_symmetric_cp.py
``````import tensorly as tl
from ._base_decomposition import DecompositionMixin
from tensorly.tenalg import outer
import numpy as np
from ..cp_tensor import validate_cp_rank

def symmetric_power_iteration(tensor, n_repeat=10, n_iteration=10, verbose=False):
"""A single Robust Symmetric Tensor Power Iteration

Parameters
----------
tensor : tl.tensor
input tensor to decompose, must be symmetric of shape (size, )*order
n_repeat : int, default is 10
number of initializations to be tried
n_iterations : int, default is 10
number of power iterations
verbose : bool
level of verbosity

Returns
-------
(eigenval, best_factor, deflated)

eigenval : float
the obtained eigenvalue
best_factor : tl.tensor
the best estimated eigenvector
deflated : tl.tensor of same shape as `tensor`
the deflated tensor (i.e. without the estimated component)
"""
order = tl.ndim(tensor)
size = tl.shape(tensor)

if not tl.shape(tensor) == (size,) * order:
raise ValueError(
"The input tensor does not have the same size along each mode."
)

# A list of candidates for each mode
scores = []
modes = list(range(1, order))

for i in range(n_repeat):
factor = tl.tensor(np.random.random_sample(size), **tl.context(tensor))

for _ in range(n_iteration):
for _ in range(order):
factor = tl.tenalg.multi_mode_dot(
tensor, [factor] * (order - 1), modes=modes
)
factor = factor / tl.norm(factor, 2)

score = tl.tenalg.multi_mode_dot(tensor, [factor] * order)
scores.append(score)  # round(score, 2))

if (i == 0) or (score > best_score):
best_score = score
best_factor = factor

if verbose:
print(f"Best score of {n_repeat}: {best_score}")

# Refine the init
for _ in range(n_iteration):
for _ in range(order):
best_factor = tl.tenalg.multi_mode_dot(
tensor, [best_factor] * (order - 1), modes=modes
)
best_factor = best_factor / tl.norm(best_factor, 2)

eigenval = tl.tenalg.multi_mode_dot(tensor, [best_factor] * order)
deflated = tensor - outer([best_factor] * order) * eigenval

if verbose:
explained = tl.norm(deflated) / tl.norm(tensor)
print(f"Eigenvalue: {eigenval}, explained: {explained}")

return eigenval, best_factor, deflated

def symmetric_parafac_power_iteration(
tensor, rank, n_repeat=10, n_iteration=10, verbose=False
):
"""Symmetric CP Decomposition via Robust Symmetric Tensor Power Iteration

Parameters
----------
tensor : tl.tensor
input tensor to decompose, must be symmetric of shape (size, )*order
rank : int
rank of the decomposition (number of rank-1 components)
n_repeat : int, default is 10
number of initializations to be tried
n_iterations : int, default is 10
number of power iterations
verbose : bool
level of verbosity

Returns
-------
(weights, factor)

weights : 1-D tl.tensor of length `rank`
contains the eigenvalue of each eigenvector
factor : 2-D tl.tensor of shape (size, rank)
each column corresponds to one eigenvector
"""
rank = validate_cp_rank(tl.shape(tensor), rank=rank)

order = tl.ndim(tensor)
size = tl.shape(tensor)

if not tl.shape(tensor) == (size,) * order:
raise ValueError(
"The input tensor does not have the same size along each mode."
)

factor = []
weights = []

for _ in range(rank):
eigenval, eigenvec, deflated = symmetric_power_iteration(
tensor, n_repeat=n_repeat, n_iteration=n_iteration, verbose=verbose
)
factor.append(eigenvec)
weights.append(eigenval)
tensor = deflated

factor = tl.stack(factor, axis=1)
weights = tl.stack(weights)

return weights, factor

class SymmetricCP(DecompositionMixin):
"""Symmetric CP Decomposition via Robust Symmetric Tensor Power Iteration

Parameters
----------
rank : int
rank of the decomposition (number of rank-1 components)
n_repeat : int, default is 10
number of initializations to be tried
n_iterations : int, default is 10
number of power iterations
verbose : bool
level of verbosity

Returns
-------
(weights, factor)

weights : 1-D tl.tensor of length `rank`
contains the eigenvalue of each eigenvector
factor : 2-D tl.tensor of shape (size, rank)
each column corresponds to one eigenvector
"""

def __init__(self, rank, n_repeat=10, n_iteration=10, verbose=False):
self.rank = rank
self.n_repeat = n_repeat
self.n_iteration = n_iteration
self.verbose = verbose

def fit_transform(self, tensor):
self.decomposition_ = symmetric_parafac_power_iteration(
tensor,
self.rank,
n_repeat=self.n_repeat,
n_iteration=self.n_iteration,
verbose=self.verbose,
)
return self.decomposition_
``````