jml.optimization
Class ShrinkageOperator
java.lang.Object
jml.optimization.ShrinkageOperator
public class ShrinkageOperator
- extends java.lang.Object
Soft-thresholding (shrinkage) operator, which is defined as
S_{t}[x] = argmin_u 1/2 * || u - x ||^2 + t||x||_1
which is actually prox_{t||.||_1}(x). The analytical form is
S_{t}[x] =
| x - t, if x > t
| x + t, if x < -t
| 0, otherwise
- Version:
- 1.0, Nov. 19th, 2013
- Author:
- Mingjie Qian
Method Summary |
static org.apache.commons.math.linear.RealMatrix |
shrinkage(org.apache.commons.math.linear.RealMatrix X,
double t)
Soft-thresholding (shrinkage) operator, which is defined as
S_{t}[x] = argmin_u 1/2 * || u - x ||^2 + t||x||_1
which is actually prox_{t||.||_1}(x). |
Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
ShrinkageOperator
public ShrinkageOperator()
shrinkage
public static org.apache.commons.math.linear.RealMatrix shrinkage(org.apache.commons.math.linear.RealMatrix X,
double t)
- Soft-thresholding (shrinkage) operator, which is defined as
S_{t}[x] = argmin_u 1/2 * || u - x ||^2 + t||x||_1
which is actually prox_{t||.||_1}(x). The analytical form is
S_{t}[x] =
| x - t, if x > t
| x + t, if x < -t
| 0, otherwise
- Parameters:
X
- a real matrixt
- threshold
- Returns:
- argmin_u 1/2 * || u - x ||^2 + t||x||_1