[MRG] FIX put back nca's tests (#143)

* FIX put back nca's tests

* Remove deprecation test for learning rate because there is no more learning rate

* FIX: update tests with new terminology ('transformer_')

Author: wdevazelhes

test/metric_learn_test.py

@@ -6,7 +6,7 @@
 from six.moves import xrange
 from sklearn.metrics import pairwise_distances
 from sklearn.datasets import load_iris, make_classification, make_regression
-from numpy.testing import assert_array_almost_equal
+from numpy.testing import assert_array_almost_equal, assert_array_equal
 from sklearn.utils.testing import assert_warns_message
 from sklearn.exceptions import ConvergenceWarning
 from sklearn.utils.validation import check_X_y
@@ -138,6 +138,99 @@ def test_iris(self):
     csep = class_separation(nca.transform(self.iris_points), self.iris_labels)
     self.assertLess(csep, 0.20)
 
+  def test_finite_differences(self):
+    """Test gradient of loss function
+
+    Assert that the gradient is almost equal to its finite differences
+    approximation.
+    """
+    # Initialize the transformation `M`, as well as `X` and `y` and `NCA`
+    X, y = make_classification()
+    M = np.random.randn(np.random.randint(1, X.shape[1] + 1), X.shape[1])
+    mask = y[:, np.newaxis] == y[np.newaxis, :]
+    nca = NCA()
+    nca.n_iter_ = 0
+
+    def fun(M):
+      return nca._loss_grad_lbfgs(M, X, mask)[0]
+
+    def grad(M):
+      return nca._loss_grad_lbfgs(M, X, mask)[1].ravel()
+
+    # compute relative error
+    rel_diff = check_grad(fun, grad, M.ravel()) / np.linalg.norm(grad(M))
+    np.testing.assert_almost_equal(rel_diff, 0., decimal=6)
+
+  def test_simple_example(self):
+    """Test on a simple example.
+
+    Puts four points in the input space where the opposite labels points are
+    next to each other. After transform the same labels points should be next
+    to each other.
+
+    """
+    X = np.array([[0, 0], [0, 1], [2, 0], [2, 1]])
+    y = np.array([1, 0, 1, 0])
+    nca = NCA(num_dims=2,)
+    nca.fit(X, y)
+    Xansformed = nca.transform(X)
+    np.testing.assert_equal(pairwise_distances(Xansformed).argsort()[:, 1],
+                            np.array([2, 3, 0, 1]))
+
+  def test_singleton_class(self):
+      X = self.iris_points
+      y = self.iris_labels
+
+      # one singleton class: test fitting works
+      singleton_class = 1
+      ind_singleton, = np.where(y == singleton_class)
+      y[ind_singleton] = 2
+      y[ind_singleton[0]] = singleton_class
+
+      nca = NCA(max_iter=30)
+      nca.fit(X, y)
+
+      # One non-singleton class: test fitting works
+      ind_1, = np.where(y == 1)
+      ind_2, = np.where(y == 2)
+      y[ind_1] = 0
+      y[ind_1[0]] = 1
+      y[ind_2] = 0
+      y[ind_2[0]] = 2
+
+      nca = NCA(max_iter=30)
+      nca.fit(X, y)
+
+      # Only singleton classes: test fitting does nothing (the gradient
+      # must be null in this case, so the final matrix must stay like
+      # the initialization)
+      ind_0, = np.where(y == 0)
+      ind_1, = np.where(y == 1)
+      ind_2, = np.where(y == 2)
+      X = X[[ind_0[0], ind_1[0], ind_2[0]]]
+      y = y[[ind_0[0], ind_1[0], ind_2[0]]]
+
+      EPS = np.finfo(float).eps
+      A = np.zeros((X.shape[1], X.shape[1]))
+      np.fill_diagonal(A,
+                       1. / (np.maximum(X.max(axis=0) - X.min(axis=0), EPS)))
+      nca = NCA(max_iter=30, num_dims=X.shape[1])
+      nca.fit(X, y)
+      assert_array_equal(nca.transformer_, A)
+
+  def test_one_class(self):
+      # if there is only one class the gradient is null, so the final matrix
+      #  must stay like the initialization
+      X = self.iris_points[self.iris_labels == 0]
+      y = self.iris_labels[self.iris_labels == 0]
+      EPS = np.finfo(float).eps
+      A = np.zeros((X.shape[1], X.shape[1]))
+      np.fill_diagonal(A,
+                       1. / (np.maximum(X.max(axis=0) - X.min(axis=0), EPS)))
+      nca = NCA(max_iter=30, num_dims=X.shape[1])
+      nca.fit(X, y)
+      assert_array_equal(nca.transformer_, A)
+
 
 class TestLFDA(MetricTestCase):
   def test_iris(self):