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Last active Jun 12, 2019
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NMF by coordinate descent
NMF by coordinate descent, designed for sparse data (without missing values)
# Author: Mathieu Blondel <>
# License: BSD 3 clause
import numpy as np
import scipy.sparse as sp
import numba
from sklearn.base import BaseEstimator
from sklearn.utils import check_random_state
from sklearn.utils.extmath import safe_sparse_dot
@numba.jit("f8(f8[:,:], f8[:,:], f8[:,:], i4, f8, f8, f8)")
def _compute_update(H, PWW, PWV, penalty, alpha, regn, regd):
violation = 0
n_components = H.shape[0]
for i in xrange(H.shape[1]):
for k in xrange(n_components):
if penalty == 2:
regn = H[k, i] * alpha
# gradient
# g = GH[k, i] where GH =, H) - PWV
g = - PWV[k, i] + regn
for j in xrange(H.shape[0]):
g += PWW[k, j] * H[j, i]
# projected gradient
pg = min(0, g) if H[k, i] == 0 else g
# Hessian
h = PWW[k, k] + regd
# Update
H[k, i] = max(H[k, i] - g / h, 0)
violation += abs(pg)
return violation
class CDNMF(BaseEstimator):
NMF by coordinate descent, designed for sparse data (without missing values)
def __init__(self, n_components=30, alpha=0.01, penalty="l2",
max_iter=50, tol=0.05,
init="random", random_state=None, verbose=0):
self.n_components = n_components
self.alpha = alpha
self.penalty = penalty
self.max_iter = max_iter
self.tol = tol
self.init = init
self.random_state = random_state
self.verbose = verbose
def _init(self, X, rs, transpose=False):
n_samples, n_features = X.shape
if self.init == "random":
W = rs.randn(self.n_components, n_features)
np.abs(W, W)
elif self.init == "sample":
ind = np.arange(n_samples)
W = X[ind[:self.n_components]]
if sp.issparse(W):
W = W.toarray()
comp = np.asfortranarray(W)
# H is initialized empty since it will be optimized first.
H = np.zeros((n_samples, self.n_components))
coef = np.ascontiguousarray(H)
if transpose:
comp = comp.T
coef = coef.T
return comp, coef
def _update(self, X, W, H, regn, regd, penalty):
PWW =, W)
PWV = safe_sparse_dot(W.T, X.T)
return _compute_update(H, PWW, PWV, penalty,
self.alpha, regn, regd)
def _fit_transform(self, X, W, H, update_W=True):
penalties = {"l1": 1, "l2": 2}
penalty = penalties[self.penalty]
if penalty == 1:
regn = self.alpha
regd = 0
regn = 0
regd = self.alpha
for t in xrange(self.max_iter):
# Update H
v = self._update(X, W, H, regn, regd, penalty)
# Update W
if update_W:
v += self._update(X.T, H.T, W.T, regn, regd, penalty)
if t == 0:
violation_init = v
if self.verbose:
print "violation:", v / violation_init
if v / violation_init <= self.tol:
if self.verbose:
print "Converged at iteration", t + 1
return W, H
def fit_transform(self, X):
n_samples, n_features = X.shape
rs = check_random_state(self.random_state)
W, H = self._init(X, rs, transpose=True)
W, H = self._fit_transform(X, W, H)
self.components_ = W.T
return H.T
def fit(self, X):
return self
def transform(self, X):
n_samples = X.shape[0]
H = np.zeros((self.n_components, n_samples))
W = self.components_.T
W, H = self._fit_transform(X, W, H, update_W=False)
return H.T
if __name__ == '__main__':
from sklearn.datasets import fetch_20newsgroups_vectorized
bunch = fetch_20newsgroups_vectorized(subset="all")
X =
y =
nmf = CDNMF(init="sample", verbose=1, random_state=0)

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@iandanforth iandanforth commented Aug 17, 2014

This could benefit from a readability cleanup, particularly for variable names

  1. Write out all acronyms at least once
  2. Expand single letter variables into names.
  3. Could use additional comments, and definitely doc strings.

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Owner Author

@mblondel mblondel commented Aug 17, 2014

Expand single letter variables into names.

This one is a matter of taste. I don't like doing maths / numerical computations on very long variable names. Point taken for 1 and 3 ;-)

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