def simplex_prox(tensor, parameter):
"""
Projects the input tensor on the simplex of radius parameter.
Parameters
----------
tensor : ndarray
parameter : float
Returns
-------
ndarray
References
----------
.. [1]: Held, Michael, Philip Wolfe, and Harlan P. Crowder.
"Validation of subgradient optimization."
Mathematical programming 6.1 (1974): 62-88.
"""
_, col = tl.shape(tensor)
tensor = tl.clip(tensor, 0, tl.max(tensor))
tensor_sort = tl.sort(tensor, axis=0, descending=True)
to_change = tl.sum(tl.where(
tensor_sort > (tl.cumsum(tensor_sort, axis=0) - parameter), 1.0, 0.0),
axis=0)
difference = tl.zeros(col)
for i in range(col):
if to_change[i] > 0:
difference = tl.index_update(
difference, tl.index[i],
tl.cumsum(tensor_sort, axis=0)[int(to_change[i] - 1), i])
difference = (difference - parameter) / to_change
return tl.clip(tensor - difference, a_min=0)
def sparsify_tensor(tensor, card):
"""Zeros out all elements in the `tensor` except `card` elements with maximum absolute values.
Parameters
----------
tensor : ndarray
card : int
Desired number of non-zero elements in the `tensor`
Returns
-------
ndarray of shape tensor.shape
"""
if card >= np.prod(tensor.shape):
return tensor
bound = tl.sort(tl.abs(tensor), axis = None)[-card]
return tl.where(tl.abs(tensor) < bound, tl.zeros(tensor.shape, **tl.context(tensor)), tensor)