kruskal.py

```
import numpy as np
from .base import fold, tensor_to_vec
from .tenalg import khatri_rao
# Author: Jean Kossaifi
def kruskal_to_tensor(factors):
"""Turns the Khatri-product of matrices into a full tensor
``factor_matrices = [|U_1, ... U_n|]`` becomes
a tensor shape ``(U[1].shape[0], U[2].shape[0], ... U[-1].shape[0])``
Parameters
----------
factors : ndarray list
list of factor matrices, all with the same number of columns
i.e. for all matrix U in factor_matrices:
U has shape ``(s_i, R)``, where R is fixed and s_i varies with i
Returns
-------
ndarray
full tensor of shape ``(U[1].shape[0], ... U[-1].shape[0])``
Notes
-----
This version works by first computing the mode-0 unfolding of the tensor
and then refolding it.
There are other possible and equivalent alternate implementation.
Version slower but closer to the mathematical definition
of a tensor decomposition:
>>> from functools import reduce
>>> def kt_to_tensor(factors):
... for r in range(factors[0].shape[1]):
... vecs = np.ix_(*[u[:, r] for u in factors])
... if r:
... res += reduce(np.multiply, vecs)
... else:
... res = reduce(np.multiply, vecs)
... return res
"""
shape = [factor.shape[0] for factor in factors]
full_tensor = np.dot(factors[0], khatri_rao(factors[1:]).T)
return fold(full_tensor, 0, shape)
def kruskal_to_unfolded(factors, mode):
"""Turns the khatri-product of matrices into an unfolded tensor
turns ``factors = [|U_1, ... U_n|]`` into a mode-`mode`
unfolding of the tensor
Parameters
----------
factors : ndarray list
list of matrices, all with the same number of columns
ie for all u in factor_matrices:
u[i] has shape (s_u_i, R), where R is fixed
mode: int
mode of the desired unfolding
Returns
-------
ndarray
unfolded tensor of shape (tensor_shape[mode], -1)
Notes
-----
Writing factors = [U_1, ..., U_n], we exploit the fact that
``U_k = U[k].dot(khatri_rao(U_1, ..., U_k-1, U_k+1, ..., U_n))``
"""
return factors[mode].dot(khatri_rao(factors, skip_matrix=mode).T)
def kruskal_to_vec(factors):
"""Turns the khatri-product of matrices into a vector
(the tensor ``factors = [|U_1, ... U_n|]``
is converted into a raveled mode-0 unfolding)
Parameters
----------
factors : ndarray list
list of matrices, all with the same number of columns
ie for all u in U: u[i] has shape (s_i, R), where R is fixed
Returns
-------
ndarray
vectorised tensor
"""
return tensor_to_vec(kruskal_to_tensor(factors))
```