PrincipalCircle {spherepc}

Principal circle on a sphere

Description

This function fits a principal circle on sphere via gradient descent algorithm.

Usage

PrincipalCircle(data, step.size = 1e-3, thres = 1e-5, maxit = 10000)

Arguments

data

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

step.size

step size of gradient descent algorithm. For convergence of the algorithm, step.size is recommended to be below 0.01. The default is 1e-3.

thres

threshold of the stopping condition. The default is 1e-5.

maxit

maximum number of iterations. The default is 10000.

Details

This function fits a principal circle on sphere via gradient descent algorithm. The function returns three-dimensional vectors whose components represent longitude and latitude of the center and the radius of the circle in regular order.

Value

three-dimensional vector.

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

GenerateCircle

Examples

library(rgl)
library(sphereplot)
library(geosphere)
#### example 1: half-great circle data
circle <- GenerateCircle(c(150, 60), radius = pi/2)
half.great.circle <- circle[circle[, 1] < 0, , drop = FALSE]
sigma <- 2
half.great.circle <- half.great.circle + sigma * rnorm(nrow(half.great.circle))
## find a principal circle

PC <- PrincipalCircle(half.great.circle)
result <- GenerateCircle(PC[1:2], PC[3])
## plot
rgl.sphgrid()
rgl.sphpoints(half.great.circle, radius = 1, col = "blue", size = 12)
rgl.sphpoints(result, radius = 1, col = "red", size = 6)

#### example 2: circular data
n <- 700                            
x <- seq(-180, 180, length.out = n)
sigma <- 5                          
y <- 45 + sigma * rnorm(n)
simul.circle <- cbind(x, y)
## find a principal circle
PC <- PrincipalCircle(simul.circle)
result <- GenerateCircle(PC[1:2], PC[3])
## plot
sphereplot::rgl.sphgrid()
sphereplot::rgl.sphpoints(simul.circle, radius = 1, col = "blue", size = 12)
sphereplot::rgl.sphpoints(result, radius = 1, col = "red", size = 6)

#### example 3: earthquake data
data(Earthquake)
names(Earthquake)
earthquake <- cbind(Earthquake$longitude, Earthquake$latitude) 
PC <- PrincipalCircle(earthquake)
result <- GenerateCircle(PC[1:2], PC[3])
## plot
sphereplot::rgl.sphgrid(col.long = "black", col.lat = "black")
sphereplot::rgl.sphpoints(earthquake, radius = 1, col = "blue", size = 12)
sphereplot::rgl.sphpoints(result, radius = 1, col = "red", size = 6)