DOC More details about the attributes in MinMaxScaler (#13029)

sklearn/preprocessing/data.py

@@ -210,6 +210,11 @@ class MinMaxScaler(BaseEstimator, TransformerMixin):
 
     where min, max = feature_range.
 
+    The transformation is calculated as::
+
+        X_scaled = scale * X + min - X.min(axis=0) * scale
+        where scale = (max - min) / (X.max(axis=0) - X.min(axis=0))
+
     This transformation is often used as an alternative to zero mean,
     unit variance scaling.
 
@@ -227,10 +232,12 @@ class MinMaxScaler(BaseEstimator, TransformerMixin):
     Attributes
     ----------
     min_ : ndarray, shape (n_features,)
-        Per feature adjustment for minimum.
+        Per feature adjustment for minimum. Equivalent to
+        ``min - X.min(axis=0) * self.scale_``
 
     scale_ : ndarray, shape (n_features,)
-        Per feature relative scaling of the data.
+        Per feature relative scaling of the data. Equivalent to
+        ``(max - min) / (X.max(axis=0) - X.min(axis=0))``
 
         .. versionadded:: 0.17
            *scale_* attribute.
@@ -409,12 +416,17 @@ def minmax_scale(X, feature_range=(0, 1), axis=0, copy=True):
     that it is in the given range on the training set, i.e. between
     zero and one.
 
-    The transformation is given by::
+    The transformation is given by (when ``axis=0``)::
 
         X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))
         X_scaled = X_std * (max - min) + min
 
     where min, max = feature_range.
+ 
+    The transformation is calculated as (when ``axis=0``)::
+
+       X_scaled = scale * X + min - X.min(axis=0) * scale
+       where scale = (max - min) / (X.max(axis=0) - X.min(axis=0))
 
     This transformation is often used as an alternative to zero mean,
     unit variance scaling.