Source code for tensorly.decomposition._cp_power

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

# Author: Jean Kossaifi <jean.kossaifi+tensors@gmail.com>

# License: BSD 3 clause

[docs]def power_iteration(tensor, n_repeat=10, n_iteration=10, verbose=False): """A single Robust Tensor Power Iteration Parameters ---------- tensor : tl.tensor input tensor to decompose n_repeat : int, default is 10 number of initializations to be tried n_iteration : int, default is 10 number of power iterations verbose : bool level of verbosity Returns ------- (eigenval, best_factor, deflated) eigenval : float the obtained eigenvalue best_factors : tl.tensor list the best estimated eigenvector, for each mode of the input tensor deflated : tl.tensor of same shape as `tensor` the deflated tensor (i.e. without the estimated component) """ order = tl.ndim(tensor) # A list of candidates for each mode scores = [] for i in range(n_repeat): factors = [tl.tensor(np.random.random_sample(s), **tl.context(tensor)) for s in tl.shape(tensor)] for _ in range(n_iteration): for mode in range(order): factor = tl.tenalg.multi_mode_dot(tensor, factors, skip=mode) factor = factor / tl.norm(factor, 2) factors[mode] = factor score = tl.tenalg.multi_mode_dot(tensor, factors) scores.append(score) #round(score, 2)) if (i == 0) or (score > best_score): best_score = score best_factors = factors if verbose: print(f'Best score of {n_repeat}: {best_score}') # Refine the init for _ in range(n_iteration): for mode in range(order): factor = tl.tenalg.multi_mode_dot(tensor, best_factors, skip=mode) factor = factor / tl.norm(factor, 2) best_factors[mode] = factor eigenval = tl.tenalg.multi_mode_dot(tensor, best_factors) deflated = tensor - outer(best_factors)*eigenval if verbose: explained = tl.norm(deflated)/tl.norm(tensor) print(f'Eigenvalue: {eigenval}, explained: {explained}') return eigenval, best_factors, deflated
[docs]def parafac_power_iteration(tensor, rank, n_repeat=10, n_iteration=10, verbose=0): """CP Decomposition via Robust Tensor Power Iteration Parameters ---------- tensor : tl.tensor input tensor to decompose rank : int rank of the decomposition (number of rank-1 components) n_repeat : int, default is 10 number of initializations to be tried n_iteration : int, default is 10 number of power iterations verbose : bool level of verbosity Returns ------- (weights, factors) weights : 1-D tl.tensor of length `rank` contains the eigenvalue of each eigenvector factors : list of 2-D tl.tensor of shape (size, rank) Each column of each factor corresponds to one eigenvector """ rank = validate_cp_rank(tl.shape(tensor), rank=rank) order = tl.ndim(tensor) factors = [] weights = [] for _ in range(rank): eigenval, eigenvec, deflated = power_iteration(tensor, n_repeat=n_repeat, n_iteration=n_iteration, verbose=verbose) factors.append(eigenvec) weights.append(eigenval) tensor = deflated factors = [tl.stack([f[i] for f in factors], axis=1) for i in range(order)] weights = tl.stack(weights) return weights, factors
[docs]class CPPower(DecompositionMixin): """CP Decomposition via Robust Tensor Power Iteration Parameters ---------- tensor : tl.tensor input tensor to decompose rank : int rank of the decomposition (number of rank-1 components) n_repeat : int, default is 10 number of initializations to be tried n_iteration : int, default is 10 number of power iterations verbose : bool level of verbosity Returns ------- (weights, factors) weights : 1-D tl.tensor of length `rank` contains the eigenvalue of each eigenvector factors : list of 2-D tl.tensor of shape (size, rank) Each column of each factor corresponds to one eigenvector """ def __init__(self, rank, n_repeat=10, n_iteration=10, verbose=0): self.rank = rank self.n_repeat = n_repeat self.n_iteration = n_iteration self.verbose = verbose
[docs] def fit_transform(self, tensor): """Decompose an input tensor Parameters ---------- tensor : tensorly tensor input tensor to decompose Returns ------- CPTensor decomposed tensor """ cp_tensor = parafac_power_iteration(tensor, rank=self.rank, n_repeat=self.n_repeat, n_iteration=self.n_iteration, verbose=self.verbose) self.decomposition_ = cp_tensor return cp_tensor
def __repr__(self): return f'Rank-{self.rank} CP decomposition via Robust Tensor Power Iteration.'