thresh.l1: Shrinkage operator

In rpca: RobustPCA: Decompose a Matrix into Low-Rank and Sparse Components

Description

Shrinkage operator: S[x] = sgn(x) max(|x| - thr, 0). For description see section 5 of Candès, E. J., Li, X., Ma, Y., & Wright, J. (2011). Robust principal component analysis?.

Usage

thresh.l1(x, thr)

Arguments

x	a vector or a matrix.
thr	threshold >= 0 to shrink with.

Value

S[x] = sgn(x) max(|x| - thr, 0)

References

Candès, E. J., Li, X., Ma, Y., & Wright, J. (2011). Robust principal component analysis?. Journal of the ACM (JACM), 58(3), 11

Yuan, X., & Yang, J. (2009). Sparse and low-rank matrix decomposition via alternating direction methods. preprint, 12.

See Also

thresh.nuclear

Examples

## The function is currently defined as
function(x,thr){sign(x)*pmax(abs(x)-thr,0)}

summary(thresh.l1(runif(100),0.3))

Example output

function (x, thr) 
{
    sign(x) * pmax(abs(x) - thr, 0)
}
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.0000  0.1800  0.2339  0.4558  0.6823 

rpca documentation built on May 2, 2019, 6:01 a.m.