1358 lines
46 KiB
Python
1358 lines
46 KiB
Python
""" Non-negative matrix factorization
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"""
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# Author: Vlad Niculae
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# Lars Buitinck
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# Mathieu Blondel <mathieu@mblondel.org>
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# Tom Dupre la Tour
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# License: BSD 3 clause
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import numbers
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import numpy as np
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import scipy.sparse as sp
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import time
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import warnings
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from math import sqrt
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from ._cdnmf_fast import _update_cdnmf_fast
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from ..base import BaseEstimator, TransformerMixin
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from ..exceptions import ConvergenceWarning
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from ..utils import check_random_state, check_array
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from ..utils.extmath import randomized_svd, safe_sparse_dot, squared_norm
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from ..utils.validation import check_is_fitted, check_non_negative
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from ..utils.validation import _deprecate_positional_args
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EPSILON = np.finfo(np.float32).eps
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def norm(x):
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"""Dot product-based Euclidean norm implementation
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See: http://fseoane.net/blog/2011/computing-the-vector-norm/
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Parameters
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----------
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x : array-like
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Vector for which to compute the norm
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"""
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return sqrt(squared_norm(x))
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def trace_dot(X, Y):
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"""Trace of np.dot(X, Y.T).
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Parameters
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----------
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X : array-like
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First matrix
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Y : array-like
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Second matrix
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"""
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return np.dot(X.ravel(), Y.ravel())
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def _check_init(A, shape, whom):
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A = check_array(A)
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if np.shape(A) != shape:
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raise ValueError('Array with wrong shape passed to %s. Expected %s, '
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'but got %s ' % (whom, shape, np.shape(A)))
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check_non_negative(A, whom)
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if np.max(A) == 0:
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raise ValueError('Array passed to %s is full of zeros.' % whom)
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def _beta_divergence(X, W, H, beta, square_root=False):
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"""Compute the beta-divergence of X and dot(W, H).
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Parameters
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----------
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X : float or array-like, shape (n_samples, n_features)
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W : float or dense array-like, shape (n_samples, n_components)
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H : float or dense array-like, shape (n_components, n_features)
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beta : float, string in {'frobenius', 'kullback-leibler', 'itakura-saito'}
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Parameter of the beta-divergence.
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If beta == 2, this is half the Frobenius *squared* norm.
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If beta == 1, this is the generalized Kullback-Leibler divergence.
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If beta == 0, this is the Itakura-Saito divergence.
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Else, this is the general beta-divergence.
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square_root : boolean, default False
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If True, return np.sqrt(2 * res)
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For beta == 2, it corresponds to the Frobenius norm.
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Returns
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-------
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res : float
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Beta divergence of X and np.dot(X, H)
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"""
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beta = _beta_loss_to_float(beta)
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# The method can be called with scalars
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if not sp.issparse(X):
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X = np.atleast_2d(X)
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W = np.atleast_2d(W)
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H = np.atleast_2d(H)
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# Frobenius norm
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if beta == 2:
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# Avoid the creation of the dense np.dot(W, H) if X is sparse.
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if sp.issparse(X):
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norm_X = np.dot(X.data, X.data)
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norm_WH = trace_dot(np.dot(np.dot(W.T, W), H), H)
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cross_prod = trace_dot((X * H.T), W)
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res = (norm_X + norm_WH - 2. * cross_prod) / 2.
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else:
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res = squared_norm(X - np.dot(W, H)) / 2.
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if square_root:
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return np.sqrt(res * 2)
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else:
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return res
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if sp.issparse(X):
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# compute np.dot(W, H) only where X is nonzero
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WH_data = _special_sparse_dot(W, H, X).data
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X_data = X.data
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else:
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WH = np.dot(W, H)
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WH_data = WH.ravel()
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X_data = X.ravel()
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# do not affect the zeros: here 0 ** (-1) = 0 and not infinity
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indices = X_data > EPSILON
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WH_data = WH_data[indices]
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X_data = X_data[indices]
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# used to avoid division by zero
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WH_data[WH_data == 0] = EPSILON
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# generalized Kullback-Leibler divergence
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if beta == 1:
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# fast and memory efficient computation of np.sum(np.dot(W, H))
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sum_WH = np.dot(np.sum(W, axis=0), np.sum(H, axis=1))
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# computes np.sum(X * log(X / WH)) only where X is nonzero
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div = X_data / WH_data
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res = np.dot(X_data, np.log(div))
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# add full np.sum(np.dot(W, H)) - np.sum(X)
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res += sum_WH - X_data.sum()
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# Itakura-Saito divergence
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elif beta == 0:
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div = X_data / WH_data
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res = np.sum(div) - np.product(X.shape) - np.sum(np.log(div))
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# beta-divergence, beta not in (0, 1, 2)
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else:
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if sp.issparse(X):
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# slow loop, but memory efficient computation of :
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# np.sum(np.dot(W, H) ** beta)
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sum_WH_beta = 0
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for i in range(X.shape[1]):
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sum_WH_beta += np.sum(np.dot(W, H[:, i]) ** beta)
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else:
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sum_WH_beta = np.sum(WH ** beta)
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sum_X_WH = np.dot(X_data, WH_data ** (beta - 1))
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res = (X_data ** beta).sum() - beta * sum_X_WH
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res += sum_WH_beta * (beta - 1)
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res /= beta * (beta - 1)
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if square_root:
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return np.sqrt(2 * res)
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else:
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return res
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def _special_sparse_dot(W, H, X):
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"""Computes np.dot(W, H), only where X is non zero."""
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if sp.issparse(X):
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ii, jj = X.nonzero()
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n_vals = ii.shape[0]
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dot_vals = np.empty(n_vals)
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n_components = W.shape[1]
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batch_size = max(n_components, n_vals // n_components)
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for start in range(0, n_vals, batch_size):
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batch = slice(start, start + batch_size)
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dot_vals[batch] = np.multiply(W[ii[batch], :],
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H.T[jj[batch], :]).sum(axis=1)
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WH = sp.coo_matrix((dot_vals, (ii, jj)), shape=X.shape)
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return WH.tocsr()
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else:
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return np.dot(W, H)
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def _compute_regularization(alpha, l1_ratio, regularization):
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"""Compute L1 and L2 regularization coefficients for W and H"""
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alpha_H = 0.
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alpha_W = 0.
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if regularization in ('both', 'components'):
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alpha_H = float(alpha)
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if regularization in ('both', 'transformation'):
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alpha_W = float(alpha)
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l1_reg_W = alpha_W * l1_ratio
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l1_reg_H = alpha_H * l1_ratio
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l2_reg_W = alpha_W * (1. - l1_ratio)
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l2_reg_H = alpha_H * (1. - l1_ratio)
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return l1_reg_W, l1_reg_H, l2_reg_W, l2_reg_H
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def _check_string_param(solver, regularization, beta_loss, init):
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allowed_solver = ('cd', 'mu')
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if solver not in allowed_solver:
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raise ValueError(
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'Invalid solver parameter: got %r instead of one of %r' %
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(solver, allowed_solver))
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allowed_regularization = ('both', 'components', 'transformation', None)
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if regularization not in allowed_regularization:
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raise ValueError(
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'Invalid regularization parameter: got %r instead of one of %r' %
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(regularization, allowed_regularization))
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# 'mu' is the only solver that handles other beta losses than 'frobenius'
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if solver != 'mu' and beta_loss not in (2, 'frobenius'):
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raise ValueError(
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'Invalid beta_loss parameter: solver %r does not handle beta_loss'
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' = %r' % (solver, beta_loss))
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if solver == 'mu' and init == 'nndsvd':
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warnings.warn("The multiplicative update ('mu') solver cannot update "
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"zeros present in the initialization, and so leads to "
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"poorer results when used jointly with init='nndsvd'. "
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"You may try init='nndsvda' or init='nndsvdar' instead.",
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UserWarning)
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beta_loss = _beta_loss_to_float(beta_loss)
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return beta_loss
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def _beta_loss_to_float(beta_loss):
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"""Convert string beta_loss to float"""
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allowed_beta_loss = {'frobenius': 2,
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'kullback-leibler': 1,
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'itakura-saito': 0}
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if isinstance(beta_loss, str) and beta_loss in allowed_beta_loss:
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beta_loss = allowed_beta_loss[beta_loss]
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if not isinstance(beta_loss, numbers.Number):
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raise ValueError('Invalid beta_loss parameter: got %r instead '
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'of one of %r, or a float.' %
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(beta_loss, allowed_beta_loss.keys()))
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return beta_loss
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def _initialize_nmf(X, n_components, init=None, eps=1e-6,
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random_state=None):
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"""Algorithms for NMF initialization.
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Computes an initial guess for the non-negative
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rank k matrix approximation for X: X = WH
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Parameters
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----------
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X : array-like, shape (n_samples, n_features)
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The data matrix to be decomposed.
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n_components : integer
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The number of components desired in the approximation.
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init : None | 'random' | 'nndsvd' | 'nndsvda' | 'nndsvdar'
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Method used to initialize the procedure.
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Default: None.
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Valid options:
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- None: 'nndsvd' if n_components <= min(n_samples, n_features),
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otherwise 'random'.
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- 'random': non-negative random matrices, scaled with:
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sqrt(X.mean() / n_components)
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- 'nndsvd': Nonnegative Double Singular Value Decomposition (NNDSVD)
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initialization (better for sparseness)
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- 'nndsvda': NNDSVD with zeros filled with the average of X
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(better when sparsity is not desired)
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- 'nndsvdar': NNDSVD with zeros filled with small random values
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(generally faster, less accurate alternative to NNDSVDa
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for when sparsity is not desired)
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- 'custom': use custom matrices W and H
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eps : float
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Truncate all values less then this in output to zero.
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random_state : int, RandomState instance, default=None
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Used when ``init`` == 'nndsvdar' or 'random'. Pass an int for
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reproducible results across multiple function calls.
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See :term:`Glossary <random_state>`.
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Returns
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-------
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W : array-like, shape (n_samples, n_components)
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Initial guesses for solving X ~= WH
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H : array-like, shape (n_components, n_features)
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Initial guesses for solving X ~= WH
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References
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----------
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C. Boutsidis, E. Gallopoulos: SVD based initialization: A head start for
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nonnegative matrix factorization - Pattern Recognition, 2008
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http://tinyurl.com/nndsvd
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"""
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check_non_negative(X, "NMF initialization")
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n_samples, n_features = X.shape
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if (init is not None and init != 'random'
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and n_components > min(n_samples, n_features)):
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raise ValueError("init = '{}' can only be used when "
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"n_components <= min(n_samples, n_features)"
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.format(init))
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if init is None:
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if n_components <= min(n_samples, n_features):
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init = 'nndsvd'
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else:
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init = 'random'
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# Random initialization
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if init == 'random':
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avg = np.sqrt(X.mean() / n_components)
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rng = check_random_state(random_state)
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H = avg * rng.randn(n_components, n_features).astype(X.dtype,
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copy=False)
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W = avg * rng.randn(n_samples, n_components).astype(X.dtype,
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copy=False)
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np.abs(H, out=H)
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np.abs(W, out=W)
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return W, H
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# NNDSVD initialization
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U, S, V = randomized_svd(X, n_components, random_state=random_state)
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W = np.zeros_like(U)
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H = np.zeros_like(V)
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# The leading singular triplet is non-negative
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# so it can be used as is for initialization.
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W[:, 0] = np.sqrt(S[0]) * np.abs(U[:, 0])
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H[0, :] = np.sqrt(S[0]) * np.abs(V[0, :])
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for j in range(1, n_components):
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x, y = U[:, j], V[j, :]
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# extract positive and negative parts of column vectors
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x_p, y_p = np.maximum(x, 0), np.maximum(y, 0)
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x_n, y_n = np.abs(np.minimum(x, 0)), np.abs(np.minimum(y, 0))
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# and their norms
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x_p_nrm, y_p_nrm = norm(x_p), norm(y_p)
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x_n_nrm, y_n_nrm = norm(x_n), norm(y_n)
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m_p, m_n = x_p_nrm * y_p_nrm, x_n_nrm * y_n_nrm
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# choose update
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if m_p > m_n:
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u = x_p / x_p_nrm
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v = y_p / y_p_nrm
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sigma = m_p
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else:
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u = x_n / x_n_nrm
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v = y_n / y_n_nrm
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sigma = m_n
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lbd = np.sqrt(S[j] * sigma)
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W[:, j] = lbd * u
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H[j, :] = lbd * v
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W[W < eps] = 0
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H[H < eps] = 0
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if init == "nndsvd":
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pass
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elif init == "nndsvda":
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avg = X.mean()
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W[W == 0] = avg
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H[H == 0] = avg
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elif init == "nndsvdar":
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rng = check_random_state(random_state)
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avg = X.mean()
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W[W == 0] = abs(avg * rng.randn(len(W[W == 0])) / 100)
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H[H == 0] = abs(avg * rng.randn(len(H[H == 0])) / 100)
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else:
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raise ValueError(
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'Invalid init parameter: got %r instead of one of %r' %
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(init, (None, 'random', 'nndsvd', 'nndsvda', 'nndsvdar')))
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return W, H
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def _update_coordinate_descent(X, W, Ht, l1_reg, l2_reg, shuffle,
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random_state):
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"""Helper function for _fit_coordinate_descent
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Update W to minimize the objective function, iterating once over all
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coordinates. By symmetry, to update H, one can call
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_update_coordinate_descent(X.T, Ht, W, ...)
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"""
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n_components = Ht.shape[1]
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HHt = np.dot(Ht.T, Ht)
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XHt = safe_sparse_dot(X, Ht)
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# L2 regularization corresponds to increase of the diagonal of HHt
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if l2_reg != 0.:
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# adds l2_reg only on the diagonal
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HHt.flat[::n_components + 1] += l2_reg
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# L1 regularization corresponds to decrease of each element of XHt
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if l1_reg != 0.:
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XHt -= l1_reg
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if shuffle:
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permutation = random_state.permutation(n_components)
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else:
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permutation = np.arange(n_components)
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# The following seems to be required on 64-bit Windows w/ Python 3.5.
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permutation = np.asarray(permutation, dtype=np.intp)
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return _update_cdnmf_fast(W, HHt, XHt, permutation)
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def _fit_coordinate_descent(X, W, H, tol=1e-4, max_iter=200, l1_reg_W=0,
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l1_reg_H=0, l2_reg_W=0, l2_reg_H=0, update_H=True,
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verbose=0, shuffle=False, random_state=None):
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"""Compute Non-negative Matrix Factorization (NMF) with Coordinate Descent
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The objective function is minimized with an alternating minimization of W
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and H. Each minimization is done with a cyclic (up to a permutation of the
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features) Coordinate Descent.
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Parameters
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----------
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X : array-like, shape (n_samples, n_features)
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Constant matrix.
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W : array-like, shape (n_samples, n_components)
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Initial guess for the solution.
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H : array-like, shape (n_components, n_features)
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Initial guess for the solution.
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tol : float, default: 1e-4
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Tolerance of the stopping condition.
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max_iter : integer, default: 200
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Maximum number of iterations before timing out.
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l1_reg_W : double, default: 0.
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L1 regularization parameter for W.
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l1_reg_H : double, default: 0.
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L1 regularization parameter for H.
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l2_reg_W : double, default: 0.
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L2 regularization parameter for W.
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l2_reg_H : double, default: 0.
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L2 regularization parameter for H.
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update_H : boolean, default: True
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Set to True, both W and H will be estimated from initial guesses.
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Set to False, only W will be estimated.
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verbose : integer, default: 0
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The verbosity level.
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shuffle : boolean, default: False
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If true, randomize the order of coordinates in the CD solver.
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random_state : int, RandomState instance, default=None
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Used to randomize the coordinates in the CD solver, when
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``shuffle`` is set to ``True``. Pass an int for reproducible
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results across multiple function calls.
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See :term:`Glossary <random_state>`.
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Returns
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-------
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W : array-like, shape (n_samples, n_components)
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Solution to the non-negative least squares problem.
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H : array-like, shape (n_components, n_features)
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Solution to the non-negative least squares problem.
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n_iter : int
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The number of iterations done by the algorithm.
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References
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----------
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Cichocki, Andrzej, and Phan, Anh-Huy. "Fast local algorithms for
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large scale nonnegative matrix and tensor factorizations."
|
|
IEICE transactions on fundamentals of electronics, communications and
|
|
computer sciences 92.3: 708-721, 2009.
|
|
"""
|
|
# so W and Ht are both in C order in memory
|
|
Ht = check_array(H.T, order='C')
|
|
X = check_array(X, accept_sparse='csr')
|
|
|
|
rng = check_random_state(random_state)
|
|
|
|
for n_iter in range(1, max_iter + 1):
|
|
violation = 0.
|
|
|
|
# Update W
|
|
violation += _update_coordinate_descent(X, W, Ht, l1_reg_W,
|
|
l2_reg_W, shuffle, rng)
|
|
# Update H
|
|
if update_H:
|
|
violation += _update_coordinate_descent(X.T, Ht, W, l1_reg_H,
|
|
l2_reg_H, shuffle, rng)
|
|
|
|
if n_iter == 1:
|
|
violation_init = violation
|
|
|
|
if violation_init == 0:
|
|
break
|
|
|
|
if verbose:
|
|
print("violation:", violation / violation_init)
|
|
|
|
if violation / violation_init <= tol:
|
|
if verbose:
|
|
print("Converged at iteration", n_iter + 1)
|
|
break
|
|
|
|
return W, Ht.T, n_iter
|
|
|
|
|
|
def _multiplicative_update_w(X, W, H, beta_loss, l1_reg_W, l2_reg_W, gamma,
|
|
H_sum=None, HHt=None, XHt=None, update_H=True):
|
|
"""update W in Multiplicative Update NMF"""
|
|
if beta_loss == 2:
|
|
# Numerator
|
|
if XHt is None:
|
|
XHt = safe_sparse_dot(X, H.T)
|
|
if update_H:
|
|
# avoid a copy of XHt, which will be re-computed (update_H=True)
|
|
numerator = XHt
|
|
else:
|
|
# preserve the XHt, which is not re-computed (update_H=False)
|
|
numerator = XHt.copy()
|
|
|
|
# Denominator
|
|
if HHt is None:
|
|
HHt = np.dot(H, H.T)
|
|
denominator = np.dot(W, HHt)
|
|
|
|
else:
|
|
# Numerator
|
|
# if X is sparse, compute WH only where X is non zero
|
|
WH_safe_X = _special_sparse_dot(W, H, X)
|
|
if sp.issparse(X):
|
|
WH_safe_X_data = WH_safe_X.data
|
|
X_data = X.data
|
|
else:
|
|
WH_safe_X_data = WH_safe_X
|
|
X_data = X
|
|
# copy used in the Denominator
|
|
WH = WH_safe_X.copy()
|
|
if beta_loss - 1. < 0:
|
|
WH[WH == 0] = EPSILON
|
|
|
|
# to avoid taking a negative power of zero
|
|
if beta_loss - 2. < 0:
|
|
WH_safe_X_data[WH_safe_X_data == 0] = EPSILON
|
|
|
|
if beta_loss == 1:
|
|
np.divide(X_data, WH_safe_X_data, out=WH_safe_X_data)
|
|
elif beta_loss == 0:
|
|
# speeds up computation time
|
|
# refer to /numpy/numpy/issues/9363
|
|
WH_safe_X_data **= -1
|
|
WH_safe_X_data **= 2
|
|
# element-wise multiplication
|
|
WH_safe_X_data *= X_data
|
|
else:
|
|
WH_safe_X_data **= beta_loss - 2
|
|
# element-wise multiplication
|
|
WH_safe_X_data *= X_data
|
|
|
|
# here numerator = dot(X * (dot(W, H) ** (beta_loss - 2)), H.T)
|
|
numerator = safe_sparse_dot(WH_safe_X, H.T)
|
|
|
|
# Denominator
|
|
if beta_loss == 1:
|
|
if H_sum is None:
|
|
H_sum = np.sum(H, axis=1) # shape(n_components, )
|
|
denominator = H_sum[np.newaxis, :]
|
|
|
|
else:
|
|
# computation of WHHt = dot(dot(W, H) ** beta_loss - 1, H.T)
|
|
if sp.issparse(X):
|
|
# memory efficient computation
|
|
# (compute row by row, avoiding the dense matrix WH)
|
|
WHHt = np.empty(W.shape)
|
|
for i in range(X.shape[0]):
|
|
WHi = np.dot(W[i, :], H)
|
|
if beta_loss - 1 < 0:
|
|
WHi[WHi == 0] = EPSILON
|
|
WHi **= beta_loss - 1
|
|
WHHt[i, :] = np.dot(WHi, H.T)
|
|
else:
|
|
WH **= beta_loss - 1
|
|
WHHt = np.dot(WH, H.T)
|
|
denominator = WHHt
|
|
|
|
# Add L1 and L2 regularization
|
|
if l1_reg_W > 0:
|
|
denominator += l1_reg_W
|
|
if l2_reg_W > 0:
|
|
denominator = denominator + l2_reg_W * W
|
|
denominator[denominator == 0] = EPSILON
|
|
|
|
numerator /= denominator
|
|
delta_W = numerator
|
|
|
|
# gamma is in ]0, 1]
|
|
if gamma != 1:
|
|
delta_W **= gamma
|
|
|
|
return delta_W, H_sum, HHt, XHt
|
|
|
|
|
|
def _multiplicative_update_h(X, W, H, beta_loss, l1_reg_H, l2_reg_H, gamma):
|
|
"""update H in Multiplicative Update NMF"""
|
|
if beta_loss == 2:
|
|
numerator = safe_sparse_dot(W.T, X)
|
|
denominator = np.dot(np.dot(W.T, W), H)
|
|
|
|
else:
|
|
# Numerator
|
|
WH_safe_X = _special_sparse_dot(W, H, X)
|
|
if sp.issparse(X):
|
|
WH_safe_X_data = WH_safe_X.data
|
|
X_data = X.data
|
|
else:
|
|
WH_safe_X_data = WH_safe_X
|
|
X_data = X
|
|
# copy used in the Denominator
|
|
WH = WH_safe_X.copy()
|
|
if beta_loss - 1. < 0:
|
|
WH[WH == 0] = EPSILON
|
|
|
|
# to avoid division by zero
|
|
if beta_loss - 2. < 0:
|
|
WH_safe_X_data[WH_safe_X_data == 0] = EPSILON
|
|
|
|
if beta_loss == 1:
|
|
np.divide(X_data, WH_safe_X_data, out=WH_safe_X_data)
|
|
elif beta_loss == 0:
|
|
# speeds up computation time
|
|
# refer to /numpy/numpy/issues/9363
|
|
WH_safe_X_data **= -1
|
|
WH_safe_X_data **= 2
|
|
# element-wise multiplication
|
|
WH_safe_X_data *= X_data
|
|
else:
|
|
WH_safe_X_data **= beta_loss - 2
|
|
# element-wise multiplication
|
|
WH_safe_X_data *= X_data
|
|
|
|
# here numerator = dot(W.T, (dot(W, H) ** (beta_loss - 2)) * X)
|
|
numerator = safe_sparse_dot(W.T, WH_safe_X)
|
|
|
|
# Denominator
|
|
if beta_loss == 1:
|
|
W_sum = np.sum(W, axis=0) # shape(n_components, )
|
|
W_sum[W_sum == 0] = 1.
|
|
denominator = W_sum[:, np.newaxis]
|
|
|
|
# beta_loss not in (1, 2)
|
|
else:
|
|
# computation of WtWH = dot(W.T, dot(W, H) ** beta_loss - 1)
|
|
if sp.issparse(X):
|
|
# memory efficient computation
|
|
# (compute column by column, avoiding the dense matrix WH)
|
|
WtWH = np.empty(H.shape)
|
|
for i in range(X.shape[1]):
|
|
WHi = np.dot(W, H[:, i])
|
|
if beta_loss - 1 < 0:
|
|
WHi[WHi == 0] = EPSILON
|
|
WHi **= beta_loss - 1
|
|
WtWH[:, i] = np.dot(W.T, WHi)
|
|
else:
|
|
WH **= beta_loss - 1
|
|
WtWH = np.dot(W.T, WH)
|
|
denominator = WtWH
|
|
|
|
# Add L1 and L2 regularization
|
|
if l1_reg_H > 0:
|
|
denominator += l1_reg_H
|
|
if l2_reg_H > 0:
|
|
denominator = denominator + l2_reg_H * H
|
|
denominator[denominator == 0] = EPSILON
|
|
|
|
numerator /= denominator
|
|
delta_H = numerator
|
|
|
|
# gamma is in ]0, 1]
|
|
if gamma != 1:
|
|
delta_H **= gamma
|
|
|
|
return delta_H
|
|
|
|
|
|
def _fit_multiplicative_update(X, W, H, beta_loss='frobenius',
|
|
max_iter=200, tol=1e-4,
|
|
l1_reg_W=0, l1_reg_H=0, l2_reg_W=0, l2_reg_H=0,
|
|
update_H=True, verbose=0):
|
|
"""Compute Non-negative Matrix Factorization with Multiplicative Update
|
|
|
|
The objective function is _beta_divergence(X, WH) and is minimized with an
|
|
alternating minimization of W and H. Each minimization is done with a
|
|
Multiplicative Update.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like, shape (n_samples, n_features)
|
|
Constant input matrix.
|
|
|
|
W : array-like, shape (n_samples, n_components)
|
|
Initial guess for the solution.
|
|
|
|
H : array-like, shape (n_components, n_features)
|
|
Initial guess for the solution.
|
|
|
|
beta_loss : float or string, default 'frobenius'
|
|
String must be in {'frobenius', 'kullback-leibler', 'itakura-saito'}.
|
|
Beta divergence to be minimized, measuring the distance between X
|
|
and the dot product WH. Note that values different from 'frobenius'
|
|
(or 2) and 'kullback-leibler' (or 1) lead to significantly slower
|
|
fits. Note that for beta_loss <= 0 (or 'itakura-saito'), the input
|
|
matrix X cannot contain zeros.
|
|
|
|
max_iter : integer, default: 200
|
|
Number of iterations.
|
|
|
|
tol : float, default: 1e-4
|
|
Tolerance of the stopping condition.
|
|
|
|
l1_reg_W : double, default: 0.
|
|
L1 regularization parameter for W.
|
|
|
|
l1_reg_H : double, default: 0.
|
|
L1 regularization parameter for H.
|
|
|
|
l2_reg_W : double, default: 0.
|
|
L2 regularization parameter for W.
|
|
|
|
l2_reg_H : double, default: 0.
|
|
L2 regularization parameter for H.
|
|
|
|
update_H : boolean, default: True
|
|
Set to True, both W and H will be estimated from initial guesses.
|
|
Set to False, only W will be estimated.
|
|
|
|
verbose : integer, default: 0
|
|
The verbosity level.
|
|
|
|
Returns
|
|
-------
|
|
W : array, shape (n_samples, n_components)
|
|
Solution to the non-negative least squares problem.
|
|
|
|
H : array, shape (n_components, n_features)
|
|
Solution to the non-negative least squares problem.
|
|
|
|
n_iter : int
|
|
The number of iterations done by the algorithm.
|
|
|
|
References
|
|
----------
|
|
Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix
|
|
factorization with the beta-divergence. Neural Computation, 23(9).
|
|
"""
|
|
start_time = time.time()
|
|
|
|
beta_loss = _beta_loss_to_float(beta_loss)
|
|
|
|
# gamma for Maximization-Minimization (MM) algorithm [Fevotte 2011]
|
|
if beta_loss < 1:
|
|
gamma = 1. / (2. - beta_loss)
|
|
elif beta_loss > 2:
|
|
gamma = 1. / (beta_loss - 1.)
|
|
else:
|
|
gamma = 1.
|
|
|
|
# used for the convergence criterion
|
|
error_at_init = _beta_divergence(X, W, H, beta_loss, square_root=True)
|
|
previous_error = error_at_init
|
|
|
|
H_sum, HHt, XHt = None, None, None
|
|
for n_iter in range(1, max_iter + 1):
|
|
# update W
|
|
# H_sum, HHt and XHt are saved and reused if not update_H
|
|
delta_W, H_sum, HHt, XHt = _multiplicative_update_w(
|
|
X, W, H, beta_loss, l1_reg_W, l2_reg_W, gamma,
|
|
H_sum, HHt, XHt, update_H)
|
|
W *= delta_W
|
|
|
|
# necessary for stability with beta_loss < 1
|
|
if beta_loss < 1:
|
|
W[W < np.finfo(np.float64).eps] = 0.
|
|
|
|
# update H
|
|
if update_H:
|
|
delta_H = _multiplicative_update_h(X, W, H, beta_loss, l1_reg_H,
|
|
l2_reg_H, gamma)
|
|
H *= delta_H
|
|
|
|
# These values will be recomputed since H changed
|
|
H_sum, HHt, XHt = None, None, None
|
|
|
|
# necessary for stability with beta_loss < 1
|
|
if beta_loss <= 1:
|
|
H[H < np.finfo(np.float64).eps] = 0.
|
|
|
|
# test convergence criterion every 10 iterations
|
|
if tol > 0 and n_iter % 10 == 0:
|
|
error = _beta_divergence(X, W, H, beta_loss, square_root=True)
|
|
|
|
if verbose:
|
|
iter_time = time.time()
|
|
print("Epoch %02d reached after %.3f seconds, error: %f" %
|
|
(n_iter, iter_time - start_time, error))
|
|
|
|
if (previous_error - error) / error_at_init < tol:
|
|
break
|
|
previous_error = error
|
|
|
|
# do not print if we have already printed in the convergence test
|
|
if verbose and (tol == 0 or n_iter % 10 != 0):
|
|
end_time = time.time()
|
|
print("Epoch %02d reached after %.3f seconds." %
|
|
(n_iter, end_time - start_time))
|
|
|
|
return W, H, n_iter
|
|
|
|
|
|
@_deprecate_positional_args
|
|
def non_negative_factorization(X, W=None, H=None, n_components=None, *,
|
|
init=None, update_H=True, solver='cd',
|
|
beta_loss='frobenius', tol=1e-4,
|
|
max_iter=200, alpha=0., l1_ratio=0.,
|
|
regularization=None, random_state=None,
|
|
verbose=0, shuffle=False):
|
|
r"""Compute Non-negative Matrix Factorization (NMF)
|
|
|
|
Find two non-negative matrices (W, H) whose product approximates the non-
|
|
negative matrix X. This factorization can be used for example for
|
|
dimensionality reduction, source separation or topic extraction.
|
|
|
|
The objective function is::
|
|
|
|
0.5 * ||X - WH||_Fro^2
|
|
+ alpha * l1_ratio * ||vec(W)||_1
|
|
+ alpha * l1_ratio * ||vec(H)||_1
|
|
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2
|
|
+ 0.5 * alpha * (1 - l1_ratio) * ||H||_Fro^2
|
|
|
|
Where::
|
|
|
|
||A||_Fro^2 = \sum_{i,j} A_{ij}^2 (Frobenius norm)
|
|
||vec(A)||_1 = \sum_{i,j} abs(A_{ij}) (Elementwise L1 norm)
|
|
|
|
For multiplicative-update ('mu') solver, the Frobenius norm
|
|
(0.5 * ||X - WH||_Fro^2) can be changed into another beta-divergence loss,
|
|
by changing the beta_loss parameter.
|
|
|
|
The objective function is minimized with an alternating minimization of W
|
|
and H. If H is given and update_H=False, it solves for W only.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like, shape (n_samples, n_features)
|
|
Constant matrix.
|
|
|
|
W : array-like, shape (n_samples, n_components)
|
|
If init='custom', it is used as initial guess for the solution.
|
|
|
|
H : array-like, shape (n_components, n_features)
|
|
If init='custom', it is used as initial guess for the solution.
|
|
If update_H=False, it is used as a constant, to solve for W only.
|
|
|
|
n_components : integer
|
|
Number of components, if n_components is not set all features
|
|
are kept.
|
|
|
|
init : None | 'random' | 'nndsvd' | 'nndsvda' | 'nndsvdar' | 'custom'
|
|
Method used to initialize the procedure.
|
|
Default: None.
|
|
|
|
Valid options:
|
|
|
|
- None: 'nndsvd' if n_components < n_features, otherwise 'random'.
|
|
|
|
- 'random': non-negative random matrices, scaled with:
|
|
sqrt(X.mean() / n_components)
|
|
|
|
- 'nndsvd': Nonnegative Double Singular Value Decomposition (NNDSVD)
|
|
initialization (better for sparseness)
|
|
|
|
- 'nndsvda': NNDSVD with zeros filled with the average of X
|
|
(better when sparsity is not desired)
|
|
|
|
- 'nndsvdar': NNDSVD with zeros filled with small random values
|
|
(generally faster, less accurate alternative to NNDSVDa
|
|
for when sparsity is not desired)
|
|
|
|
- 'custom': use custom matrices W and H
|
|
|
|
.. versionchanged:: 0.23
|
|
The default value of `init` changed from 'random' to None in 0.23.
|
|
|
|
update_H : boolean, default: True
|
|
Set to True, both W and H will be estimated from initial guesses.
|
|
Set to False, only W will be estimated.
|
|
|
|
solver : 'cd' | 'mu'
|
|
Numerical solver to use:
|
|
|
|
- 'cd' is a Coordinate Descent solver that uses Fast Hierarchical
|
|
Alternating Least Squares (Fast HALS).
|
|
|
|
- 'mu' is a Multiplicative Update solver.
|
|
|
|
.. versionadded:: 0.17
|
|
Coordinate Descent solver.
|
|
|
|
.. versionadded:: 0.19
|
|
Multiplicative Update solver.
|
|
|
|
beta_loss : float or string, default 'frobenius'
|
|
String must be in {'frobenius', 'kullback-leibler', 'itakura-saito'}.
|
|
Beta divergence to be minimized, measuring the distance between X
|
|
and the dot product WH. Note that values different from 'frobenius'
|
|
(or 2) and 'kullback-leibler' (or 1) lead to significantly slower
|
|
fits. Note that for beta_loss <= 0 (or 'itakura-saito'), the input
|
|
matrix X cannot contain zeros. Used only in 'mu' solver.
|
|
|
|
.. versionadded:: 0.19
|
|
|
|
tol : float, default: 1e-4
|
|
Tolerance of the stopping condition.
|
|
|
|
max_iter : integer, default: 200
|
|
Maximum number of iterations before timing out.
|
|
|
|
alpha : double, default: 0.
|
|
Constant that multiplies the regularization terms.
|
|
|
|
l1_ratio : double, default: 0.
|
|
The regularization mixing parameter, with 0 <= l1_ratio <= 1.
|
|
For l1_ratio = 0 the penalty is an elementwise L2 penalty
|
|
(aka Frobenius Norm).
|
|
For l1_ratio = 1 it is an elementwise L1 penalty.
|
|
For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.
|
|
|
|
regularization : 'both' | 'components' | 'transformation' | None
|
|
Select whether the regularization affects the components (H), the
|
|
transformation (W), both or none of them.
|
|
|
|
random_state : int, RandomState instance, default=None
|
|
Used for NMF initialisation (when ``init`` == 'nndsvdar' or
|
|
'random'), and in Coordinate Descent. Pass an int for reproducible
|
|
results across multiple function calls.
|
|
See :term:`Glossary <random_state>`.
|
|
|
|
verbose : integer, default: 0
|
|
The verbosity level.
|
|
|
|
shuffle : boolean, default: False
|
|
If true, randomize the order of coordinates in the CD solver.
|
|
|
|
Returns
|
|
-------
|
|
W : array-like, shape (n_samples, n_components)
|
|
Solution to the non-negative least squares problem.
|
|
|
|
H : array-like, shape (n_components, n_features)
|
|
Solution to the non-negative least squares problem.
|
|
|
|
n_iter : int
|
|
Actual number of iterations.
|
|
|
|
Examples
|
|
--------
|
|
>>> import numpy as np
|
|
>>> X = np.array([[1,1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
|
|
>>> from sklearn.decomposition import non_negative_factorization
|
|
>>> W, H, n_iter = non_negative_factorization(X, n_components=2,
|
|
... init='random', random_state=0)
|
|
|
|
References
|
|
----------
|
|
Cichocki, Andrzej, and P. H. A. N. Anh-Huy. "Fast local algorithms for
|
|
large scale nonnegative matrix and tensor factorizations."
|
|
IEICE transactions on fundamentals of electronics, communications and
|
|
computer sciences 92.3: 708-721, 2009.
|
|
|
|
Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix
|
|
factorization with the beta-divergence. Neural Computation, 23(9).
|
|
"""
|
|
X = check_array(X, accept_sparse=('csr', 'csc'),
|
|
dtype=[np.float64, np.float32])
|
|
check_non_negative(X, "NMF (input X)")
|
|
beta_loss = _check_string_param(solver, regularization, beta_loss, init)
|
|
|
|
if X.min() == 0 and beta_loss <= 0:
|
|
raise ValueError("When beta_loss <= 0 and X contains zeros, "
|
|
"the solver may diverge. Please add small values to "
|
|
"X, or use a positive beta_loss.")
|
|
|
|
n_samples, n_features = X.shape
|
|
if n_components is None:
|
|
n_components = n_features
|
|
|
|
if not isinstance(n_components, numbers.Integral) or n_components <= 0:
|
|
raise ValueError("Number of components must be a positive integer;"
|
|
" got (n_components=%r)" % n_components)
|
|
if not isinstance(max_iter, numbers.Integral) or max_iter < 0:
|
|
raise ValueError("Maximum number of iterations must be a positive "
|
|
"integer; got (max_iter=%r)" % max_iter)
|
|
if not isinstance(tol, numbers.Number) or tol < 0:
|
|
raise ValueError("Tolerance for stopping criteria must be "
|
|
"positive; got (tol=%r)" % tol)
|
|
|
|
# check W and H, or initialize them
|
|
if init == 'custom' and update_H:
|
|
_check_init(H, (n_components, n_features), "NMF (input H)")
|
|
_check_init(W, (n_samples, n_components), "NMF (input W)")
|
|
if H.dtype != X.dtype or W.dtype != X.dtype:
|
|
raise TypeError("H and W should have the same dtype as X. Got "
|
|
"H.dtype = {} and W.dtype = {}."
|
|
.format(H.dtype, W.dtype))
|
|
elif not update_H:
|
|
_check_init(H, (n_components, n_features), "NMF (input H)")
|
|
if H.dtype != X.dtype:
|
|
raise TypeError("H should have the same dtype as X. Got H.dtype = "
|
|
"{}.".format(H.dtype))
|
|
# 'mu' solver should not be initialized by zeros
|
|
if solver == 'mu':
|
|
avg = np.sqrt(X.mean() / n_components)
|
|
W = np.full((n_samples, n_components), avg, dtype=X.dtype)
|
|
else:
|
|
W = np.zeros((n_samples, n_components), dtype=X.dtype)
|
|
else:
|
|
W, H = _initialize_nmf(X, n_components, init=init,
|
|
random_state=random_state)
|
|
|
|
l1_reg_W, l1_reg_H, l2_reg_W, l2_reg_H = _compute_regularization(
|
|
alpha, l1_ratio, regularization)
|
|
|
|
if solver == 'cd':
|
|
W, H, n_iter = _fit_coordinate_descent(X, W, H, tol, max_iter,
|
|
l1_reg_W, l1_reg_H,
|
|
l2_reg_W, l2_reg_H,
|
|
update_H=update_H,
|
|
verbose=verbose,
|
|
shuffle=shuffle,
|
|
random_state=random_state)
|
|
elif solver == 'mu':
|
|
W, H, n_iter = _fit_multiplicative_update(X, W, H, beta_loss, max_iter,
|
|
tol, l1_reg_W, l1_reg_H,
|
|
l2_reg_W, l2_reg_H, update_H,
|
|
verbose)
|
|
|
|
else:
|
|
raise ValueError("Invalid solver parameter '%s'." % solver)
|
|
|
|
if n_iter == max_iter and tol > 0:
|
|
warnings.warn("Maximum number of iterations %d reached. Increase it to"
|
|
" improve convergence." % max_iter, ConvergenceWarning)
|
|
|
|
return W, H, n_iter
|
|
|
|
|
|
class NMF(TransformerMixin, BaseEstimator):
|
|
r"""Non-Negative Matrix Factorization (NMF)
|
|
|
|
Find two non-negative matrices (W, H) whose product approximates the non-
|
|
negative matrix X. This factorization can be used for example for
|
|
dimensionality reduction, source separation or topic extraction.
|
|
|
|
The objective function is::
|
|
|
|
0.5 * ||X - WH||_Fro^2
|
|
+ alpha * l1_ratio * ||vec(W)||_1
|
|
+ alpha * l1_ratio * ||vec(H)||_1
|
|
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2
|
|
+ 0.5 * alpha * (1 - l1_ratio) * ||H||_Fro^2
|
|
|
|
Where::
|
|
|
|
||A||_Fro^2 = \sum_{i,j} A_{ij}^2 (Frobenius norm)
|
|
||vec(A)||_1 = \sum_{i,j} abs(A_{ij}) (Elementwise L1 norm)
|
|
|
|
For multiplicative-update ('mu') solver, the Frobenius norm
|
|
(0.5 * ||X - WH||_Fro^2) can be changed into another beta-divergence loss,
|
|
by changing the beta_loss parameter.
|
|
|
|
The objective function is minimized with an alternating minimization of W
|
|
and H.
|
|
|
|
Read more in the :ref:`User Guide <NMF>`.
|
|
|
|
Parameters
|
|
----------
|
|
n_components : int or None
|
|
Number of components, if n_components is not set all features
|
|
are kept.
|
|
|
|
init : None | 'random' | 'nndsvd' | 'nndsvda' | 'nndsvdar' | 'custom'
|
|
Method used to initialize the procedure.
|
|
Default: None.
|
|
Valid options:
|
|
|
|
- None: 'nndsvd' if n_components <= min(n_samples, n_features),
|
|
otherwise random.
|
|
|
|
- 'random': non-negative random matrices, scaled with:
|
|
sqrt(X.mean() / n_components)
|
|
|
|
- 'nndsvd': Nonnegative Double Singular Value Decomposition (NNDSVD)
|
|
initialization (better for sparseness)
|
|
|
|
- 'nndsvda': NNDSVD with zeros filled with the average of X
|
|
(better when sparsity is not desired)
|
|
|
|
- 'nndsvdar': NNDSVD with zeros filled with small random values
|
|
(generally faster, less accurate alternative to NNDSVDa
|
|
for when sparsity is not desired)
|
|
|
|
- 'custom': use custom matrices W and H
|
|
|
|
solver : 'cd' | 'mu'
|
|
Numerical solver to use:
|
|
'cd' is a Coordinate Descent solver.
|
|
'mu' is a Multiplicative Update solver.
|
|
|
|
.. versionadded:: 0.17
|
|
Coordinate Descent solver.
|
|
|
|
.. versionadded:: 0.19
|
|
Multiplicative Update solver.
|
|
|
|
beta_loss : float or string, default 'frobenius'
|
|
String must be in {'frobenius', 'kullback-leibler', 'itakura-saito'}.
|
|
Beta divergence to be minimized, measuring the distance between X
|
|
and the dot product WH. Note that values different from 'frobenius'
|
|
(or 2) and 'kullback-leibler' (or 1) lead to significantly slower
|
|
fits. Note that for beta_loss <= 0 (or 'itakura-saito'), the input
|
|
matrix X cannot contain zeros. Used only in 'mu' solver.
|
|
|
|
.. versionadded:: 0.19
|
|
|
|
tol : float, default: 1e-4
|
|
Tolerance of the stopping condition.
|
|
|
|
max_iter : integer, default: 200
|
|
Maximum number of iterations before timing out.
|
|
|
|
random_state : int, RandomState instance, default=None
|
|
Used for initialisation (when ``init`` == 'nndsvdar' or
|
|
'random'), and in Coordinate Descent. Pass an int for reproducible
|
|
results across multiple function calls.
|
|
See :term:`Glossary <random_state>`.
|
|
|
|
alpha : double, default: 0.
|
|
Constant that multiplies the regularization terms. Set it to zero to
|
|
have no regularization.
|
|
|
|
.. versionadded:: 0.17
|
|
*alpha* used in the Coordinate Descent solver.
|
|
|
|
l1_ratio : double, default: 0.
|
|
The regularization mixing parameter, with 0 <= l1_ratio <= 1.
|
|
For l1_ratio = 0 the penalty is an elementwise L2 penalty
|
|
(aka Frobenius Norm).
|
|
For l1_ratio = 1 it is an elementwise L1 penalty.
|
|
For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.
|
|
|
|
.. versionadded:: 0.17
|
|
Regularization parameter *l1_ratio* used in the Coordinate Descent
|
|
solver.
|
|
|
|
verbose : bool, default=False
|
|
Whether to be verbose.
|
|
|
|
shuffle : boolean, default: False
|
|
If true, randomize the order of coordinates in the CD solver.
|
|
|
|
.. versionadded:: 0.17
|
|
*shuffle* parameter used in the Coordinate Descent solver.
|
|
|
|
Attributes
|
|
----------
|
|
components_ : array, [n_components, n_features]
|
|
Factorization matrix, sometimes called 'dictionary'.
|
|
|
|
n_components_ : integer
|
|
The number of components. It is same as the `n_components` parameter
|
|
if it was given. Otherwise, it will be same as the number of
|
|
features.
|
|
|
|
reconstruction_err_ : number
|
|
Frobenius norm of the matrix difference, or beta-divergence, between
|
|
the training data ``X`` and the reconstructed data ``WH`` from
|
|
the fitted model.
|
|
|
|
n_iter_ : int
|
|
Actual number of iterations.
|
|
|
|
Examples
|
|
--------
|
|
>>> import numpy as np
|
|
>>> X = np.array([[1, 1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
|
|
>>> from sklearn.decomposition import NMF
|
|
>>> model = NMF(n_components=2, init='random', random_state=0)
|
|
>>> W = model.fit_transform(X)
|
|
>>> H = model.components_
|
|
|
|
References
|
|
----------
|
|
Cichocki, Andrzej, and P. H. A. N. Anh-Huy. "Fast local algorithms for
|
|
large scale nonnegative matrix and tensor factorizations."
|
|
IEICE transactions on fundamentals of electronics, communications and
|
|
computer sciences 92.3: 708-721, 2009.
|
|
|
|
Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix
|
|
factorization with the beta-divergence. Neural Computation, 23(9).
|
|
"""
|
|
@_deprecate_positional_args
|
|
def __init__(self, n_components=None, *, init=None, solver='cd',
|
|
beta_loss='frobenius', tol=1e-4, max_iter=200,
|
|
random_state=None, alpha=0., l1_ratio=0., verbose=0,
|
|
shuffle=False):
|
|
self.n_components = n_components
|
|
self.init = init
|
|
self.solver = solver
|
|
self.beta_loss = beta_loss
|
|
self.tol = tol
|
|
self.max_iter = max_iter
|
|
self.random_state = random_state
|
|
self.alpha = alpha
|
|
self.l1_ratio = l1_ratio
|
|
self.verbose = verbose
|
|
self.shuffle = shuffle
|
|
|
|
def _more_tags(self):
|
|
return {'requires_positive_X': True}
|
|
|
|
def fit_transform(self, X, y=None, W=None, H=None):
|
|
"""Learn a NMF model for the data X and returns the transformed data.
|
|
|
|
This is more efficient than calling fit followed by transform.
|
|
|
|
Parameters
|
|
----------
|
|
X : {array-like, sparse matrix}, shape (n_samples, n_features)
|
|
Data matrix to be decomposed
|
|
|
|
y : Ignored
|
|
|
|
W : array-like, shape (n_samples, n_components)
|
|
If init='custom', it is used as initial guess for the solution.
|
|
|
|
H : array-like, shape (n_components, n_features)
|
|
If init='custom', it is used as initial guess for the solution.
|
|
|
|
Returns
|
|
-------
|
|
W : array, shape (n_samples, n_components)
|
|
Transformed data.
|
|
"""
|
|
X = self._validate_data(X, accept_sparse=('csr', 'csc'),
|
|
dtype=[np.float64, np.float32])
|
|
|
|
W, H, n_iter_ = non_negative_factorization(
|
|
X=X, W=W, H=H, n_components=self.n_components, init=self.init,
|
|
update_H=True, solver=self.solver, beta_loss=self.beta_loss,
|
|
tol=self.tol, max_iter=self.max_iter, alpha=self.alpha,
|
|
l1_ratio=self.l1_ratio, regularization='both',
|
|
random_state=self.random_state, verbose=self.verbose,
|
|
shuffle=self.shuffle)
|
|
|
|
self.reconstruction_err_ = _beta_divergence(X, W, H, self.beta_loss,
|
|
square_root=True)
|
|
|
|
self.n_components_ = H.shape[0]
|
|
self.components_ = H
|
|
self.n_iter_ = n_iter_
|
|
|
|
return W
|
|
|
|
def fit(self, X, y=None, **params):
|
|
"""Learn a NMF model for the data X.
|
|
|
|
Parameters
|
|
----------
|
|
X : {array-like, sparse matrix}, shape (n_samples, n_features)
|
|
Data matrix to be decomposed
|
|
|
|
y : Ignored
|
|
|
|
Returns
|
|
-------
|
|
self
|
|
"""
|
|
self.fit_transform(X, **params)
|
|
return self
|
|
|
|
def transform(self, X):
|
|
"""Transform the data X according to the fitted NMF model
|
|
|
|
Parameters
|
|
----------
|
|
X : {array-like, sparse matrix}, shape (n_samples, n_features)
|
|
Data matrix to be transformed by the model
|
|
|
|
Returns
|
|
-------
|
|
W : array, shape (n_samples, n_components)
|
|
Transformed data
|
|
"""
|
|
check_is_fitted(self)
|
|
|
|
W, _, n_iter_ = non_negative_factorization(
|
|
X=X, W=None, H=self.components_, n_components=self.n_components_,
|
|
init=self.init, update_H=False, solver=self.solver,
|
|
beta_loss=self.beta_loss, tol=self.tol, max_iter=self.max_iter,
|
|
alpha=self.alpha, l1_ratio=self.l1_ratio, regularization='both',
|
|
random_state=self.random_state, verbose=self.verbose,
|
|
shuffle=self.shuffle)
|
|
|
|
return W
|
|
|
|
def inverse_transform(self, W):
|
|
"""Transform data back to its original space.
|
|
|
|
Parameters
|
|
----------
|
|
W : {array-like, sparse matrix}, shape (n_samples, n_components)
|
|
Transformed data matrix
|
|
|
|
Returns
|
|
-------
|
|
X : {array-like, sparse matrix}, shape (n_samples, n_features)
|
|
Data matrix of original shape
|
|
|
|
.. versionadded:: 0.18
|
|
"""
|
|
check_is_fitted(self)
|
|
return np.dot(W, self.components_)
|