This is `nprotreg`

, an `R`

package that exploits nonparametric rotations in the analysis of Sphere-Sphere regression models.

The package implements methods proposed by Di Marzio, Panzera & Taylor (2018).

Thanks to package `nprotreg`

, regressing data represented as points on a hypersphere you can * simulate a very flexible regression model where, for each location of the manifold, a specific rotation matrix is applied to obtain a spherical response; * fit Sphere-Sphere regression models by allowing for approximations of rotation matrices based on a series expansion; * reduce estimation bias applying iterative estimation procedures within a Newton-Raphson learning scheme; * use cross-validation to select smoothing parameters.

The following script shows how to fit a Sphere-Sphere regression model using simulated data via package `nprotreg`

.

```
library(nprotreg)
# Define a matrix of explanatory points.
number_of_explanatory_points <- 50
explanatory_points <- get_equally_spaced_points(
number_of_explanatory_points)
# Define a matrix of response points by simulation.
# - define the response local rotation model (eg Model 2 in Table 1 of [Di Marzio, Panzera & Taylor (2018)])
local_rotation_composer <- function(point) {
independent_components <- (1 / 2) *
c(exp(2.0 * point[3]), - exp(2.0 * point[2]), exp(2.0 * point[1]))
}
# - define a rotation (error) perturbation model using random skew symmetric matrix:
local_error_sampler <- function(point) {
rnorm(3,mean=0,sd=.25)
}
response_points <- simulate_regression(explanatory_points,
local_rotation_composer,
local_error_sampler)
# Define a matrix of evaluation points for prediction.
evaluation_points <- rbind(
cbind(.5, 0, .8660254),
cbind(-.5, 0, .8660254),
cbind(1, 0, 0),
cbind(0, 1, 0),
cbind(-1, 0, 0),
cbind(0, -1, 0),
cbind(.5, 0, -.8660254),
cbind(-.5, 0, -.8660254)
)
# Use a default weights generator.
weights_generator <- weight_explanatory_points
# Set the concentration parameter (kappa).
concentration <- 5
# Fit regression.
fit_info <- fit_regression(
evaluation_points,
explanatory_points,
response_points,
concentration,
weights_generator,
number_of_expansion_terms = 1,
number_of_iterations = 2
)
```

See the documentation for addressing additional scenarios.

To download and install the package from the CRAN repository, execute the following command:

`install.packages("nprotreg")`