score_pairs refactor (#333)

* Remove 3.9 from compatibility

* First draft of refactoring BaseMetricLearner and Mahalanobis Learner

* Avoid warning related to score_pairs deprecation in tests of pair_calibraiton

* Minor fix

* Replaced score_pairs with pair_distance in tests

* Replace score_pairs with pair_distance inb docs.

* Fix weird commit

* Update classifiers to use pair_similarity

* Updated rst docs

* Fix identation

* Update docs of score_pairs, get_metric

* Add deprecation Test. Fix identation

* Fixed changes requested 1

* Fixed changes requested 2

* Add equivalence test, p_dist == p_score

* Fix tests and identation.

* Fixed changes requested 3

* Fix identation

* Last requested changes

* Last small detail

doc/introduction.rst

@@ -123,26 +123,3 @@ to the following resources:
   Survey <http://dx.doi.org/10.1561/2200000019>`_ (2012)
 - **Book:** `Metric Learning
   <http://dx.doi.org/10.2200/S00626ED1V01Y201501AIM030>`_ (2015)
-
-.. Methods [TO MOVE TO SUPERVISED/WEAK SECTIONS]
-.. =============================================
-
-.. Currently, each metric learning algorithm supports the following methods:
-
-.. -  ``fit(...)``, which learns the model.
-.. -  ``get_mahalanobis_matrix()``, which returns a Mahalanobis matrix
-.. -  ``get_metric()``, which returns a function that takes as input two 1D
-      arrays and outputs the learned metric score on these two points
-..    :math:`M = L^{\top}L` such that distance between vectors ``x`` and
-..    ``y`` can be computed as :math:`\sqrt{\left(x-y\right)M\left(x-y\right)}`.
-.. -  ``components_from_metric(metric)``, which returns a transformation matrix
-..    :math:`L \in \mathbb{R}^{D \times d}`, which can be used to convert a
-..    data matrix :math:`X \in \mathbb{R}^{n \times d}` to the
-..    :math:`D`-dimensional learned metric space :math:`X L^{\top}`,
-..    in which standard Euclidean distances may be used.
-.. -  ``transform(X)``, which applies the aforementioned transformation.
-.. - ``score_pairs(pairs)`` which returns the distance between pairs of
-..   points. ``pairs`` should be a 3D array-like of pairs of shape ``(n_pairs,
-..   2, n_features)``, or it can be a 2D array-like of pairs indicators of
-..   shape ``(n_pairs, 2)`` (see section :ref:`preprocessor_section` for more
-..   details).

doc/supervised.rst

@@ -69,10 +69,10 @@ Also, as explained before, our metric learners has learn a distance between
 points. You can use this distance in two main ways:
 
 - You can either return the distance between pairs of points using the
-  `score_pairs` function:
+  `pair_distance` function:
 
->>> nca.score_pairs([[[3.5, 3.6], [5.6, 2.4]], [[1.2, 4.2], [2.1, 6.4]]])
-array([0.49627072, 3.65287282])
+>>> nca.pair_distance([[[3.5, 3.6], [5.6, 2.4]], [[1.2, 4.2], [2.1, 6.4]], [[3.3, 7.8], [10.9, 0.1]]])
+array([0.49627072, 3.65287282, 6.06079877])
 
 - Or you can return a function that will return the distance (in the new
   space) between two 1D arrays (the coordinates of the points in the original
@@ -82,6 +82,18 @@ array([0.49627072, 3.65287282])
 >>> metric_fun([3.5, 3.6], [5.6, 2.4])
 0.4962707194621285
 
+- Alternatively, you can use `pair_score` to return the **score** between
+  pairs of points (the larger the score, the more similar the pair).
+  For Mahalanobis learners, it is equal to the opposite of the distance.
+
+>>> score = nca.pair_score([[[3.5, 3.6], [5.6, 2.4]], [[1.2, 4.2], [2.1, 6.4]], [[3.3, 7.8], [10.9, 0.1]]])
+>>> score
+array([-0.49627072, -3.65287282, -6.06079877])
+
+This is useful because `pair_score` matches the **score** semantic of 
+scikit-learn's `Classification metrics
+<https://scikit-learn.org/stable/modules/model_evaluation.html#classification-metrics>`_.
+
 .. note::
 
     If the metric learner that you use learns a :ref:`Mahalanobis distance
@@ -93,7 +105,6 @@ array([0.49627072, 3.65287282])
     array([[0.43680409, 0.89169412],
            [0.89169412, 1.9542479 ]])
 
-.. TODO: remove the "like it is the case etc..." if it's not the case anymore
 
 Scikit-learn compatibility
 --------------------------
@@ -105,6 +116,7 @@ All supervised algorithms are scikit-learn estimators
 scikit-learn model selection routines 
 (`sklearn.model_selection.cross_val_score`,
 `sklearn.model_selection.GridSearchCV`, etc).
+You can also use some of the scoring functions from `sklearn.metrics`.
 
 Algorithms
 ==========

doc/weakly_supervised.rst

@@ -160,9 +160,9 @@ Also, as explained before, our metric learner has learned a distance between
 points. You can use this distance in two main ways:
 
 - You can either return the distance between pairs of points using the
-  `score_pairs` function:
+  `pair_distance` function:
 
->>> mmc.score_pairs([[[3.5, 3.6, 5.2], [5.6, 2.4, 6.7]],
+>>> mmc.pair_distance([[[3.5, 3.6, 5.2], [5.6, 2.4, 6.7]],
 ...                  [[1.2, 4.2, 7.7], [2.1, 6.4, 0.9]]])
 array([7.27607365, 0.88853014])
 
@@ -175,6 +175,18 @@ array([7.27607365, 0.88853014])
 >>> metric_fun([3.5, 3.6, 5.2], [5.6, 2.4, 6.7])
 7.276073646278203
 
+- Alternatively, you can use `pair_score` to return the **score** between
+  pairs of points (the larger the score, the more similar the pair).
+  For Mahalanobis learners, it is equal to the opposite of the distance.
+
+>>> score = mmc.pair_score([[[3.5, 3.6], [5.6, 2.4]], [[1.2, 4.2], [2.1, 6.4]], [[3.3, 7.8], [10.9, 0.1]]])
+>>> score
+array([-0.49627072, -3.65287282, -6.06079877])
+
+  This is useful because `pair_score` matches the **score** semantic of 
+  scikit-learn's `Classification metrics
+  <https://scikit-learn.org/stable/modules/model_evaluation.html#classification-metrics>`_.
+
 .. note::
 
     If the metric learner that you use learns a :ref:`Mahalanobis distance
@@ -187,8 +199,6 @@ array([[ 0.58603894, -5.69883982, -1.66614919],
        [-5.69883982, 55.41743549, 16.20219519],
        [-1.66614919, 16.20219519,  4.73697721]])
 
-.. TODO: remove the "like it is the case etc..." if it's not the case anymore
-
 .. _sklearn_compat_ws:
 
 Prediction and scoring
@@ -344,8 +354,8 @@ returns the `sklearn.metrics.roc_auc_score` (which is threshold-independent).
 
 .. note::
    See :ref:`fit_ws` for more details on metric learners functions that are
-   not specific to learning on pairs, like `transform`, `score_pairs`,
-   `get_metric` and `get_mahalanobis_matrix`.
+   not specific to learning on pairs, like `transform`, `pair_distance`,
+   `pair_score`, `get_metric` and `get_mahalanobis_matrix`.
 
 Algorithms
 ----------
@@ -691,8 +701,8 @@ of triplets that have the right predicted ordering.
 
 .. note::
    See :ref:`fit_ws` for more details on metric learners functions that are
-   not specific to learning on pairs, like `transform`, `score_pairs`,
-   `get_metric` and `get_mahalanobis_matrix`.
+   not specific to learning on pairs, like `transform`, `pair_distance`,
+   `pair_score`, `get_metric` and `get_mahalanobis_matrix`.
 
 
 
@@ -859,8 +869,8 @@ of quadruplets have the right predicted ordering.
 
 .. note::
    See :ref:`fit_ws` for more details on metric learners functions that are
-   not specific to learning on pairs, like `transform`, `score_pairs`,
-   `get_metric` and `get_mahalanobis_matrix`.
+   not specific to learning on pairs, like `transform`, `pair_distance`,
+   `pair_score`, `get_metric` and `get_mahalanobis_matrix`.