SPC.Hauberg {spherepc}

principal curves by Hauberg on a sphere

Description

This function fits a principal curve by Hauberg on the unit 2-sphere.

Usage

SPC.Hauberg(data, q = 0.1, T = nrow(data), step.size = 1e-3, maxit = 10, 
type = "Intrinsic", thres = 1e-2, deletePoints = FALSE, plot.proj = FALSE, 
kernel = "quartic", col1 = "blue", col2 = "green", col3 = "red")

Arguments

data

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

q

numeric value of the smoothing parameter. The parameter plays the same role, as the bandwidth does in kernel regression, in the SPC function. The value should be a numeric value between 0.01 and 0.5. The default is 0.1.

T

the number of points making up the resulting curve. The default is 1000.

step.size

step size of the PrincipalCircle function. The default is 0.001. The resulting principal circle is used by an initialization of the SPC.

maxit

maximum number of iterations. The default is 30.

type

type of mean on sphere. The default is "Intrinsic" and the alternative is "extrinsic".

thres

threshold of the stopping condition. The default is 0.01.

deletePoints

logical value. The argument is an option of whether to delete points or not. If deletePoints is FALSE, this function leaves the points in curves which do not have adjacent data for each expectation step. As a result, the function usually returns a closed curve, i.e. a curve without endpoints. If deletePoints is TRUE, this function deletes the points in curves which do not have adjacent data for each expectation step. As a result, The SPC function usually returns an open curve, i.e. a curve with endpoints. The default is FALSE.

plot.proj

logical value. If the argument is TRUE, the projection line for each data is plotted. The default is FALSE.

kernel

kind of kernel function. The default is quartic kernel and alternatives are indicator or Gaussian.

col1

color of data. The default is blue.

col2

color of points in the principal curves. The default is green.

col3

color of resulting principal curves. The default is red.

Details

This function fits a principal curve proposed by Hauberg on the sphere, and requires to load the 'rgl', 'sphereplot', and 'geosphere' R packages.

Value

plot and a list consisting of

prin.curves

spatial locations (denoted by degrees) of points in the resulting principal curves.

line

connecting line bewteen points of prin.curves.

converged

whether or not the algorithm converged.

iteration

the number of iterations of the algorithm.

recon.error

sum of squared distances from the data to their projections.

num.dist.pt

the number of distinct projections.

plot

plotting of the data and principal curves.

Note

This function requires to load 'rgl', 'sphereplot', and 'geosphere' R packages.

Author(s)

Jongmin Lee

References

Hauberg, S. (2016). Principal curves on Riemannian manifolds. IEEE Transactions on Pattern Analysis and Machine Intelligence, 38, 1915-1921.

Jang-Hyun Kim, Jongmin Lee and Hee-Seok Oh. (2020). Spherical Principal Curves <arXiv:2003.02578>.

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>.

See Also

SPC, Proj.Hauberg.

Examples

library(rgl)
library(sphereplot)
library(geosphere)

#### example 1: earthquake data
data(Earthquake)
names(Earthquake)
earthquake <- cbind(Earthquake$longitude, Earthquake$latitude)
SPC.Hauberg(earthquake, q = 0.1)

#### example 2: waveform data
## longitude and latitude are expressed in degrees
n <- 200
alpha <- 1/3; freq <- 4                           # amplitude and frequency of wave
sigma <- 2                                        # noise level
lon <- seq(-180, 180, length.out = n)             # uniformly sampled longitude
lat <- alpha * 180/pi * sin(freq * lon * pi/180) + 10.        # latitude vector
## add Gaussian noises on latitude vector
lat1 <- lat + sigma * rnorm(length(lon))
wave <- cbind(lon, lat1)
## implement principal curves by Hauberg to the waveform data
SPC.Hauberg(wave, q = 0.05)