DOC Update docs for StandardScaler.scale_ to include 0 variance (scikit-learn#19124)

KunjParikh · thomasjpfan · jeremiedbb · commit be8169ad4f7d · 2021-01-19T11:28:01.000+01:00
Co-authored-by: Thomas J. Fan &lt;thomasjpfan@gmail.com&gt;
diff --git a/sklearn/preprocessing/_data.py b/sklearn/preprocessing/_data.py
@@ -617,8 +617,11 @@ class StandardScaler(TransformerMixin, BaseEstimator):
     Attributes
     ----------
     scale_ : ndarray of shape (n_features,) or None
-        Per feature relative scaling of the data. This is calculated using
-        `np.sqrt(var_)`. Equal to ``None`` when ``with_std=False``.
+        Per feature relative scaling of the data to achieve zero mean and unit
+        variance. Generally this is calculated using `np.sqrt(var_)`. If a
+        variance is zero, we can't achieve unit variance, and the data is left
+        as-is, giving a scaling factor of 1. `scale_` is equal to `None`
+        when `with_std=False`.
 
         .. versionadded:: 0.17
            *scale_*
