pyproximal.projection.L01BallProj#
- class pyproximal.projection.L01BallProj(radius)[source]#
\(L_{0,1}\) ball projection.
- Parameters
- radius
int Radius
- radius
Notes
Given an \(L_{0,1}\) ball defined as:
\[L_{0,1}^{r} = \{ \mathbf{x}: \text{count}([||\mathbf{x}_1||_1, ||\mathbf{x}_2||_1, ..., ||\mathbf{x}_1||_1] \ne 0) \leq r \}\]its orthogonal projection is computed by finding the \(r\) highest largest entries of a vector obtained by applying the \(L_1\) norm to each column of a matrix \(\mathbf{x}\) (in absolute value), keeping those and zero-ing all the other entries. Note that this is the proximal operator of the corresponding indicator function \(\mathcal{I}_{L_{0,1}^{r}}\).
Methods
__init__(radius)