nngraph: standardize instead of center and rescale

Rescaling was useful before the adaptive setting (to the mean of the
distances) of the kernel width. It is now useless. Centering can be
combined with normalizing to unit variance to standardize the data.

pygsp/graphs/nngraphs/bunny.py

@@ -34,7 +34,5 @@ def __init__(self, **kwargs):
             'distance': 8,
         }
 
-        super(Bunny, self).__init__(data['bunny'],
-                                    center=False, rescale=False,
-                                    kind='radius', radius=0.02,
+        super(Bunny, self).__init__(data['bunny'], kind='radius', radius=0.02,
                                     plotting=plotting, **kwargs)

pygsp/graphs/nngraphs/cube.py

@@ -89,9 +89,7 @@ def __init__(self,
             'distance': 9,
         }
 
-        super(Cube, self).__init__(pts, k=10,
-                                   center=False, rescale=False,
-                                   plotting=plotting, **kwargs)
+        super(Cube, self).__init__(pts, k=10, plotting=plotting, **kwargs)
 
     def _get_extra_repr(self):
         attrs = {'radius': '{:.2f}'.format(self.radius),

pygsp/graphs/nngraphs/nngraph.py

@@ -209,18 +209,6 @@ def _radius_flann(features, radius, metric, order):
 }
 
 
-def center_features(features):
-    return features - np.mean(features, axis=0)
-
-
-def rescale_features(features):
-    n_vertices, dimensionality = features.shape
-    bounding_radius = 0.5 * np.linalg.norm(np.amax(features, axis=0) -
-                                           np.amin(features, axis=0), 2)
-    scale = np.power(n_vertices, 1 / min(dimensionality, 3)) / 10
-    return features * scale / bounding_radius
-
-
 class NNGraph(Graph):
     r"""Nearest-neighbor graph.
 
@@ -244,10 +232,9 @@ class NNGraph(Graph):
     features : ndarray
         An `N`-by-`d` matrix, where `N` is the number of nodes in the graph and
         `d` is the number of features.
-    center : bool, optional
-        Whether to center the features to have zero mean.
-    rescale : bool, optional
-        Whether to scale the features so that they lie in an l2-ball.
+    standardize : bool, optional
+        Whether to rescale the features so that each feature has a mean of 0
+        and standard deviation of 1 (unit variance).
     metric : {'euclidean', 'manhattan', 'minkowski', 'max_dist'}, optional
         Metric used to compute pairwise distances.
     order : float, optional
@@ -290,7 +277,7 @@ class NNGraph(Graph):
 
     """
 
-    def __init__(self, features, center=True, rescale=True,
+    def __init__(self, features, standardize=False,
                  metric='euclidean', order=3,
                  kind='knn', k=10, radius=0.01,
                  kernel_width=None,
@@ -318,10 +305,10 @@ def __init__(self, features, center=True, rescale=True,
         if kind == 'radius' and radius is not None and radius <= 0:
             raise ValueError('The radius must be greater than 0.')
 
-        if center:
-            features = center_features(features)
-        if rescale:
-            features = rescale_features(features)
+        if standardize:
+            # Don't alter the original data (users would be surprised).
+            features = features - np.mean(features, axis=0)
+            features /= np.std(features, axis=0)
 
         nn_function = _nn_functions[kind][backend]
         if kind == 'knn':
@@ -373,8 +360,7 @@ def __init__(self, features, center=True, rescale=True,
         W = utils.symmetrize(W, method='average')
 
         # features is stored in coords, potentially standardized
-        self.center = center
-        self.rescale = rescale
+        self.standardize = standardize
         self.metric = metric
         self.order = order
         self.kind = kind
@@ -387,8 +373,7 @@ def __init__(self, features, center=True, rescale=True,
 
     def _get_extra_repr(self):
         return {
-            'center': self.center,
-            'rescale': self.rescale,
+            'standardize': self.standardize,
             'metric': self.metric,
             'order': self.order,
             'kind': self.kind,

pygsp/graphs/nngraphs/sensor.py

@@ -75,9 +75,7 @@ def __init__(self, N=64, k=6, distributed=False, seed=None, **kwargs):
 
             coords = rs.uniform(0, 1, (N, 2))
 
-        super(Sensor, self).__init__(coords, k=k,
-                                     rescale=False, center=False,
-                                     plotting=plotting, **kwargs)
+        super(Sensor, self).__init__(coords, k=k, plotting=plotting, **kwargs)
 
     def _get_extra_repr(self):
         return {'k': self.k,

pygsp/graphs/nngraphs/sphere.py

@@ -64,9 +64,7 @@ def __init__(self,
             'vertex_size': 80,
         }
 
-        super(Sphere, self).__init__(pts, k=10,
-                                     center=False, rescale=False,
-                                     plotting=plotting, **kwargs)
+        super(Sphere, self).__init__(pts, k=10, plotting=plotting, **kwargs)
 
     def _get_extra_repr(self):
         attrs = {'radius': '{:.2f}'.format(self.radius),

pygsp/graphs/nngraphs/twomoons.py

@@ -97,7 +97,6 @@ def __init__(self, moontype='standard', dim=2, kernel_width=0.05,
         }
 
         super(TwoMoons, self).__init__(coords, kernel_width=kernel_width, k=5,
-                                       center=False, rescale=False,
                                        plotting=plotting, **kwargs)
 
     def _get_extra_repr(self):

pygsp/tests/test_graphs.py

@@ -368,15 +368,10 @@ def test_nngraph(self, n_vertices=30):
                         self.assertRaises(ValueError, graphs.NNGraph, features,
                                           kind=kind, backend=backend)
                     else:
-                        graphs.NNGraph(features, metric=metric, kind=kind,
-                                       backend=backend,
-                                       center=False)
-                        graphs.NNGraph(features, metric=metric,
-                                       kind=kind, backend=backend,
-                                       rescale=False)
-                        graphs.NNGraph(features, metric=metric,
-                                       kind=kind, backend=backend,
-                                       center=False, rescale=False)
+                        for standardize in [True, False]:
+                            graphs.NNGraph(features, standardize=standardize,
+                                           metric=metric, kind=kind,
+                                           backend=backend)
 
         # Invalid parameters.
         self.assertRaises(ValueError, graphs.NNGraph, features,