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.
<- 50
number_of_explanatory_points
<- get_equally_spaced_points(
explanatory_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)])
<- function(point) {
local_rotation_composer <- (1 / 2) *
independent_components 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:
<- function(point) {
local_error_sampler rnorm(3,mean=0,sd=.25)
}
<- simulate_regression(explanatory_points,
response_points
local_rotation_composer,
local_error_sampler)
# Define a matrix of evaluation points for prediction.
<- rbind(
evaluation_points 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.
<- weight_explanatory_points
weights_generator
# Set the concentration parameter (kappa).
<- 5
concentration
# Fit regression.
<- fit_regression(
fit_info
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")`