pyproximal.projection.L10BallProj#

class pyproximal.projection.L10BallProj(radius: int)[source]#

\(L_{1,0}\) ball projection.

Parameters
radiusint

Radius

Notes

Given an \(L_{1,0}\) ball defined as:

\[L_{1,0}^{r} = \{ \mathbf{x}: \text{count}([||\mathbf{x}_1||_1, ||\mathbf{x}_2||_1, ..., ||\mathbf{x}_1||_1] \ne 0) \leq r \}\]

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 \(\mathcal{I}_{L_{1,0}^{r}}\).

Methods

__init__(radius)