DOC Generalise norm notation in NMF docstring.
@@ -867,7 +867,7 @@ def non_negative_factorization(X, W=None, H=None, n_components=None, *,
.. math::
- 0.5 * ||X - WH||_{Fro}^2 + alpha * l1_{ratio} * ||vec(W)||_1
+ 0.5 * ||X - WH||_{loss}^2 + alpha * l1_{ratio} * ||vec(W)||_1
+ alpha * l1_{ratio} * ||vec(H)||_1
@@ -881,9 +881,9 @@ def non_negative_factorization(X, W=None, H=None, n_components=None, *,
:math:`||vec(A)||_1 = \\sum_{i,j} abs(A_{ij})` (Elementwise L1 norm)
- For multiplicative-update ('mu') solver, the Frobenius norm
- :math:`(0.5 * ||X - WH||_{Fro}^2)` can be changed into another
- beta-divergence loss, by changing the beta_loss parameter.
+ The generic norm :math:`||X - WH||_{loss}^2` may represent
+ the Frobenius norm or another supported beta-divergence loss.
+ The choice between options is controlled by 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.
@@ -1104,7 +1104,7 @@ class NMF(TransformerMixin, BaseEstimator):
.. math::
- 0.5 * ||X - WH||_{Fro}^2 + alpha * l1_{ratio} * ||vec(W)||_1
+ 0.5 * ||X - WH||_{loss}^2 + alpha * l1_{ratio} * ||vec(W)||_1
+ alpha * l1_{ratio} * ||vec(H)||_1
@@ -1118,9 +1118,9 @@ class NMF(TransformerMixin, BaseEstimator):
:math:`||vec(A)||_1 = \\sum_{i,j} abs(A_{ij})` (Elementwise L1 norm)
- For multiplicative-update ('mu') solver, the Frobenius norm
- (:math:`0.5 * ||X - WH||_{Fro}^2`) can be changed into another
- beta-divergence loss, by changing the beta_loss parameter.
+ The generic norm :math:`||X - WH||_{loss}` may represent
+ the Frobenius norm or another supported beta-divergence loss.
+ The choice between options is controlled by the `beta_loss` parameter.
The objective function is minimized with an alternating minimization of W
and H.
