdata=None)[source]
-This function performs prediction on regression model on new data if available or current stored data in object
-Usage: obj.predict()
-
-
-
-- 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 regression.elastic_regression(f, y, time)[source]
-This class provides elastic regression for functional data using the
-SRVF framework accounting for warping
-Usage: obj = elastic_regression(f,y,time)
-
-- Parameters:
-
-f – numpy ndarray of shape (M,N) of N functions with M samples
y – numpy array of N responses
time – vector of size M describing the sample points
B – optional matrix describing Basis elements
alpha – alpha parameter of model
beta – beta(t) of model
fn – aligned functions - numpy ndarray of shape (M,N) of M functions with N samples
qn – aligned srvfs - similar structure to fn
gamma – calculated warping functions
q – original training SRSFs
b – basis coefficients
SSE – sum of squared error
-
-Author : J. D. Tucker (JDT) <jdtuck AT sandia.gov>
-Date : 29-Oct-2021
-
--
-calc_model(B=None, lam=0, df=20, max_itr=20, cores=- 1, smooth=False)[source]
-This function identifies a regression model with phase-variability
-using elastic pca
-
-- Parameters:
-
-B – optional matrix describing Basis elements
lam – regularization parameter (default 0)
df – number of degrees of freedom B-spline (default 20)
max_itr – maximum number of iterations (default 20)
cores – number of cores for parallel processing (default all)
-
-
-
-
--
-predict(newdata=None)[source]
-This function performs prediction on regression model on new data if available or current stored data in object
-Usage: obj.predict()
-
-
-
-- 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
-
-
-
-
-
-
--
-regression.logistic_warp(beta, time, q, y)[source]
-calculates optimal warping for function logistic regression
-
-- Parameters:
-
-beta – numpy ndarray of shape (M,N) of N functions with M samples
time – vector of size N describing the sample points
q – numpy ndarray of shape (M,N) of N functions with M samples
y – numpy ndarray of shape (1,N) responses
-- Return type:
-numpy array
-- Return gamma:
-warping function
-
-
-
-
--
-regression.logit_gradient(b, X, y)[source]
-calculates gradient of the logistic loss
-
-- Parameters:
-
-b – numpy ndarray of shape (M,N) of N functions with M samples
X – numpy ndarray of shape (M,N) of N functions with M samples
y – numpy ndarray of shape (1,N) responses
-- Return type:
-numpy array
-- Return grad:
-gradient of logistic loss
-
-
-
-
--
-regression.logit_hessian(s, b, X, y)[source]
-calculates hessian of the logistic loss
-
-- Parameters:
-
-s – numpy ndarray of shape (M,N) of N functions with M samples
b – numpy ndarray of shape (M,N) of N functions with M samples
X – numpy ndarray of shape (M,N) of N functions with M samples
y – numpy ndarray of shape (1,N) responses
-- Return type:
-numpy array
-- Return out:
-hessian of logistic loss
-
-
-
-
--
-regression.logit_loss(b, X, y)[source]
-logistic loss function, returns Sum{-log(phi(t))}
-
-- Parameters:
-
-b – numpy ndarray of shape (M,N) of N functions with M samples
X – numpy ndarray of shape (M,N) of N functions with M samples
y – numpy ndarray of shape (1,N) of N responses
-- Return type:
-numpy array
-- Return out:
-loss value
-
-
-
-
--
-regression.mlogit_gradient(b, X, Y)[source]
-calculates gradient of the multinomial logistic loss
-
-- Parameters:
-
-b – numpy ndarray of shape (M,N) of N functions with M samples
X – numpy ndarray of shape (M,N) of N functions with M samples
y – numpy ndarray of shape (1,N) responses
-- Return type:
-numpy array
-- Return grad:
-gradient
-
-
-
-
--
-regression.mlogit_loss(b, X, Y)[source]
-calculates multinomial logistic loss (negative log-likelihood)
-
-- Parameters:
-
-b – numpy ndarray of shape (M,N) of N functions with M samples
X – numpy ndarray of shape (M,N) of N functions with M samples
y – numpy ndarray of shape (1,N) responses
-- Return type:
-numpy array
-- Return nll:
-negative log-likelihood
-
-
-
-
--
-regression.mlogit_warp_grad(alpha, beta, time, q, y, max_itr=8000, tol=1e-10, delta=0.008, display=0)[source]
-calculates optimal warping for functional multinomial logistic regression
-
-- Parameters:
-
-alpha – scalar
beta – numpy ndarray of shape (M,N) of N functions with M samples
time – vector of size M describing the sample points
q – numpy ndarray of shape (M,N) of N functions with M samples
y – numpy ndarray of shape (1,N) responses
max_itr – maximum number of iterations (Default=8000)
tol – stopping tolerance (Default=1e-10)
delta – gradient step size (Default=0.008)
display – display iterations (Default=0)
-- Return type:
-tuple of numpy array
-- Return gam_old:
-warping function
-
-
-
-
--
-regression.phi(t)[source]
-calculates logistic function, returns 1 / (1 + exp(-t))
-
-- Parameters:
-t – scalar
-- Return type:
-numpy array
-- Return out:
-return value
-
-
-
-
--
-regression.regression_warp(beta, time, q, y, alpha)[source]
-calculates optimal warping for function linear regression
-
-- Parameters:
-
-beta – numpy ndarray of shape (M,N) of M functions with N samples
time – vector of size N describing the sample points
q – numpy ndarray of shape (M,N) of M functions with N samples
y – numpy ndarray of shape (1,N) of M functions with N samples responses
alpha – numpy scalar
-- Return type:
-numpy array
-- Return gamma_new:
-warping function
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diff --git a/doc/build/html/search.html b/doc/build/html/search.html
index 6f963a34..79ee3d80 100644
--- a/doc/build/html/search.html
+++ b/doc/build/html/search.html
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Search — fdasrsf 2.4.0 documentation
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Search — fdasrsf 2.4.1 documentation
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diff --git a/doc/build/html/searchindex.js b/doc/build/html/searchindex.js
index d0394ce9..71cf2b9f 100644
--- a/doc/build/html/searchindex.js
+++ b/doc/build/html/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"docnames": ["boxplots", "curve_example", "curve_functions", "curve_statistics", "elastic_glm_regression", "fPCA", "fPLS", "fpca_example", "geodesic", "image", "index", "kmeans", "pcr_regression", "regression", "time_warping", "time_warping_example", "tolerance", "umap_metric", "user_guide", "utility_functions"], "filenames": ["boxplots.rst", "curve_example.ipynb", "curve_functions.rst", "curve_statistics.rst", "elastic_glm_regression.rst", "fPCA.rst", "fPLS.rst", "fpca_example.ipynb", "geodesic.rst", "image.rst", "index.rst", "kmeans.rst", "pcr_regression.rst", "regression.rst", "time_warping.rst", "time_warping_example.ipynb", "tolerance.rst", "umap_metric.rst", "user_guide.rst", "utility_functions.rst"], "titles": ["Elastic Functional Boxplots", "Elastic Curve Alignment", "Curve Functions", "Curve Registration", "Elastic GLM Regression", "Functional Principal Component Analysis", "Functional Principal Least Squares", "Elastic Functional Principal Component Analysis", "SRVF Geodesic Computation", "Elastic Image Warping", "Welcome to fdasrsf\u2019s documentation!", "Elastic Functional Clustering", "Elastic Principal Component Regression", "Elastic Regression", "Functional Alignment", "Elastic Functional Alignment", "Elastic Functional Tolerance Bounds", "UMAP EFDA Metrics", "User Guide", "Utility Functions"], "terms": {"moduleauthor": [0, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19], "j": [0, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19], "derek": [0, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19], "tucker": [0, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19], "jdtuck": [0, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19], "sandia": [0, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19], "gov": [0, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19], "class": [0, 3, 4, 5, 12, 13, 14], "ampbox": [0, 16], "fdawarp": [0, 5, 7, 12, 14, 15, 16], "sourc": [0, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 19], "thi": [0, 2, 3, 4, 5, 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