nngraph: fix symmetrization

Symmetrizing with the average was setting the distance between v1 and v2
as the average between 0 and the true distance if v1 was the k-NN of v2
but v2 was not in the k-NN of v1.

Moreover, symmetrizing before taking the mean assures that every
distance is counted twice (only some would be counted twice otherwise).

doc/tutorials/optimization.rst

@@ -85,7 +85,7 @@ We start with the graph TV regularization. We will use the :class:`pyunlocbox.so
     >>> prob1 = pyunlocbox.solvers.solve([d, r, f], solver=solver,
     ...                                  x0=x0, rtol=0, maxit=1000)
     Solution found after 1000 iterations:
-        objective function f(sol) = 2.250584e+02
+        objective function f(sol) = 2.138668e+02
         stopping criterion: MAXIT
     >>>
     >>> fig, ax = G.plot(prob1['sol'])
@@ -107,7 +107,7 @@ This figure shows the label signal recovered by graph total variation regulariza
     >>> prob2 = pyunlocbox.solvers.solve([r, f], solver=solver,
     ...                                  x0=x0, rtol=0, maxit=1000)
     Solution found after 1000 iterations:
-        objective function f(sol) = 6.504290e+01
+        objective function f(sol) = 7.413918e+01
         stopping criterion: MAXIT
     >>>
     >>> fig, ax = G.plot(prob2['sol'])

pygsp/filters/filter.py

@@ -254,7 +254,7 @@ def filter(self, s, method='chebyshev', order=30):
         >>> _ = G.plot(s1, ax=axes[0])
         >>> _ = G.plot(s2, ax=axes[1])
         >>> print('{:.5f}'.format(np.linalg.norm(s1 - s2)))
-        0.26808
+        0.28049
 
         Perfect reconstruction with Itersine, a tight frame:
 
@@ -449,7 +449,7 @@ def estimate_frame_bounds(self, x=None):
         A=1.708, B=2.359
         >>> A, B = g.estimate_frame_bounds(G.e)
         >>> print('A={:.3f}, B={:.3f}'.format(A, B))
-        A=1.723, B=2.359
+        A=1.712, B=2.348
 
         The frame bounds can be seen in the plot of the filter bank as the
         minimum and maximum of their squared sum (the black curve):

pygsp/graphs/fourier.py

@@ -78,7 +78,7 @@ def coherence(self):
         >>> graph.compute_fourier_basis()
         >>> minimum = 1 / np.sqrt(graph.n_vertices)
         >>> print('{:.2f} in [{:.2f}, 1]'.format(graph.coherence, minimum))
-        0.88 in [0.12, 1]
+        0.93 in [0.12, 1]
         >>>
         >>> # Plot the most localized eigenvector.
         >>> import matplotlib.pyplot as plt

pygsp/graphs/nngraphs/nngraph.py

@@ -340,6 +340,10 @@ def __init__(self, features, standardize=False,
             start = end
         W = sparse.csr_matrix((value, (row, col)), (n_vertices, n_vertices))
 
+        # Enforce symmetry. May have been broken by k-NN. Checking symmetry
+        # with np.abs(W - W.T).sum() is as costly as the symmetrization itself.
+        W = utils.symmetrize(W, method='fill')
+
         if kernel_width is None:
             kernel_width = np.mean(W.data) if W.nnz > 0 else np.nan
             # Alternative: kernel_width = radius / 2 or radius / np.log(2).
@@ -350,10 +354,6 @@ def kernel(distance, width):
 
         W.data = kernel(W.data, kernel_width)
 
-        # Enforce symmetry. May have been broken by k-NN. Checking symmetry
-        # with np.abs(W - W.T).sum() is as costly as the symmetrization itself.
-        W = utils.symmetrize(W, method='average')
-
         # features is stored in coords, potentially standardized
         self.standardize = standardize
         self.metric = metric

pygsp/tests/test_filters.py

@@ -228,7 +228,7 @@ def test_modulation_gabor(self):
         f2 = filters.Gabor(self._G, f)
         s1 = f1.filter(self._signal)
         s2 = f2.filter(self._signal)
-        np.testing.assert_allclose(s1, -s2, atol=1e-5)
+        np.testing.assert_allclose(s1, s2, atol=1e-5)
 
     def test_halfcosine(self):
         f = filters.HalfCosine(self._G, Nf=4)