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Title:

Nonlinear Functional Principal Component Analysis using Neural Networks

Version:

1.0

Description:

Implementation for 'nFunNN' method, which is a novel nonlinear functional principal component analysis method using neural networks. The crucial function of this package is nFunNNmodel().

License:

GPL (≥ 3)

Encoding:

UTF-8

RoxygenNote:

7.1.1

Imports:

fda, splines, stats, torch

NeedsCompilation:

Packaged:

2024-04-26 01:50:25 UTC; 11013

Author:

Rou Zhong [aut, cre], Jingxiao Zhang [aut]

Maintainer:

Rou Zhong <zhong_rou@163.com>

Repository:

CRAN

Date/Publication:

2024-04-28 09:40:02 UTC

Curve reconstruction

Description

Curve reconstruction by the trained transformed functional autoassociative neural network.

Usage

nFunNN_CR(model, X_ob, L, t_grid)

Arguments

model

The trained transformed functional autoassociative neural network obtained from nFunNNmodel.

X_ob

A matrix denoting the observed data from subjects that we aim to predict.

L

An integer denoting the number of B-spline basis functions for the parameters in the network.

t_grid

A vector denoting the observation time grids on [0, 1].

Value

A torch tensor denoting the predicted values.

Examples


n <- 2000
m <- 51
t_grid <- seq(0, 1, length.out = m)
m_est <- 101
t_grid_est <- seq(0, 1, length.out = m_est)
err_sd <- 0.1
Z_1a <- stats::rnorm(n, 0, 3)
Z_2a <- stats::rnorm(n, 0, 2)
Z_a <- cbind(Z_1a, Z_2a)
Phi <- cbind(sin(2 * pi * t_grid), cos(2 * pi * t_grid))
Phi_est <- cbind(sin(2 * pi * t_grid_est), cos(2 * pi * t_grid_est))
X <- Z_a %*% t(Phi)
X_to_est <- Z_a %*% t(Phi_est)
X_ob <- X + matrix(stats::rnorm(n * m, 0, err_sd), nr = n, nc = m)
L_smooth <- 10
L <- 10
J <- 20
K <- 2
R <- 20
nFunNN_res <- nFunNNmodel(X_ob, t_grid, t_grid_est, L_smooth,
L, J, K, R, lr = 0.001, n_epoch = 1500, batch_size = 100)
model <- nFunNN_res$model
X_pre <- nFunNN_CR(model, X_ob, L, t_grid)
sqrt(torch::nnf_mse_loss(X_pre, torch::torch_tensor(X_to_est))$item())

Nonlinear FPCA using neural networks

Description

Nonlinear functional principal component analysis using a transformed functional autoassociative neural network.

Usage

nFunNNmodel(
  X_ob,
  t_grid,
  t_grid_est,
  L_smooth,
  L,
  J,
  K,
  R,
  lr = 0.001,
  batch_size,
  n_epoch
)

Arguments

X_ob

A matrix denoting the observed data.

t_grid

A vector denoting the observation time grids on [0, 1].

t_grid_est

A vector denoting the time grids that have to be predicted on [0, 1].

L_smooth

An integer denoting the number of B-spline basis functions that used to smooth the observed data for the computation of the loss function.

L

An integer denoting the number of B-spline basis functions for the parameters in the network.

J

An integer denoting the number of neurons in the first hidden layer.

K

An integer denoting the number of principal components.

R

An integer denoting the number of neurons in the third hidden layer.

lr

A scalar denoting the learning rate. (default: 0.001)

batch_size

An integer denoting the batch size.

n_epoch

An integer denoting the number of epochs.

Value

A list containing the following components:

model

The resulting neural network trained by the observed data.

loss

A vector denoting the averaged loss in each epoch.

Comp_time

An object of class "difftime" denoting the computation time in seconds.

Examples


n <- 2000
m <- 51
t_grid <- seq(0, 1, length.out = m)
m_est <- 101
t_grid_est <- seq(0, 1, length.out = m_est)
err_sd <- 0.1
Z_1a <- stats::rnorm(n, 0, 3)
Z_2a <- stats::rnorm(n, 0, 2)
Z_a <- cbind(Z_1a, Z_2a)
Phi <- cbind(sin(2 * pi * t_grid), cos(2 * pi * t_grid))
Phi_est <- cbind(sin(2 * pi * t_grid_est), cos(2 * pi * t_grid_est))
X <- Z_a %*% t(Phi)
X_to_est <- Z_a %*% t(Phi_est)
X_ob <- X + matrix(stats::rnorm(n * m, 0, err_sd), nr = n, nc = m)
L_smooth <- 10
L <- 10
J <- 20
K <- 2
R <- 20
nFunNN_res <- nFunNNmodel(X_ob, t_grid, t_grid_est, L_smooth,
L, J, K, R, lr = 0.001, n_epoch = 1500, batch_size = 100)