def test_neighborhood_preserving_embedding(self): np.random.seed(1234) pts = np.random.random((5, 3)) expected = [[-0.433578], [0.761129], [-0.482382]] G = neighbor_graph(pts, k=3) actual = G.neighborhood_preserving_embedding(pts, num_vecs=1) assert_array_almost_equal(expected, actual)
def test_locally_linear_embedding(self): np.random.seed(1234) pts = np.random.random((5, 3)) expected = locally_linear_embedding(pts, 3, 1)[0] G = neighbor_graph(pts, k=3).barycenter_edge_weights(pts, copy=False) actual = G.locally_linear_embedding(num_dims=1) assert_signless_array_almost_equal(expected, actual)
def main():
np.random.seed(1234)
X, theta = swiss_roll(8, 500, return_theta=True)
print('Figure 1 of 3: bare coordinates in 3d')
ax = Axes3D(plt.figure())
ax.scatter(*X.T, c=theta)
print('Figure 2 of 3: 5-NN graph in original coordinates')
g = neighbor_graph(X, k=5).symmetrize('max')
g.plot(X, directed=False, weighted=False, fig='new', edge_style='k-',
vertex_style=dict(c=theta))
print('Writing swiss_roll.html for force-directed layout demo')
g.to_html('swiss_roll.html', directed=False, weighted=False,
vertex_colors=theta)
print('Figure 3 of 3: 2d Isomap embedding of 5-NN graph')
emb = g.isomap(num_dims=2)
_, ax = plt.subplots(figsize=(10, 5))
g.plot(emb, directed=False, weighted=False, ax=ax, edge_style='k-',
vertex_style=dict(c=theta))
ax.xaxis.set_ticks([])
ax.yaxis.set_ticks([])
plt.show()
def main():
np.random.seed(1234)
X, theta = swiss_roll(8, 300, return_theta=True, radius=0.5)
GT = np.column_stack((theta, X[:, 1]))
g = neighbor_graph(X, k=6)
g = g.from_adj_matrix(g.matrix('dense'))
ct = 12
_, axes = plt.subplots(nrows=2,
ncols=2,
figsize=(8, 8),
sharex=True,
sharey=True)
_plot_diff(axes[0, 0], GT, g, g.minimum_spanning_subtree(), title='MST')
_plot_diff(axes[0, 1],
GT,
g,
g.circle_tear(cycle_len_thresh=ct),
title='Circle Tear (%d)' % ct)
_plot_diff(axes[1, 0],
GT,
g,
g.cycle_cut(cycle_len_thresh=ct),
title='Cycle Cut (%d)' % ct)
_plot_diff(axes[1, 1], GT, g, g.isograph(), title='Isograph')
plt.show()
def test_shortest_path_subtree(self):
n = X.shape[0]
G = neighbor_graph(X, k=4)
e_data = [0.163, 0.199, 0.079, 0.188, 0.173, 0.122, 0.136, 0.136, 0.197]
e_row = [3, 0, 14, 0, 0, 3, 0, 3, 3]
e_col = [1, 3, 5, 7, 10, 13, 14, 18, 19]
expected = np.zeros((n,n))
expected[e_row, e_col] = e_data
spt = G.shortest_path_subtree(0, directed=True)
assert_array_almost_equal(spt.matrix('dense'), expected, decimal=3)
# test undirected case
G.symmetrize(method='max', copy=False)
e_data = [0.185,0.379,0.199,0.32,0.205,0.255,0.188,0.508,0.192,0.173,0.279,
0.258,0.122,0.136,0.316,0.326,0.278,0.136,0.197,0.185,0.379,0.199,
0.32,0.205,0.255,0.188,0.508,0.192,0.173,0.279,0.258,0.122,0.136,
0.316,0.326,0.278,0.136,0.197]
e_row = [10,8,0,6,0,1,0,5,6,0,0,6,3,0,17,8,1,3,3,1,2,3,4,5,6,7,8,9,10,11,12,
13,14,15,16,17,18,19]
e_col = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,10,8,0,6,0,1,0,5,6,
0,0,6,3,0,17,8,1,3,3]
expected[:] = 0
expected[e_row, e_col] = e_data
spt = G.shortest_path_subtree(0, directed=False)
assert_array_almost_equal(spt.matrix('dense'), expected, decimal=3)
def _make_blob_graphs(self, k=11): pts = np.random.random(size=(20, 2)) pts[10:] += 2 labels = np.zeros(20) labels[10:] = 1 G_sparse = neighbor_graph(pts, k=k).symmetrize() G_dense = Graph.from_adj_matrix(G_sparse.matrix(dense=True)) return (G_sparse, G_dense), labels
def _make_blob_graphs(self, k=11):
pts = np.random.random(size=(20, 2))
pts[10:] += 2
labels = np.zeros(20)
labels[10:] = 1
G_sparse = neighbor_graph(pts, k=k).symmetrize()
G_dense = Graph.from_adj_matrix(G_sparse.matrix('dense'))
return (G_sparse, G_dense), labels
def main():
x, labels = prepare_data(SCORECARD_FILE)
print('%d schools w/ %d features each' % x.shape)
# plot k-means clusters over the first two PCs
pcs = PCA(n_components=2).fit_transform(x)
y_kmeans = KMeans(n_clusters=4).fit_predict(x)
clouds_kmeans = word_clouds(y_kmeans, labels)
_, ax = plt.subplots(figsize=(14, 6))
scatter_labeled(pcs, labels, ax=ax, colors=y_kmeans, cmap='Dark2',
color_labels=clouds_kmeans, edgecolor='none')
ax.set_title('Top 2 PCs, k-means labels')
ax.xaxis.set_ticks([])
ax.yaxis.set_ticks([])
# build a kNN graph
print('Building a 10-NN graph, based on cosine distance...')
dist = pairwise_distances(x, metric='cosine')
knn = neighbor_graph(dist, precomputed=True, k=10).symmetrize(method='max')
knn = knn.from_adj_matrix(knn.matrix(csr=True)) # XXX: hack to sparsify
print(knn.connected_components(return_labels=False), 'connected components')
# compute some statistics
apsp = knn.shortest_path(directed=False, unweighted=True)
eccen = apsp.max(axis=0)
d = eccen.argmax()
print('diameter = %d: "%s" <-> "%s"' % (eccen.max(), labels[d],
labels[apsp[d].argmax()]))
print('radius = %d: "%s"' % (eccen.min(), labels[eccen.argmin()]))
# find a spectral clustering
print('Computing spectral clustering...')
y_spectral = knn.cluster_spectral(9)
y_spectral = np.argsort(np.argsort(-np.bincount(y_spectral)))[y_spectral]
clouds_spectral = word_clouds(y_spectral, labels)
# plot the new clustering over a 2d Isomap embedding
print('Embedding to 2d with Isomap...')
emb = knn.isomap(num_dims=2, directed=False)
_, ax = plt.subplots(figsize=(14, 6))
knn.plot(emb, ax=ax, directed=False, weighted=False, edge_style='k-',
vertex_style=dict(marker=',', c='k', s=1, zorder=0))
scatter_labeled(emb, labels, ax=ax, colors=y_spectral, cmap='Set1',
color_labels=clouds_spectral, zorder=2, edgecolor='none')
ax.set_title('Isomap embedding, spectral clustering labels')
ax.xaxis.set_ticks([])
ax.yaxis.set_ticks([])
# plot the reordered distance matrix
order = np.argsort(y_spectral)
_, ax = plt.subplots(figsize=(8, 8))
imshow_labeled(dist[order][:,order], labels[order], y_spectral, ax=ax)
ax.set_title('Pairwise cosine distance matrix')
plt.show()
def test_cycle_cut(self):
G = neighbor_graph(X, k=4).symmetrize(method='max', copy=False)
# hack: the atomic cycle finder chooses a random vertex to start from
np.random.seed(1234)
res = G.cycle_cut(cycle_len_thresh=5, directed=False)
diff = G.matrix('dense') - res.matrix('dense')
ii, jj = np.nonzero(diff)
assert_array_equal(ii, [1,1,6,17])
assert_array_equal(jj, [6,17,1,1])
def main():
print("Select coordinates for graph vertices:")
plt.plot([])
coords = np.array(plt.ginput(n=-1, timeout=-1))
k = int(input("Number of nearest neighbors: "))
g = neighbor_graph(coords, k=k)
print("Resulting graph:")
g.plot(coords, vertex_style='ro')()
def main():
print("Select coordinates for graph vertices:")
plt.plot([])
coords = np.array(plt.ginput(n=-1, timeout=-1))
k = int(input("Number of nearest neighbors: "))
g = neighbor_graph(coords, k=k)
print("Resulting graph:")
g.plot(coords, vertex_style='ro')()
def test_cycle_cut(self):
G = neighbor_graph(X, k=4).symmetrize(method='max', copy=False)
# hack: the atomic cycle finder chooses a random vertex to start from
np.random.seed(1234)
res = G.cycle_cut(cycle_len_thresh=5, directed=False)
diff = G.matrix('dense') - res.matrix('dense')
ii, jj = np.nonzero(diff)
assert_array_equal(ii, [1, 1, 6, 17])
assert_array_equal(jj, [6, 17, 1, 1])
def test_connected_subgraphs(self):
G = Graph.from_edge_pairs(PAIRS)
subgraphs = list(G.connected_subgraphs(directed=False, ordered=False))
self.assertEqual(len(subgraphs), 2)
assert_array_equal(subgraphs[0].pairs(), PAIRS[:6])
assert_array_equal(subgraphs[1].pairs(), [[0,1],[1,0]])
G = neighbor_graph(X, k=2)
subgraphs = list(G.connected_subgraphs(directed=True, ordered=True))
self.assertEqual(len(subgraphs), 3)
self.assertEqual([g.num_vertices() for g in subgraphs], [9,6,5])
def test_connected_subgraphs(self):
G = Graph.from_edge_pairs(PAIRS)
subgraphs = list(G.connected_subgraphs(directed=False, ordered=False))
self.assertEqual(len(subgraphs), 2)
assert_array_equal(subgraphs[0].pairs(), PAIRS[:6])
assert_array_equal(subgraphs[1].pairs(), [[0, 1], [1, 0]])
G = neighbor_graph(X, k=2)
subgraphs = list(G.connected_subgraphs(directed=True, ordered=True))
self.assertEqual(len(subgraphs), 3)
self.assertEqual([g.num_vertices() for g in subgraphs], [9, 6, 5])
def test_neighborhood_subgraph(self):
G = neighbor_graph(X, k=4)
# simple 1-neighbor subgraph
g, mask = G.neighborhood_subgraph(0, radius=1, weighted=False,
return_mask=True)
assert_array_equal(mask.nonzero()[0], [0,3,7,10,14])
self.assertEqual(g.num_vertices(), 5)
self.assertEqual(g.num_edges(), 13)
# distance-based subgraph
g, mask = G.neighborhood_subgraph(12, radius=0.5, return_mask=True)
assert_array_equal(mask.nonzero()[0], [2,4,6,9,12,15,17])
self.assertEqual(g.num_vertices(), 7)
self.assertEqual(g.num_edges(), 23)
def test_circle_tear(self):
G = neighbor_graph(X, k=4).symmetrize(method='max', copy=False)
# test MST start
res = G.circle_tear(spanning_tree='mst', cycle_len_thresh=5)
diff = G.matrix('dense') - res.matrix('dense')
ii, jj = np.nonzero(diff)
assert_array_equal(ii, [5,8,8,11])
assert_array_equal(jj, [8,5,11,8])
# test SPT start with a fixed starting vertex
res = G.circle_tear(spanning_tree='spt', cycle_len_thresh=5, spt_idx=8)
diff = G.matrix('dense') - res.matrix('dense')
ii, jj = np.nonzero(diff)
assert_array_equal(ii, [1,1,6,17])
assert_array_equal(jj, [6,17,1,1])
def test_minimum_spanning_subtree(self):
n = X.shape[0]
G = neighbor_graph(X, k=4)
e_data = [0.279,0.136,0.255,0.041,0.124,0.186,0.131,0.122,0.136,0.185,0.226,
0.061,0.255,0.022,0.061,0.054,0.053,0.326,0.185,0.191,0.054,0.177,
0.279,0.226,0.224,0.041,0.122,0.177,0.136,0.053,0.186,0.224,0.131,
0.326,0.022,0.191,0.136,0.124]
e_row = [0,0,1,1,1,2,2,3,3,4,4,5,6,6,7,7,7,8,9,9,10,10,11,12,12,13,13,13,14,
14,15,15,16,16,17,17,18,19]
e_col = [11,14,6,13,19,15,16,13,18,9,12,7,1,17,5,10,14,16,4,17,7,13,0,4,15,
1,3,10,0,7,2,12,2,8,6,9,3,1]
expected = np.zeros((n,n))
expected[e_row, e_col] = e_data
mst = G.minimum_spanning_subtree()
assert_array_almost_equal(mst.matrix('dense'), expected, decimal=3)
def test_circle_tear(self):
G = neighbor_graph(X, k=4).symmetrize(method='max', copy=False)
# test MST start
res = G.circle_tear(spanning_tree='mst', cycle_len_thresh=5)
diff = G.matrix('dense') - res.matrix('dense')
ii, jj = np.nonzero(diff)
assert_array_equal(ii, [5, 8, 8, 11])
assert_array_equal(jj, [8, 5, 11, 8])
# test SPT start with a fixed starting vertex
res = G.circle_tear(spanning_tree='spt', cycle_len_thresh=5, spt_idx=8)
diff = G.matrix('dense') - res.matrix('dense')
ii, jj = np.nonzero(diff)
assert_array_equal(ii, [1, 1, 6, 17])
assert_array_equal(jj, [6, 17, 1, 1])
def test_isograph(self):
# make roughly U-shaped data
theta = np.linspace(0, 2 * np.pi, 10)[1:]
data = np.column_stack((np.sin(theta) * 2, np.cos(theta)))
G = neighbor_graph(data, k=2)
g = G.isograph()
self.assertIsNot(g, G)
diff = G.matrix('dense') - g.matrix('dense')
ii, jj = np.nonzero(diff)
assert_array_equal(ii, [3, 4])
assert_array_equal(jj, [4, 3])
# test case with large epsilon
g = G.isograph(min_weight=999)
self.assertIsNot(g, G)
assert_array_equal(g.matrix('dense'), G.matrix('dense'))
def test_neighborhood_subgraph(self):
G = neighbor_graph(X, k=4)
# simple 1-neighbor subgraph
g, mask = G.neighborhood_subgraph(0,
radius=1,
weighted=False,
return_mask=True)
assert_array_equal(mask.nonzero()[0], [0, 3, 7, 10, 14])
self.assertEqual(g.num_vertices(), 5)
self.assertEqual(g.num_edges(), 13)
# distance-based subgraph
g, mask = G.neighborhood_subgraph(12, radius=0.5, return_mask=True)
assert_array_equal(mask.nonzero()[0], [2, 4, 6, 9, 12, 15, 17])
self.assertEqual(g.num_vertices(), 7)
self.assertEqual(g.num_edges(), 23)
def main():
np.random.seed(1234)
X, theta = swiss_roll(8, 300, return_theta=True, radius=0.5)
GT = np.column_stack((theta, X[:,1]))
g = neighbor_graph(X, k=6)
g = g.from_adj_matrix(g.matrix('dense'))
ct = 12
_, axes = plt.subplots(nrows=2, ncols=2, figsize=(8, 8),
sharex=True, sharey=True)
_plot_diff(axes[0,0], GT, g, g.minimum_spanning_subtree(), title='MST')
_plot_diff(axes[0,1], GT, g, g.circle_tear(cycle_len_thresh=ct),
title='Circle Tear (%d)' % ct)
_plot_diff(axes[1,0], GT, g, g.cycle_cut(cycle_len_thresh=ct),
title='Cycle Cut (%d)' % ct)
_plot_diff(axes[1,1], GT, g, g.isograph(), title='Isograph')
plt.show()
def test_isograph(self):
# make roughly U-shaped data
theta = np.linspace(0, 2*np.pi, 10)[1:]
data = np.column_stack((np.sin(theta)*2, np.cos(theta)))
G = neighbor_graph(data, k=2)
g = G.isograph()
self.assertIsNot(g, G)
diff = G.matrix('dense') - g.matrix('dense')
ii, jj = np.nonzero(diff)
assert_array_equal(ii, [3, 4])
assert_array_equal(jj, [4, 3])
# test case with large epsilon
g = G.isograph(min_weight=999)
self.assertIsNot(g, G)
assert_array_equal(g.matrix('dense'), G.matrix('dense'))
def test_regression(self):
t = np.linspace(0, 1, 31)
pts = np.column_stack((np.sin(t), np.cos(t)))
G = neighbor_graph(pts, k=3).symmetrize()
y_mask = slice(None, None, 2)
# test the interpolated case
x = G.regression(t[y_mask], y_mask)
assert_array_equal(t, np.linspace(0, 1, 31)) # ensure t hasn't changed
self.assertLess(np.linalg.norm(t - x), 0.15)
# test the boolean mask case
y_mask = np.zeros_like(t, dtype=bool)
y_mask[::2] = True
x = G.regression(t[y_mask], y_mask)
self.assertLess(np.linalg.norm(t - x), 0.15)
# test the penalized case
x = G.regression(t[y_mask], y_mask, smoothness_penalty=1e-4)
self.assertLess(np.linalg.norm(t - x), 0.15)
# test no kernel + dense laplacian case
dG = Graph.from_adj_matrix(G.matrix('dense'))
x = dG.regression(t[y_mask], y_mask, kernel='none')
self.assertLess(np.linalg.norm(t - x), 0.25)
x = dG.regression(t[y_mask],
y_mask,
smoothness_penalty=1e-4,
kernel='none')
self.assertLess(np.linalg.norm(t - x), 0.25)
# test the multidimensional regression case
tt = np.column_stack((t, t[::-1]))
x = G.regression(tt[y_mask], y_mask)
self.assertLess(np.linalg.norm(tt - x), 0.2)
# check for bad inputs
with self.assertRaisesRegexp(ValueError, r'^Invalid shape of y array'):
G.regression([], y_mask)
def test_minimum_spanning_subtree(self):
n = X.shape[0]
G = neighbor_graph(X, k=4)
e_data = [
0.279, 0.136, 0.255, 0.041, 0.124, 0.186, 0.131, 0.122, 0.136,
0.185, 0.226, 0.061, 0.255, 0.022, 0.061, 0.054, 0.053, 0.326,
0.185, 0.191, 0.054, 0.177, 0.279, 0.226, 0.224, 0.041, 0.122,
0.177, 0.136, 0.053, 0.186, 0.224, 0.131, 0.326, 0.022, 0.191,
0.136, 0.124
]
e_row = [
0, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 7, 8, 9, 9, 10, 10,
11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 19
]
e_col = [
11, 14, 6, 13, 19, 15, 16, 13, 18, 9, 12, 7, 1, 17, 5, 10, 14, 16,
4, 17, 7, 13, 0, 4, 15, 1, 3, 10, 0, 7, 2, 12, 2, 8, 6, 9, 3, 1
]
expected = np.zeros((n, n))
expected[e_row, e_col] = e_data
mst = G.minimum_spanning_subtree()
assert_array_almost_equal(mst.matrix('dense'), expected, decimal=3)
def test_shortest_path_subtree(self):
n = X.shape[0]
G = neighbor_graph(X, k=4)
e_data = [
0.163, 0.199, 0.079, 0.188, 0.173, 0.122, 0.136, 0.136, 0.197
]
e_row = [3, 0, 14, 0, 0, 3, 0, 3, 3]
e_col = [1, 3, 5, 7, 10, 13, 14, 18, 19]
expected = np.zeros((n, n))
expected[e_row, e_col] = e_data
spt = G.shortest_path_subtree(0, directed=True)
assert_array_almost_equal(spt.matrix('dense'), expected, decimal=3)
# test undirected case
G.symmetrize(method='max', copy=False)
e_data = [
0.185, 0.379, 0.199, 0.32, 0.205, 0.255, 0.188, 0.508, 0.192,
0.173, 0.279, 0.258, 0.122, 0.136, 0.316, 0.326, 0.278, 0.136,
0.197, 0.185, 0.379, 0.199, 0.32, 0.205, 0.255, 0.188, 0.508,
0.192, 0.173, 0.279, 0.258, 0.122, 0.136, 0.316, 0.326, 0.278,
0.136, 0.197
]
e_row = [
10, 8, 0, 6, 0, 1, 0, 5, 6, 0, 0, 6, 3, 0, 17, 8, 1, 3, 3, 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
]
e_col = [
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
10, 8, 0, 6, 0, 1, 0, 5, 6, 0, 0, 6, 3, 0, 17, 8, 1, 3, 3
]
expected[:] = 0
expected[e_row, e_col] = e_data
spt = G.shortest_path_subtree(0, directed=False)
assert_array_almost_equal(spt.matrix('dense'), expected, decimal=3)
def test_regression(self):
t = np.linspace(0, 1, 31)
pts = np.column_stack((np.sin(t), np.cos(t)))
G = neighbor_graph(pts, k=3).symmetrize()
y_mask = slice(None, None, 2)
# test the interpolated case
x = G.regression(t[y_mask], y_mask)
assert_array_equal(t, np.linspace(0, 1, 31)) # ensure t hasn't changed
self.assertLess(np.linalg.norm(t - x), 0.15)
# test the boolean mask case
y_mask = np.zeros_like(t, dtype=bool)
y_mask[::2] = True
x = G.regression(t[y_mask], y_mask)
self.assertLess(np.linalg.norm(t - x), 0.15)
# test the penalized case
x = G.regression(t[y_mask], y_mask, smoothness_penalty=1e-4)
self.assertLess(np.linalg.norm(t - x), 0.15)
# test no kernel + dense laplacian case
dG = Graph.from_adj_matrix(G.matrix(dense=True))
x = dG.regression(t[y_mask], y_mask, kernel='none')
self.assertLess(np.linalg.norm(t - x), 0.25)
x = dG.regression(t[y_mask], y_mask, smoothness_penalty=1e-4, kernel='none')
self.assertLess(np.linalg.norm(t - x), 0.25)
# test the multidimensional regression case
tt = np.column_stack((t, t[::-1]))
x = G.regression(tt[y_mask], y_mask)
self.assertLess(np.linalg.norm(tt - x), 0.2)
# check for bad inputs
with self.assertRaisesRegexp(ValueError, r'^Invalid shape of y array'):
G.regression([], y_mask)
def ngraph(*a, **k):
return neighbor_graph(*a,**k).matrix(dense=True)
def ngraph(*a, **k):
return neighbor_graph(*a, **k).matrix('dense')
def ngraph(*a, **k):
return neighbor_graph(*a,**k).matrix('dense')
def time_neighbor_graph(self, epsilon, k, weighting):
gc.neighbor_graph(self.X, k=k, epsilon=epsilon, weighting=weighting)
def time_neighbor_graph_precomputed(self, epsilon, k, weighting):
gc.neighbor_graph(self.D,
k=k,
epsilon=epsilon,
weighting=weighting,
precomputed=True)