Source code for tensorly.decomposition._cp

import numpy as np
import warnings

import tensorly as tl
from ._base_decomposition import DecompositionMixin
from ..random import random_cp
from ..base import unfold
from ..cp_tensor import (cp_to_tensor, CPTensor,
                         unfolding_dot_khatri_rao, cp_norm,
                         cp_normalize, validate_cp_rank)

# Authors: Jean Kossaifi <jean.kossaifi+tensors@gmail.com>
#          Chris Swierczewski <csw@amazon.com>
#          Sam Schneider <samjohnschneider@gmail.com>
#          Aaron Meurer <asmeurer@gmail.com>

# License: BSD 3 clause

def initialize_cp(tensor, rank, init='svd', svd='numpy_svd', random_state=None, normalize_factors=False):
    r"""Initialize factors used in `parafac`.

    The type of initialization is set using `init`. If `init == 'random'` then
    initialize factor matrices with uniform distribution using `random_state`. If `init == 'svd'` then
    initialize the `m`th factor matrix using the `rank` left singular vectors
    of the `m`th unfolding of the input tensor. If init is a previously initialized `cp tensor`, all
    the weights are pulled in the last factor and then the weights are set to "1" for the output tensor.

    Parameters
    ----------
    tensor : ndarray
    rank : int
    init : {'svd', 'random', cptensor}, optional
    svd : str, default is 'numpy_svd'
        function to use to compute the SVD, acceptable values in tensorly.SVD_FUNS
    non_negative : bool, default is False
        if True, non-negative factors are returned

    Returns
    -------
    factors : CPTensor
        An initial cp tensor.

    """
    rng = tl.check_random_state(random_state)

    if init == 'random':
        kt = random_cp(tl.shape(tensor), rank, normalise_factors=False, random_state=rng, **tl.context(tensor))

    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)

        factors = []
        for mode in range(tl.ndim(tensor)):
            U, S, _ = svd_fun(unfold(tensor, mode), n_eigenvecs=rank)

            # Put SVD initialization on the same scaling as the tensor in case normalize_factors=False
            if mode == 0:
                idx = min(rank, tl.shape(S)[0])
                U = tl.index_update(U, tl.index[:, :idx], U[:, :idx] * S[:idx])

            if tensor.shape[mode] < rank:
                # TODO: this is a hack but it seems to do the job for now
                random_part = tl.tensor(rng.random_sample((U.shape[0], rank - tl.shape(tensor)[mode])), **tl.context(tensor))
                U = tl.concatenate([U, random_part], axis=1)

            factors.append(U[:, :rank])

        kt = CPTensor((None, factors))

    elif isinstance(init, (tuple, list, CPTensor)):
        # TODO: Test this
        try:         
            if normalize_factors is True:
                warnings.warn('It is not recommended to initialize a tensor with normalizing. Consider normalizing the tensor before using this function')
            
            kt = CPTensor(init)
            weights, factors = kt
            
            if tl.all(weights == 1):
                kt = CPTensor((None, factors))
            else:
                weights_avg = tl.prod(weights) ** (1.0 / tl.shape(weights)[0])
                for i in range(len(factors)):
                    factors[i] = factors[i] * weights_avg
                kt = CPTensor((None, factors))
        except ValueError:
            raise ValueError(
                'If initialization method is a mapping, then it must '
                'be possible to convert it to a CPTensor instance'
            )
    else:
        raise ValueError('Initialization method "{}" not recognized'.format(init))

    if normalize_factors:
        kt = cp_normalize(kt)

    return kt


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)


def error_calc(tensor, norm_tensor, weights, factors, sparsity, mask, mttkrp=None):
    r""" Perform the error calculation. Different forms are used here depending upon 
    the available information. If `mttkrp=None` or masking is being performed, then the
    full tensor must be constructed. Otherwise, the mttkrp is used to reduce the calculation cost.

    Parameters
    ----------
    tensor : tensor
    norm_tensor : float
        The l2 norm of tensor.
    weights : tensor
        The current CP weights
    factors : tensor
        The current CP factors
    sparsity : float or int
        Whether we allow for a sparse component
    mask : bool
        Whether masking is being performed.
    mttkrp : tensor or None
        The mttkrp product, if available.

    Returns
    -------
    unnorml_rec_error : float
        The unnormalized reconstruction error.
    tensor : tensor
        The tensor, in case it has been updated by masking.
    norm_tensor: float
        The tensor norm, in case it has been updated by masking.
    """

    # If we have to update the mask we already have to build the full tensor
    if (mask is not None) or (mttkrp is None):
        low_rank_component = cp_to_tensor((weights, factors))

        # Update the tensor based on the mask
        if mask is not None:
            tensor = tensor * mask + low_rank_component * (1 - mask)
            norm_tensor = tl.norm(tensor, 2)

        if sparsity:
            sparse_component = sparsify_tensor(tensor - low_rank_component, sparsity)
        else:
            sparse_component = 0.0
    
        unnorml_rec_error = tl.norm(tensor - low_rank_component - sparse_component, 2)
    else:
        if sparsity:
            low_rank_component = cp_to_tensor((weights, factors))
            sparse_component = sparsify_tensor(tensor - low_rank_component, sparsity)
        
            unnorml_rec_error = tl.norm(tensor - low_rank_component - sparse_component, 2)
        else:
            # ||tensor - rec||^2 = ||tensor||^2 + ||rec||^2 - 2*<tensor, rec>
            factors_norm = cp_norm((weights, factors))

            # mttkrp and factor for the last mode. This is equivalent to the
            # inner product <tensor, factorization>
            iprod = tl.sum(tl.sum(mttkrp * factors[-1], axis=0) * weights)
            unnorml_rec_error = tl.sqrt(tl.abs(norm_tensor**2 + factors_norm**2 - 2 * iprod))

    return unnorml_rec_error, tensor, norm_tensor


[docs]def parafac(tensor, rank, n_iter_max=100, init='svd', svd='numpy_svd', normalize_factors=False, orthogonalise=False, tol=1e-8, random_state=None, verbose=0, return_errors=False, sparsity=None, l2_reg=0, mask=None, cvg_criterion='abs_rec_error', fixed_modes=None, svd_mask_repeats=5, linesearch=False): """CANDECOMP/PARAFAC decomposition via alternating least squares (ALS) Computes a rank-`rank` decomposition of `tensor` [1]_ such that:: tensor = [|weights; factors[0], ..., factors[-1] |]. Parameters ---------- tensor : ndarray rank : int Number of components. n_iter_max : int Maximum number of iteration init : {'svd', 'random', CPTensor}, optional Type of factor matrix initialization. If a CPTensor is passed, this is directly used for initalization. See `initialize_factors`. svd : str, default is 'numpy_svd' function to use to compute the SVD, acceptable values in tensorly.SVD_FUNS normalize_factors : if True, aggregate the weights of each factor in a 1D-tensor of shape (rank, ), which will contain the norms of the factors tol : float, optional (Default: 1e-6) Relative reconstruction error tolerance. The algorithm is considered to have found the global minimum when the reconstruction error is less than `tol`. random_state : {None, int, np.random.RandomState} verbose : int, optional Level of verbosity return_errors : bool, optional Activate return of iteration errors mask : ndarray array of booleans with the same shape as ``tensor`` should be 0 where the values are missing and 1 everywhere else. Note: if tensor is sparse, then mask should also be sparse with a fill value of 1 (or True). Allows for missing values [2]_ cvg_criterion : {'abs_rec_error', 'rec_error'}, optional Stopping criterion for ALS, works if `tol` is not None. If 'rec_error', ALS stops at current iteration if ``(previous rec_error - current rec_error) < tol``. If 'abs_rec_error', ALS terminates when `|previous rec_error - current rec_error| < tol`. sparsity : float or int If `sparsity` is not None, we approximate tensor as a sum of low_rank_component and sparse_component, where low_rank_component = cp_to_tensor((weights, factors)). `sparsity` denotes desired fraction or number of non-zero elements in the sparse_component of the `tensor`. fixed_modes : list, default is None A list of modes for which the initial value is not modified. The last mode cannot be fixed due to error computation. svd_mask_repeats: int If using a tensor with masked values, this initializes using SVD multiple times to remove the effect of these missing values on the initialization. linesearch : bool, default is False Whether to perform line search as proposed by Bro [3]. Returns ------- CPTensor : (weight, factors) * weights : 1D array of shape (rank, ) * all ones if normalize_factors is False (default) * weights of the (normalized) factors otherwise * factors : List of factors of the CP decomposition element `i` is of shape ``(tensor.shape[i], rank)`` * sparse_component : nD array of shape tensor.shape. Returns only if `sparsity` is not None. errors : list A list of reconstruction errors at each iteration of the algorithms. References ---------- .. [1] T.G.Kolda and B.W.Bader, "Tensor Decompositions and Applications", SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009. .. [2] Tomasi, Giorgio, and Rasmus Bro. "PARAFAC and missing values." Chemometrics and Intelligent Laboratory Systems 75.2 (2005): 163-180. .. [3] R. Bro, "Multi-Way Analysis in the Food Industry: Models, Algorithms, and Applications", PhD., University of Amsterdam, 1998 """ rank = validate_cp_rank(tl.shape(tensor), rank=rank) if orthogonalise and not isinstance(orthogonalise, int): orthogonalise = n_iter_max if linesearch: acc_pow = 2.0 # Extrapolate to the iteration^(1/acc_pow) ahead acc_fail = 0 # How many times acceleration have failed max_fail = 4 # Increase acc_pow with one after max_fail failure weights, factors = initialize_cp(tensor, rank, init=init, svd=svd, random_state=random_state, normalize_factors=normalize_factors) if mask is not None and init == "svd": for _ in range(svd_mask_repeats): tensor = tensor * mask + tl.cp_to_tensor((weights, factors), mask=1 - mask) weights, factors = initialize_cp(tensor, rank, init=init, svd=svd, random_state=random_state, normalize_factors=normalize_factors) rec_errors = [] norm_tensor = tl.norm(tensor, 2) Id = tl.eye(rank, **tl.context(tensor)) * l2_reg if fixed_modes is None: fixed_modes = [] if tl.ndim(tensor)-1 in fixed_modes: warnings.warn('You asked for fixing the last mode, which is not supported.\n The last mode will not be fixed. Consider using tl.moveaxis()') fixed_modes.remove(tl.ndim(tensor)-1) modes_list = [mode for mode in range(tl.ndim(tensor)) if mode not in fixed_modes] if sparsity: sparse_component = tl.zeros_like(tensor) if isinstance(sparsity, float): sparsity = int(sparsity * np.prod(tensor.shape)) else: sparsity = int(sparsity) for iteration in range(n_iter_max): if orthogonalise and iteration <= orthogonalise: factors = [tl.qr(f)[0] if min(tl.shape(f)) >= rank else f for i, f in enumerate(factors)] if linesearch and iteration % 2 == 0: factors_last = [tl.copy(f) for f in factors] weights_last = tl.copy(weights) if verbose > 1: print("Starting iteration", iteration + 1) for mode in modes_list: if verbose > 1: print("Mode", mode, "of", tl.ndim(tensor)) pseudo_inverse = tl.tensor(np.ones((rank, rank)), **tl.context(tensor)) for i, factor in enumerate(factors): if i != mode: pseudo_inverse = pseudo_inverse * tl.dot(tl.transpose(factor), factor) pseudo_inverse += Id mttkrp = unfolding_dot_khatri_rao(tensor, (None, factors), mode) factor = tl.transpose(tl.solve(tl.transpose(pseudo_inverse), tl.transpose(mttkrp))) if normalize_factors: scales = tl.norm(factor, 2, axis=0) weights = tl.where(scales==0, tl.ones(tl.shape(scales), **tl.context(factor)), scales) factor = factor / tl.reshape(weights, (1, -1)) factors[mode] = factor # Will we be performing a line search iteration if linesearch and iteration % 2 == 0 and iteration > 5: line_iter = True else: line_iter = False # Calculate the current unnormalized error if we need it if (tol or return_errors) and line_iter is False: unnorml_rec_error, tensor, norm_tensor = error_calc(tensor, norm_tensor, weights, factors, sparsity, mask, mttkrp) else: if mask is not None: tensor = tensor * mask + tl.cp_to_tensor((weights, factors), mask=1 - mask) # Start line search if requested. if line_iter is True: jump = iteration ** (1.0 / acc_pow) new_weights = weights_last + (weights - weights_last) * jump new_factors = [factors_last[ii] + (factors[ii] - factors_last[ii]) * jump for ii in range(tl.ndim(tensor))] new_rec_error, new_tensor, new_norm_tensor = error_calc(tensor, norm_tensor, new_weights, new_factors, sparsity, mask) if (new_rec_error / new_norm_tensor) < rec_errors[-1]: factors, weights = new_factors, new_weights tensor, norm_tensor = new_tensor, new_norm_tensor unnorml_rec_error = new_rec_error acc_fail = 0 if verbose: print("Accepted line search jump of {}.".format(jump)) else: unnorml_rec_error, tensor, norm_tensor = error_calc(tensor, norm_tensor, weights, factors, sparsity, mask, mttkrp) acc_fail += 1 if verbose: print("Line search failed for jump of {}.".format(jump)) if acc_fail == max_fail: acc_pow += 1.0 acc_fail = 0 if verbose: print("Reducing acceleration.") rec_error = unnorml_rec_error / norm_tensor rec_errors.append(rec_error) if tol: if iteration >= 1: rec_error_decrease = rec_errors[-2] - rec_errors[-1] if verbose: print("iteration {}, reconstruction error: {}, decrease = {}, unnormalized = {}".format(iteration, rec_error, rec_error_decrease, unnorml_rec_error)) if cvg_criterion == 'abs_rec_error': stop_flag = abs(rec_error_decrease) < tol elif cvg_criterion == 'rec_error': stop_flag = rec_error_decrease < tol else: raise TypeError("Unknown convergence criterion") if stop_flag: if verbose: print("PARAFAC converged after {} iterations".format(iteration)) break else: if verbose: print('reconstruction error={}'.format(rec_errors[-1])) cp_tensor = CPTensor((weights, factors)) if sparsity: sparse_component = sparsify_tensor(tensor - cp_to_tensor((weights, factors)), sparsity) cp_tensor = (cp_tensor, sparse_component) if return_errors: return cp_tensor, rec_errors else: return cp_tensor
[docs]def sample_khatri_rao(matrices, n_samples, skip_matrix=None, return_sampled_rows=False, random_state=None): """Random subsample of the Khatri-Rao product of the given list of matrices If one matrix only is given, that matrix is directly returned. Parameters ---------- matrices : ndarray list list of matrices with the same number of columns, i.e.:: for i in len(matrices): matrices[i].shape = (n_i, m) n_samples : int number of samples to be taken from the Khatri-Rao product skip_matrix : None or int, optional, default is None if not None, index of a matrix to skip random_state : None, int or numpy.random.RandomState if int, used to set the seed of the random number generator if numpy.random.RandomState, used to generate random_samples returned_sampled_rows : bool, default is False if True, also returns a list of the rows sampled from the full khatri-rao product Returns ------- sampled_Khatri_Rao : ndarray The sampled matricised tensor Khatri-Rao with `n_samples` rows indices : tuple list a list of indices sampled for each mode indices_kr : int list list of length `n_samples` containing the sampled row indices """ if random_state is None or not isinstance(random_state, np.random.RandomState): rng = tl.check_random_state(random_state) warnings.warn('You are creating a new random number generator at each call.\n' 'If you are calling sample_khatri_rao inside a loop this will be slow:' ' best to create a rng outside and pass it as argument (random_state=rng).') else: rng = random_state if skip_matrix is not None: matrices = [matrices[i] for i in range(len(matrices)) if i != skip_matrix] rank = tl.shape(matrices[0])[1] sizes = [tl.shape(m)[0] for m in matrices] # For each matrix, randomly choose n_samples indices for which to compute the khatri-rao product indices_list = [rng.randint(0, tl.shape(m)[0], size=n_samples, dtype=int) for m in matrices] if return_sampled_rows: # Compute corresponding rows of the full khatri-rao product indices_kr = np.zeros((n_samples), dtype=int) for size, indices in zip(sizes, indices_list): indices_kr = indices_kr * size + indices # Compute the Khatri-Rao product for the chosen indices sampled_kr = tl.ones((n_samples, rank), **tl.context(matrices[0])) for indices, matrix in zip(indices_list, matrices): sampled_kr = sampled_kr * matrix[indices, :] if return_sampled_rows: return sampled_kr, indices_list, indices_kr else: return sampled_kr, indices_list
[docs]def randomised_parafac(tensor, rank, n_samples, n_iter_max=100, init='random', svd='numpy_svd', tol=10e-9, max_stagnation=20, return_errors=False, random_state=None, verbose=1): """Randomised CP decomposition via sampled ALS Parameters ---------- tensor : ndarray rank : int number of components n_samples : int number of samples per ALS step n_iter_max : int maximum number of iteration init : {'svd', 'random'}, optional svd : str, default is 'numpy_svd' function to use to compute the SVD, acceptable values in tensorly.SVD_FUNS tol : float, optional tolerance: the algorithm stops when the variation in the reconstruction error is less than the tolerance max_stagnation: int, optional, default is 0 if not zero, the maximum allowed number of iterations with no decrease in fit random_state : {None, int, np.random.RandomState}, default is None return_errors : bool, default is False if True, return a list of all errors verbose : int, optional level of verbosity Returns ------- factors : ndarray list list of positive factors of the CP decomposition element `i` is of shape ``(tensor.shape[i], rank)`` References ---------- .. [3] Casey Battaglino, Grey Ballard and Tamara G. Kolda, "A Practical Randomized CP Tensor Decomposition", """ rank = validate_cp_rank(tl.shape(tensor), rank=rank) rng = tl.check_random_state(random_state) weights, factors = initialize_cp(tensor, rank, init=init, svd=svd, random_state=random_state) rec_errors = [] n_dims = tl.ndim(tensor) norm_tensor = tl.norm(tensor, 2) min_error = 0 weights = tl.ones(rank, **tl.context(tensor)) for iteration in range(n_iter_max): for mode in range(n_dims): kr_prod, indices_list = sample_khatri_rao(factors, n_samples, skip_matrix=mode, random_state=rng) indices_list = [i.tolist() for i in indices_list] # Keep all the elements of the currently considered mode indices_list.insert(mode, slice(None, None, None)) # MXNet will not be happy if this is a list insteaf of a tuple indices_list = tuple(indices_list) if mode: sampled_unfolding = tensor[indices_list] else: sampled_unfolding = tl.transpose(tensor[indices_list]) pseudo_inverse = tl.dot(tl.transpose(kr_prod), kr_prod) factor = tl.dot(tl.transpose(kr_prod), sampled_unfolding) factor = tl.transpose(tl.solve(pseudo_inverse, factor)) factors[mode] = factor if max_stagnation or tol: rec_error = tl.norm(tensor - cp_to_tensor((weights, factors)), 2) / norm_tensor if not min_error or rec_error < min_error: min_error = rec_error stagnation = -1 stagnation += 1 rec_errors.append(rec_error) if iteration > 1: if verbose: print('reconstruction error={}, variation={}.'.format( rec_errors[-1], rec_errors[-2] - rec_errors[-1])) if (tol and abs(rec_errors[-2] - rec_errors[-1]) < tol) or \ (stagnation and (stagnation > max_stagnation)): if verbose: print('converged in {} iterations.'.format(iteration)) break if return_errors: return CPTensor((weights, factors)), rec_errors else: return CPTensor((weights, factors))
[docs]class CP(DecompositionMixin): """Candecomp-Parafac decomposition via Alternating-Least Square Computes a rank-`rank` decomposition of `tensor` [1]_ such that:: tensor = [|weights; factors[0], ..., factors[-1] |]. Parameters ---------- tensor : ndarray rank : int Number of components. n_iter_max : int Maximum number of iteration init : {'svd', 'random'}, optional Type of factor matrix initialization. See `initialize_factors`. svd : str, default is 'numpy_svd' function to use to compute the SVD, acceptable values in tensorly.SVD_FUNS normalize_factors : if True, aggregate the weights of each factor in a 1D-tensor of shape (rank, ), which will contain the norms of the factors tol : float, optional (Default: 1e-6) Relative reconstruction error tolerance. The algorithm is considered to have found the global minimum when the reconstruction error is less than `tol`. random_state : {None, int, np.random.RandomState} verbose : int, optional Level of verbosity return_errors : bool, optional Activate return of iteration errors mask : ndarray array of booleans with the same shape as ``tensor`` should be 0 where the values are missing and 1 everywhere else. Note: if tensor is sparse, then mask should also be sparse with a fill value of 1 (or True). Allows for missing values [2]_ cvg_criterion : {'abs_rec_error', 'rec_error'}, optional Stopping criterion for ALS, works if `tol` is not None. If 'rec_error', ALS stops at current iteration if ``(previous rec_error - current rec_error) < tol``. If 'abs_rec_error', ALS terminates when `|previous rec_error - current rec_error| < tol`. sparsity : float or int If `sparsity` is not None, we approximate tensor as a sum of low_rank_component and sparse_component, where low_rank_component = cp_to_tensor((weights, factors)). `sparsity` denotes desired fraction or number of non-zero elements in the sparse_component of the `tensor`. fixed_modes : list, default is None A list of modes for which the initial value is not modified. The last mode cannot be fixed due to error computation. svd_mask_repeats: int If using a tensor with masked values, this initializes using SVD multiple times to remove the effect of these missing values on the initialization. linesearch : bool, default is False Whether to perform line search as proposed by Bro [3]. Returns ------- CPTensor : (weight, factors) * weights : 1D array of shape (rank, ) * all ones if normalize_factors is False (default), * weights of the (normalized) factors otherwise * factors : List of factors of the CP decomposition element `i ` is of shape (tensor.shape[i], rank) * sparse_component : nD array of shape tensor.shape. Returns only if `sparsity` is not None. errors : list A list of reconstruction errors at each iteration of the algorithms. References ---------- .. [1] T.G.Kolda and B.W.Bader, "Tensor Decompositions and Applications", SIAM REVIEW, vol. 51, n. 3, pp. 455-500, 2009. .. [2] Tomasi, Giorgio, and Rasmus Bro. "PARAFAC and missing values." Chemometrics and Intelligent Laboratory Systems 75.2 (2005): 163-180. .. [3] R. Bro, "Multi-Way Analysis in the Food Industry: Models, Algorithms, and Applications", PhD., University of Amsterdam, 1998 """ def __init__(self, rank, n_iter_max=100, init='svd', svd='numpy_svd', normalize_factors=False, orthogonalise=False, tol=1e-8, random_state=None, verbose=0, sparsity=None, l2_reg=0, mask=None, cvg_criterion='abs_rec_error', fixed_modes=None, svd_mask_repeats=5, linesearch=False): self.rank = rank self.n_iter_max = n_iter_max self.init = init self.svd = svd self.normalize_factors = normalize_factors self.orthogonalise = orthogonalise self.tol = tol self.random_state = random_state self.verbose = verbose self.sparsity = sparsity self.l2_reg = l2_reg self.mask = mask self.cvg_criterion = cvg_criterion self.fixed_modes = fixed_modes self.svd_mask_repeats = svd_mask_repeats self.linesearch = linesearch
[docs] def fit_transform(self, tensor): """Decompose an input tensor Parameters ---------- tensor : tensorly tensor input tensor to decompose Returns ------- CPTensor decomposed tensor """ cp_tensor, errors = parafac( tensor, rank=self.rank, n_iter_max=self.n_iter_max, init=self.init, svd=self.svd, normalize_factors=self.normalize_factors, orthogonalise=self.orthogonalise, tol=self.tol, random_state=self.random_state, verbose=self.verbose, sparsity=self.sparsity, l2_reg=self.l2_reg, mask=self.mask, cvg_criterion=self.cvg_criterion, fixed_modes=self.fixed_modes, svd_mask_repeats=self.svd_mask_repeats, linesearch=self.linesearch, return_errors=True, ) self.decomposition_ = cp_tensor self.errors_ = errors return self.decomposition_
def __repr__(self): return f'Rank-{self.rank} CP decomposition.'
[docs]class RandomizedCP(DecompositionMixin): """Randomised CP decomposition via sampled ALS Parameters ---------- tensor : ndarray rank : int number of components n_samples : int number of samples per ALS step n_iter_max : int maximum number of iteration init : {'svd', 'random'}, optional svd : str, default is 'numpy_svd' function to use to compute the SVD, acceptable values in tensorly.SVD_FUNS tol : float, optional tolerance: the algorithm stops when the variation in the reconstruction error is less than the tolerance max_stagnation: int, optional, default is 0 if not zero, the maximum allowed number of iterations with no decrease in fit random_state : {None, int, np.random.RandomState}, default is None verbose : int, optional level of verbosity Returns ------- factors : ndarray list list of positive factors of the CP decomposition element `i` is of shape ``(tensor.shape[i], rank)`` References ---------- .. [3] Casey Battaglino, Grey Ballard and Tamara G. Kolda, "A Practical Randomized CP Tensor Decomposition", """ def __init__(self, rank, n_samples, n_iter_max=100, init='random', svd='numpy_svd', tol=10e-9, max_stagnation=20, random_state=None, verbose=1): self.rank = rank self.n_samples = n_samples self.n_iter_max = n_iter_max self.init = init self.svd = svd self.tol = tol self.max_stagnation = max_stagnation self.random_state = random_state self.verbose = verbose def fit_transform(self, tensor): self.decomposition_, self.errors_ = randomised_parafac(tensor, rank=self.rank, n_samples=self.n_samples, n_iter_max=self.n_iter_max, init=self.init, svd=self.svd, tol=self.tol, return_errors=True, max_stagnation=self.max_stagnation, random_state=self.random_state, verbose=self.verbose) return self.decomposition_