train_function: Main fitting algorithm of FSPDM method

In feiding333/FSPDM: Supervised Functional PCA by Symmetric Positive Definite Covariance Matrix Construction

Description

Main fitting algorithm of FSPDM method

Usage

train_function(Data_generated, Eig_num, k, beta, theta, sigma2,
  lambda1 = 0, lambda2 = 0, lambda3 = 0, lambda4 = 0,
  testIndexes = NULL, sigma2_list = NULL, maxout = 1)

Arguments

Data_generated	a list constaining the observed value of functional data, covariates and penalty matrix
Eig_num	the number of eigenfunction users want to use
k	dimension of spline basis with respect to covariate in eigenfunctions
beta	the start point of beta parameters, can be set with all zeros
theta	the start point of theta parameters, can be set with all zeros
sigma2	the start point of sigma2 parameters, can be set with small positive value
lambda1	the tuning parameters of smoothness penalty with respect to t in mean function
lambda2	the tuning parameters of smoothness penalty with respect to covariate in mean function
lambda3	the tuning parameters of smoothness penalty with respect to t in eigenfunction
lambda4	he tuning parameters of smoothness penalty with respect to covariate in eigenfunction
testIndexes	test Index if use cv
sigma2_list	measurement error if have
maxout	algorithm setting, default 1

Value

a list constains all estimator of SFPDM method

Examples

tmin = 0 # the start point of the curve
tmax = 1 # the end point of the curve, i.e. the cuvre's regin is from tmin to tmax
ymin = 0 # the minimum of the covariates
ymax = 1 # the maximum of the covariate
num_bin = 20 # number of bin in initial steps of our algorithm
order = 4 # spline order
nknots =8 # number of knots
splineObj_t = new(orthoSpline,tmin,tmax,order,nknots)
# degree freedom of spline basis
M1 = splineObj_t$getDoF()
## basis with respect to y to get the tensor product basis
yknots = 3
splineObj_y = new(orthoSpline,ymin,ymax,order,(yknots))
# degree freedom of spline basis
M2 = splineObj_y$getDoF()
## basis with d that is in matrix C
# basis with respect y (d^T), in C matrix
dknots = 5
splineObj_d = new(orthoSpline,ymin,ymax,order,dknots)
# degree freedom of spline basis
M3 = splineObj_d$getDoF()
k = M3
Spline_func = c(splineObj_t,splineObj_d,splineObj_y)
## set the number of principle components
Eig_num = r =  3
## the the number of spline basis used
## spline basis for t
M1 = 10
M2 = 5
M3 = k = 7
theta = rep(0,M1*M2)
sigma2 = 0.01
beta = rep(0,r*M1*M3)
parameter_best = train_function (Data_generated = Data_generated,Eig_num = Eig_num,k = k, beta = beta,theta = theta,sigma2 = sigma2)

feiding333/FSPDM documentation built on Feb. 6, 2020, 4:48 a.m.