def soft_sparsity_prox(tensor, threshold):
"""
Projects the input tensor on the set of tensors with l1 norm smaller than threshold, using Soft Thresholding.
Parameters
----------
tensor : ndarray
threshold :
Returns
-------
ndarray
References
----------
.. [1]: Schenker, C., Cohen, J. E., & Acar, E. (2020). A Flexible Optimization Framework for
Regularized Matrix-Tensor Factorizations with Linear Couplings.
IEEE Journal of Selected Topics in Signal Processing.
Notes
-----
.. math::
\\begin{equation}
\\lambda: prox_\\lambda (||tensor||_1) \\leq parameter
\\end{equation}
"""
return simplex_prox(tl.abs(tensor), threshold) * tl.sign(tensor)
def soft_thresholding(tensor, threshold):
"""Soft-thresholding operator
sign(tensor) * max[abs(tensor) - threshold, 0]
Parameters
----------
tensor : ndarray
threshold : float or ndarray with shape tensor.shape
* If float the threshold is applied to the whole tensor
* If ndarray, one threshold is applied per elements, 0 values are ignored
Returns
-------
ndarray
thresholded tensor on which the operator has been applied
Examples
--------
Basic shrinkage
>>> import tensorly.backend as T
>>> from tensorly.tenalg.proximal import soft_thresholding
>>> tensor = tl.tensor([[1, -2, 1.5], [-4, 3, -0.5]])
>>> soft_thresholding(tensor, 1.1)
array([[ 0. , -0.9, 0.4],
[-2.9, 1.9, 0. ]])
Example with missing values
>>> mask = tl.tensor([[0, 0, 1], [1, 0, 1]])
>>> soft_thresholding(tensor, mask*1.1)
array([[ 1. , -2. , 0.4],
[-2.9, 3. , 0. ]])
See also
--------
inplace_soft_thresholding : Inplace version of the soft-thresholding operator
svd_thresholding : SVD-thresholding operator
"""
return tl.sign(tensor) * tl.clip(tl.abs(tensor) - threshold, a_min=0)