ExtrinsicMean {spherepc}

Finding Extrinsic Mean

Description

This function identifies the extrinsic mean of data on the unit 2-sphere.

Usage

ExtrinsicMean(data, weights = rep(1, nrow(data)))

Arguments

data

matrix or data frame consisting of spatial locations with two columns. Each row represents longitude and latitude (denoted by degrees).

weights

vector of weights.

Details

This function identifies the extrinsic mean of data.

Value

two-dimensional vector.

Note

In the case of spheres, if data set is not contained in a hemisphere, then it is possible that the extrinsic mean of the data set does not exists; for example, a great circle.

Author(s)

Jongmin Lee

References

Jongmin Lee, Jang-Hyun Kim and Hee-Seok Oh. (2021). Spherical Principal Curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43, 2165-2171. <doi.org/10.1109/TPAMI.2020.3025327>. Jang-Hyun Kim, Jongmin Lee and Hee-Seok Oh. (2020). Spherical Principal Curves <arXiv:2003.02578>.

See Also

IntrinsicMean.

Examples

#### comparison of Intrinsic mean and extrinsic mean.
#### example: noisy circular data set.
library(rgl)
library(sphereplot)
library(geosphere)
n <- 500                  # the number of samples.
x <- 360 * runif(n) - 180
sigma <- 5
y <- 60 + sigma * rnorm(n)
simul.circle <- cbind(x, y)
data <- simul.circle
In.mean <- IntrinsicMean(data)
Ex.mean <- ExtrinsicMean(data)
## plot (color of data is "blue"; that of intrinsic mean is "red" and 
## that of extrinsic mean is "green".)
sphereplot::rgl.sphgrid()    
sphereplot::rgl.sphpoints(data, radius = 1, col = "blue", size = 12)
sphereplot::rgl.sphpoints(In.mean[1], In.mean[2], radius = 1, col = "red", size = 12)
sphereplot::rgl.sphpoints(Ex.mean[1], Ex.mean[2], radius = 1, col = "green", size = 12)