def _compute_projections(tensor_slices, factors, svd_fun, out=None):
A, B, C = factors
if out is None:
out = [
T.zeros((tensor_slice.shape[0], C.shape[1]),
**T.context(tensor_slice))
for tensor_slice in tensor_slices
]
slice_idxes = range(T.shape(A)[0])
for projection, i, tensor_slice in zip(out, slice_idxes, tensor_slices):
a_i = A[i]
lhs = T.dot(B, T.transpose(a_i * C))
rhs = T.transpose(tensor_slice)
U, S, Vh = svd_fun(T.dot(lhs, rhs), n_eigenvecs=A.shape[1])
out[i] = tl.index_update(projection, tl.index[:],
T.transpose(T.dot(U, Vh)))
return out
def initialize_decomposition(tensor_slices,
rank,
init='random',
svd='numpy_svd',
random_state=None):
r"""Initiate a random PARAFAC2 decomposition given rank and tensor slices
Parameters
----------
tensor_slices : Iterable of ndarray
rank : int
init : {'random', 'svd', CPTensor, Parafac2Tensor}, optional
random_state : `np.random.RandomState`
Returns
-------
parafac2_tensor : Parafac2Tensor
List of initialized factors of the CP decomposition where element `i`
is of shape (tensor.shape[i], rank)
"""
context = tl.context(tensor_slices[0])
shapes = [m.shape for m in tensor_slices]
if init == 'random':
return random_parafac2(shapes,
rank,
full=False,
random_state=random_state,
**context)
elif init == 'svd':
try:
svd_fun = tl.SVD_FUNS[svd]
except KeyError:
message = 'Got svd={}. However, for the current backend ({}), the possible choices are {}'.format(
svd, tl.get_backend(), tl.SVD_FUNS)
raise ValueError(message)
padded_tensor = _pad_by_zeros(tensor_slices)
A = T.ones((padded_tensor.shape[0], rank), **context)
unfolded_mode_2 = unfold(padded_tensor, 2)
if T.shape(unfolded_mode_2)[0] < rank:
raise ValueError(
"Cannot perform SVD init if rank ({}) is greater than the number of columns in each tensor slice ({})"
.format(rank,
T.shape(unfolded_mode_2)[0]))
C = svd_fun(unfold(padded_tensor, 2), n_eigenvecs=rank)[0]
B = T.eye(rank, **context)
projections = _compute_projections(tensor_slices, (A, B, C), svd_fun)
return Parafac2Tensor((None, [A, B, C], projections))
elif isinstance(init, (tuple, list, Parafac2Tensor, CPTensor)):
try:
decomposition = Parafac2Tensor.from_CPTensor(
init, parafac2_tensor_ok=True)
except ValueError:
raise ValueError(
'If initialization method is a mapping, then it must '
'be possible to convert it to a Parafac2Tensor instance')
if decomposition.rank != rank:
raise ValueError(
'Cannot init with a decomposition of different rank')
return decomposition
raise ValueError('Initialization method "{}" not recognized'.format(init))