This function makes an iteration of PCA-Gaussianization process — GPCA_iteration • RMAWGEN

This function makes an iteration of PCA-Gaussianization process

GPCA_iteration(x_prev, extremes = TRUE, nearPD = FALSE)

Arguments

x_prev: previous set of random variable x
extremes: see normalizeGaussian_severalstations
nearPD: logical. Default is FALSE. If TRUE covariance matrix is corrected through Nearest Positive Definite Matrix procedure, i.e. nearPD

Value

A GPCA_iteration S3 object which contains the following objects:

x_prev Previous set of random variable, x_prev input variable

x_gauss_prev Marginal Gaussianization of x_prev obtained through normalizeGaussian_severalstations

B_prev rotation matrix (i. e. eigenvector matrix of the covariance matrix of x_gauss_prev

x_next results obtained by multiplying B_prev by x_gauss_prev (see equation 1 of the reference)

Note

This function is based on equation (1) of "PCA Gaussianization for One-Class Remote Sensing Image" by V. Laparra et al., https://www.uv.es/lapeva/papers/SPIE09_one_class.pdf and https://ieeexplore.ieee.org/document/5413808/

See also

GPCA,GPCA_iteration,inv_GPCA_iteration,inv_GPCA

Author

Emanuele Cordano

Examples

library(RMAWGEN)
set.seed(1222)
N <- 20
x <- rexp(N)
y <- x+rnorm(N)
df <- data.frame(x=x,y=y)

GPCA <- GPCA_iteration(df,extremes=TRUE)

x <- rnorm(N)
y <- x+rnorm(N)
dfn <- data.frame(x=x,y=y)

GPCAn <- GPCA_iteration(dfn,extremes=TRUE)