pyproximal.L21_plus_L1

class pyproximal.L21_plus_L1(sigma=1.0, rho=0.8)

L21 + L1 norm proximal operator.

Proximal operator of the \(L_{2,1} + L_1\) mixed-norm: \(f(\mathbf{X}) = \sigma \rho \|\mathbf{X}\|_1 + \sigma (1 - \rho) \|\mathbf{X}\|_{2,1}\)

Parameters

sigmaint, optional

Multiplicative coefficient of \(L_{2,1} + L_1\) mixed-norm

rhoint, optional

Balancing between sparsity of \(L_1\) and grouping of \(L_{2,1}\)

Notes

The proximal operator of the \(L_{2,1} + L_1\) mixed-norm is simply the product of each individual proximal operator [1].

1

Gramfort, Alexandre, Daniel Strohmeier, Jens Haueisen, Matti Hamalainen, and Matthieu Kowalski. “Functional brain imaging with M/EEG using structured sparsity in time-frequency dictionaries.” In Biennial International Conference on Information Processing in Medical Imaging, pp. 600-611. Springer, Berlin, Heidelberg, 2011.

Methods

__init__([sigma, rho])
affine_addition(v)	Affine addition
chain(g)	Chain
grad(x)	Compute gradient
postcomposition(sigma)	Postcomposition
precomposition(a, b)	Precomposition
prox(**kwargs)
proxdual(**kwargs)