clean_euler_ridge: Clean ridge points coming from spurious fits

In polykde: Polyspherical Kernel Density Estimation

Clean ridge points coming from spurious fits

Description

Remove points from the ridge that are spurious. The cleaning is done by removing end points in the Euler algorithm that did not converge, do not have a negative second eigenvalue, or are in low-density regions.

Usage

clean_euler_ridge(e, X, p_out = NULL)

Arguments

e	outcome from euler_ridge or parallel_euler_ridge.
X	a matrix of size c(n, sum(d) + r) with the sample.
p_out	proportion of outliers to remove. Defaults to NULL (no cleaning).

Value

A list with the same structure as that returned by euler_ridge, but with the spurious points. The removed points are informed in the removed field.

Examples

## Test on S^2 with some spurious end points

# Sample
r <- 1
d <- 2
n <- 50
ind_dj <- comp_ind_dj(d = d)
set.seed(987202226)
X <- r_path_s2r(n = n, r = r, spiral = FALSE, Theta = cbind(c(1, 0, 0)),
                sigma = 0.2)[, , 1]
col_X <- rep(gray(0), n)
col_X_alp <- rep(gray(0, alpha = 0.25), n)

# Euler
h_rid <- 0.5
h_eu <- h_rid^2
N <- 30
eps <- 1e-6
X0 <- r_unif_polysph(n = n, d = d)
Y <- euler_ridge(x = X0, X = X, d = d, h = h_rid, h_euler = h_eu,
                 N = N, eps = eps, keep_paths = TRUE)
Y_removed <- clean_euler_ridge(e = Y, X = X)$removed
col_X[Y_removed] <- 2
col_X_alp[Y_removed] <- 2

# Visualization
i <- N # Between 1 and N
sc3 <- scatterplot3d::scatterplot3d(Y$paths[, , 1], color = col_X_alp,
                                    pch = 19, xlim = c(-1, 1),
                                    ylim = c(-1, 1), zlim = c(-1, 1),
                                    xlab = "x", ylab = "y", zlab = "z")
sc3$points3d(rbind(Y$paths[, , i]), col = col_X, pch = 16, cex = 0.75)
for (k in seq_len(nrow(Y$paths))) {

  sc3$points3d(t(Y$paths[k, , ]), col = col_X_alp[k], type = "l")

}

polykde documentation built on April 16, 2025, 1:11 a.m.