423 lines
15 KiB
Python
423 lines
15 KiB
Python
"""
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Benchmarks of Non-Negative Matrix Factorization
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"""
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# Authors: Tom Dupre la Tour (benchmark)
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# Chih-Jen Linn (original projected gradient NMF implementation)
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# Anthony Di Franco (projected gradient, Python and NumPy port)
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# License: BSD 3 clause
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from __future__ import print_function
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from time import time
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import sys
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import warnings
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import numbers
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import numpy as np
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import matplotlib.pyplot as plt
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import pandas
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from sklearn.utils.testing import ignore_warnings
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from sklearn.feature_extraction.text import TfidfVectorizer
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from sklearn.decomposition.nmf import NMF
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from sklearn.decomposition.nmf import _initialize_nmf
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from sklearn.decomposition.nmf import _beta_divergence
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from sklearn.decomposition.nmf import INTEGER_TYPES, _check_init
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from sklearn.externals.joblib import Memory
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from sklearn.exceptions import ConvergenceWarning
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from sklearn.utils.extmath import safe_sparse_dot, squared_norm
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from sklearn.utils import check_array
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from sklearn.utils.validation import check_is_fitted, check_non_negative
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mem = Memory(cachedir='.', verbose=0)
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###################
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# Start of _PGNMF #
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###################
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# This class implements a projected gradient solver for the NMF.
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# The projected gradient solver was removed from scikit-learn in version 0.19,
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# and a simplified copy is used here for comparison purpose only.
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# It is not tested, and it may change or disappear without notice.
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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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"""
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return np.sqrt(squared_norm(x))
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def _nls_subproblem(X, W, H, tol, max_iter, alpha=0., l1_ratio=0.,
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sigma=0.01, beta=0.1):
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"""Non-negative least square solver
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Solves a non-negative least squares subproblem using the projected
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gradient descent algorithm.
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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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Constant matrix.
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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
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Tolerance of the stopping condition.
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max_iter : int
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Maximum number of iterations before timing out.
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alpha : double, default: 0.
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Constant that multiplies the regularization terms. Set it to zero to
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have no regularization.
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l1_ratio : double, default: 0.
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The regularization mixing parameter, with 0 <= l1_ratio <= 1.
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For l1_ratio = 0 the penalty is an L2 penalty.
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For l1_ratio = 1 it is an L1 penalty.
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For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.
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sigma : float
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Constant used in the sufficient decrease condition checked by the line
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search. Smaller values lead to a looser sufficient decrease condition,
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thus reducing the time taken by the line search, but potentially
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increasing the number of iterations of the projected gradient
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procedure. 0.01 is a commonly used value in the optimization
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literature.
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beta : float
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Factor by which the step size is decreased (resp. increased) until
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(resp. as long as) the sufficient decrease condition is satisfied.
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Larger values allow to find a better step size but lead to longer line
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search. 0.1 is a commonly used value in the optimization literature.
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Returns
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-------
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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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grad : array-like, shape (n_components, n_features)
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The gradient.
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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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C.-J. Lin. Projected gradient methods for non-negative matrix
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factorization. Neural Computation, 19(2007), 2756-2779.
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http://www.csie.ntu.edu.tw/~cjlin/nmf/
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"""
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WtX = safe_sparse_dot(W.T, X)
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WtW = np.dot(W.T, W)
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# values justified in the paper (alpha is renamed gamma)
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gamma = 1
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for n_iter in range(1, max_iter + 1):
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grad = np.dot(WtW, H) - WtX
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if alpha > 0 and l1_ratio == 1.:
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grad += alpha
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elif alpha > 0:
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grad += alpha * (l1_ratio + (1 - l1_ratio) * H)
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# The following multiplication with a boolean array is more than twice
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# as fast as indexing into grad.
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if _norm(grad * np.logical_or(grad < 0, H > 0)) < tol:
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break
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Hp = H
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for inner_iter in range(20):
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# Gradient step.
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Hn = H - gamma * grad
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# Projection step.
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Hn *= Hn > 0
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d = Hn - H
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gradd = np.dot(grad.ravel(), d.ravel())
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dQd = np.dot(np.dot(WtW, d).ravel(), d.ravel())
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suff_decr = (1 - sigma) * gradd + 0.5 * dQd < 0
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if inner_iter == 0:
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decr_gamma = not suff_decr
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if decr_gamma:
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if suff_decr:
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H = Hn
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break
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else:
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gamma *= beta
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elif not suff_decr or (Hp == Hn).all():
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H = Hp
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break
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else:
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gamma /= beta
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Hp = Hn
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if n_iter == max_iter:
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warnings.warn("Iteration limit reached in nls subproblem.",
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ConvergenceWarning)
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return H, grad, n_iter
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def _fit_projected_gradient(X, W, H, tol, max_iter, nls_max_iter, alpha,
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l1_ratio):
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gradW = (np.dot(W, np.dot(H, H.T)) -
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safe_sparse_dot(X, H.T, dense_output=True))
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gradH = (np.dot(np.dot(W.T, W), H) -
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safe_sparse_dot(W.T, X, dense_output=True))
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init_grad = squared_norm(gradW) + squared_norm(gradH.T)
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# max(0.001, tol) to force alternating minimizations of W and H
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tolW = max(0.001, tol) * np.sqrt(init_grad)
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tolH = tolW
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for n_iter in range(1, max_iter + 1):
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# stopping condition as discussed in paper
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proj_grad_W = squared_norm(gradW * np.logical_or(gradW < 0, W > 0))
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proj_grad_H = squared_norm(gradH * np.logical_or(gradH < 0, H > 0))
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if (proj_grad_W + proj_grad_H) / init_grad < tol ** 2:
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break
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# update W
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Wt, gradWt, iterW = _nls_subproblem(X.T, H.T, W.T, tolW, nls_max_iter,
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alpha=alpha, l1_ratio=l1_ratio)
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W, gradW = Wt.T, gradWt.T
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if iterW == 1:
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tolW = 0.1 * tolW
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# update H
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H, gradH, iterH = _nls_subproblem(X, W, H, tolH, nls_max_iter,
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alpha=alpha, l1_ratio=l1_ratio)
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if iterH == 1:
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tolH = 0.1 * tolH
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H[H == 0] = 0 # fix up negative zeros
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if n_iter == max_iter:
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Wt, _, _ = _nls_subproblem(X.T, H.T, W.T, tolW, nls_max_iter,
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alpha=alpha, l1_ratio=l1_ratio)
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W = Wt.T
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return W, H, n_iter
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class _PGNMF(NMF):
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"""Non-Negative Matrix Factorization (NMF) with projected gradient solver.
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This class is private and for comparison purpose only.
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It may change or disappear without notice.
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"""
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def __init__(self, n_components=None, solver='pg', init=None,
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tol=1e-4, max_iter=200, random_state=None,
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alpha=0., l1_ratio=0., nls_max_iter=10):
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super(_PGNMF, self).__init__(
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n_components=n_components, init=init, solver=solver, tol=tol,
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max_iter=max_iter, random_state=random_state, alpha=alpha,
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l1_ratio=l1_ratio)
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self.nls_max_iter = nls_max_iter
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def fit(self, X, y=None, **params):
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self.fit_transform(X, **params)
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return self
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def transform(self, X):
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check_is_fitted(self, 'components_')
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H = self.components_
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W, _, self.n_iter_ = self._fit_transform(X, H=H, update_H=False)
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return W
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def inverse_transform(self, W):
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check_is_fitted(self, 'components_')
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return np.dot(W, self.components_)
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def fit_transform(self, X, y=None, W=None, H=None):
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W, H, self.n_iter = self._fit_transform(X, W=W, H=H, update_H=True)
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self.components_ = H
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return W
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def _fit_transform(self, X, y=None, W=None, H=None, update_H=True):
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X = check_array(X, accept_sparse=('csr', 'csc'))
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check_non_negative(X, "NMF (input X)")
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n_samples, n_features = X.shape
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n_components = self.n_components
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if n_components is None:
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n_components = n_features
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if (not isinstance(n_components, INTEGER_TYPES) or
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n_components <= 0):
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raise ValueError("Number of components must be a positive integer;"
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" got (n_components=%r)" % n_components)
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if not isinstance(self.max_iter, INTEGER_TYPES) or self.max_iter < 0:
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raise ValueError("Maximum number of iterations must be a positive "
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"integer; got (max_iter=%r)" % self.max_iter)
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if not isinstance(self.tol, numbers.Number) or self.tol < 0:
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raise ValueError("Tolerance for stopping criteria must be "
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"positive; got (tol=%r)" % self.tol)
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# check W and H, or initialize them
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if self.init == 'custom' and update_H:
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_check_init(H, (n_components, n_features), "NMF (input H)")
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_check_init(W, (n_samples, n_components), "NMF (input W)")
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elif not update_H:
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_check_init(H, (n_components, n_features), "NMF (input H)")
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W = np.zeros((n_samples, n_components))
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else:
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W, H = _initialize_nmf(X, n_components, init=self.init,
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random_state=self.random_state)
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if update_H: # fit_transform
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W, H, n_iter = _fit_projected_gradient(
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X, W, H, self.tol, self.max_iter, self.nls_max_iter,
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self.alpha, self.l1_ratio)
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else: # transform
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Wt, _, n_iter = _nls_subproblem(X.T, H.T, W.T, self.tol,
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self.nls_max_iter,
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alpha=self.alpha,
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l1_ratio=self.l1_ratio)
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W = Wt.T
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if n_iter == self.max_iter and self.tol > 0:
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warnings.warn("Maximum number of iteration %d reached. Increase it"
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" to improve convergence." % self.max_iter,
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ConvergenceWarning)
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return W, H, n_iter
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#################
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# End of _PGNMF #
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#################
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def plot_results(results_df, plot_name):
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if results_df is None:
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return None
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plt.figure(figsize=(16, 6))
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colors = 'bgr'
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markers = 'ovs'
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ax = plt.subplot(1, 3, 1)
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for i, init in enumerate(np.unique(results_df['init'])):
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plt.subplot(1, 3, i + 1, sharex=ax, sharey=ax)
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for j, method in enumerate(np.unique(results_df['method'])):
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mask = np.logical_and(results_df['init'] == init,
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results_df['method'] == method)
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selected_items = results_df[mask]
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plt.plot(selected_items['time'], selected_items['loss'],
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color=colors[j % len(colors)], ls='-',
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marker=markers[j % len(markers)],
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label=method)
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plt.legend(loc=0, fontsize='x-small')
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plt.xlabel("Time (s)")
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plt.ylabel("loss")
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plt.title("%s" % init)
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plt.suptitle(plot_name, fontsize=16)
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@ignore_warnings(category=ConvergenceWarning)
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# use joblib to cache the results.
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# X_shape is specified in arguments for avoiding hashing X
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@mem.cache(ignore=['X', 'W0', 'H0'])
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def bench_one(name, X, W0, H0, X_shape, clf_type, clf_params, init,
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n_components, random_state):
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W = W0.copy()
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H = H0.copy()
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clf = clf_type(**clf_params)
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st = time()
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W = clf.fit_transform(X, W=W, H=H)
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end = time()
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H = clf.components_
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this_loss = _beta_divergence(X, W, H, 2.0, True)
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duration = end - st
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return this_loss, duration
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def run_bench(X, clfs, plot_name, n_components, tol, alpha, l1_ratio):
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start = time()
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results = []
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for name, clf_type, iter_range, clf_params in clfs:
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print("Training %s:" % name)
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for rs, init in enumerate(('nndsvd', 'nndsvdar', 'random')):
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print(" %s %s: " % (init, " " * (8 - len(init))), end="")
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W, H = _initialize_nmf(X, n_components, init, 1e-6, rs)
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for max_iter in iter_range:
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clf_params['alpha'] = alpha
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clf_params['l1_ratio'] = l1_ratio
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clf_params['max_iter'] = max_iter
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clf_params['tol'] = tol
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clf_params['random_state'] = rs
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clf_params['init'] = 'custom'
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clf_params['n_components'] = n_components
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this_loss, duration = bench_one(name, X, W, H, X.shape,
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clf_type, clf_params,
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init, n_components, rs)
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init_name = "init='%s'" % init
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results.append((name, this_loss, duration, init_name))
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# print("loss: %.6f, time: %.3f sec" % (this_loss, duration))
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print(".", end="")
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sys.stdout.flush()
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print(" ")
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# Use a panda dataframe to organize the results
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results_df = pandas.DataFrame(results,
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columns="method loss time init".split())
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print("Total time = %0.3f sec\n" % (time() - start))
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# plot the results
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plot_results(results_df, plot_name)
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return results_df
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def load_20news():
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print("Loading 20 newsgroups dataset")
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print("-----------------------------")
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from sklearn.datasets import fetch_20newsgroups
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dataset = fetch_20newsgroups(shuffle=True, random_state=1,
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remove=('headers', 'footers', 'quotes'))
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vectorizer = TfidfVectorizer(max_df=0.95, min_df=2, stop_words='english')
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tfidf = vectorizer.fit_transform(dataset.data)
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return tfidf
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def load_faces():
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print("Loading Olivetti face dataset")
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print("-----------------------------")
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from sklearn.datasets import fetch_olivetti_faces
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faces = fetch_olivetti_faces(shuffle=True)
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return faces.data
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def build_clfs(cd_iters, pg_iters, mu_iters):
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clfs = [("Coordinate Descent", NMF, cd_iters, {'solver': 'cd'}),
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("Projected Gradient", _PGNMF, pg_iters, {'solver': 'pg'}),
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("Multiplicative Update", NMF, mu_iters, {'solver': 'mu'}),
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]
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return clfs
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if __name__ == '__main__':
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alpha = 0.
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l1_ratio = 0.5
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n_components = 10
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tol = 1e-15
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# first benchmark on 20 newsgroup dataset: sparse, shape(11314, 39116)
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plot_name = "20 Newsgroups sparse dataset"
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cd_iters = np.arange(1, 30)
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pg_iters = np.arange(1, 6)
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mu_iters = np.arange(1, 30)
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clfs = build_clfs(cd_iters, pg_iters, mu_iters)
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X_20news = load_20news()
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run_bench(X_20news, clfs, plot_name, n_components, tol, alpha, l1_ratio)
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# second benchmark on Olivetti faces dataset: dense, shape(400, 4096)
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plot_name = "Olivetti Faces dense dataset"
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cd_iters = np.arange(1, 30)
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pg_iters = np.arange(1, 12)
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mu_iters = np.arange(1, 30)
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clfs = build_clfs(cd_iters, pg_iters, mu_iters)
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X_faces = load_faces()
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run_bench(X_faces, clfs, plot_name, n_components, tol, alpha, l1_ratio,)
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plt.show()
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