soft_thresholding function

Soft thresholding operator

soft_thresholding gives the soft threshold value of $y$ given the threshold. When threshold increasing, $y$ shrinks to zero.

soft_thresholding(y, threshold)

Arguments

• y: input real value
• threshold: threshold value

Examples

# clean up
rm(list = ls())
library(plde)
# soft thresholding operater
soft_thresholding(3, 1)
soft_thresholding(-3, 1)
# if the threshold value is large enough, it shrinks to zero
soft_thresholding(-3, 4)
soft_thresholding(3, 4)
# Plot of the soft thresholding operater
y = seq(-3, 3, length = 100)
st = NULL
for (i in 1 : length(y))
   st[i] = soft_thresholding(y[i], 1)
plot(y, y, col = "gray", type = "l", ylab = "ST")
lines(y, st, col = "blue")

Author(s)

JungJun Lee, Jae-Hwan Jhong, Young-Rae Cho, SungHwan Kim, Ja-yong Koo

References

JungJun Lee, Jae-Hwan Jhong, Young-Rae Cho, SungHwan Kim and Ja-Yong Koo. "Penalized Log-density Estimation Using Legendre Polynomials." Submitted to Communications in Statistics - Simulation and Computation (2017), in revision.