proj_simplex¶

odl.solvers.nonsmooth.proximal_operators.proj_simplex(x, diameter=1, out=None)[source]¶

Projection onto simplex.

Projection onto:

``{ x \in X | x_i \geq 0, \sum_i x_i = r}``

with $r$ being the diameter. It is computed by the formula proposed in [D+2008].

Parameters

spaceLinearSpace: Space / domain X.
diameterpositive float, optional: Diameter of the simplex.

Returns

prox_factorycallable: Factory for the proximal operator to be initialized.

See also

proj_l1: projection onto l1-norm ball

Notes

The projection onto a simplex is not of closed-form but can be solved by a non-iterative algorithm, see [D+2008] for details.

References

[D+2008] Duchi, J., Shalev-Shwartz, S., Singer, Y., and Chandra, T. Efficient Projections onto the L1-ball for Learning in High dimensions. ICML 2008, pp. 272-279. http://doi.org/10.1145/1390156.1390191