def compute_Ws(X, num_ccs):
with Timer('Calculating pairwise distances...'):
D = pairwise_distances(X, metric='sqeuclidean')
np.save('mnist_D.npy', D)
# k-nn
with Timer('Calculating knn graph...'):
for k in xrange(1,10):
Wknn = neighbor_graph(D, precomputed=True, k=k, symmetrize=True)
n = connected_components(Wknn, directed=False, return_labels=False)
if n <= num_ccs:
break
else:
assert False, 'k too low'
np.save('mnist_Wknn.npy', Wknn)
print 'knn (k=%d)' % k
# b-matching
with Timer('Calculating b-matching graph...'):
# using 8 decimal places kills the disk
Wbma = hacky_b_matching(D, k, fmt='%.1f')
np.save('mnist_Wbma.npy', Wbma)
# msg
with Timer('Calculating MSG graph...'):
Wmsg = manifold_spanning_graph(X, 2, num_ccs=num_ccs)
np.save('mnist_Wmsg.npy', Wmsg)
return D, Wknn, Wbma, Wmsg
def average_error_rate(num_trials=100):
knn_err = np.empty((num_trials,2))
eps_err = np.empty((num_trials,2))
bma_err = np.empty((num_trials,2))
msg_err = np.empty((num_trials,2))
for i in xrange(num_trials):
X, GT = make_test_data(verify=True)
D = pairwise_distances(X, metric='sqeuclidean')
W = neighbor_graph(D, precomputed=True, k=5, symmetrize=True)
knn_err[i] = error_ratio(W, GT, return_tuple=True)
W = neighbor_graph(D, precomputed=True, epsilon=1.0)
eps_err[i] = error_ratio(W, GT, return_tuple=True)
W = hacky_b_matching(D, 5)
bma_err[i] = error_ratio(W, GT, return_tuple=True)
W = manifold_spanning_graph(X, 2)
msg_err[i] = error_ratio(W, GT, return_tuple=True)
errors = np.hstack((knn_err[:,:1],eps_err[:,:1],bma_err[:,:1],msg_err[:,:1]))
edges = np.hstack((knn_err[:,1:],eps_err[:,1:],bma_err[:,1:],msg_err[:,1:]))
labels = ('$k$-nearest','$\\epsilon$-close','$b$-matching','MSG')
pyplot.figure(figsize=(5,6))
ax = pyplot.gca()
ax.boxplot(errors, widths=0.75)
ax.set_xticklabels(labels, fontsize=12)
ymin,ymax = pyplot.ylim()
pyplot.ylim((ymin-1, ymax))
savefig('average_error.png')
pyplot.figure(figsize=(5,6))
ax = pyplot.gca()
ax.boxplot(edges, widths=0.75)
ax.set_xticklabels(labels, fontsize=12)
savefig('average_edges.png')
def average_error_rate(num_trials=100):
knn_err = np.empty((num_trials, 2))
eps_err = np.empty((num_trials, 2))
bma_err = np.empty((num_trials, 2))
msg_err = np.empty((num_trials, 2))
for i in xrange(num_trials):
X, GT = make_test_data(verify=True)
D = pairwise_distances(X, metric='sqeuclidean')
W = neighbor_graph(D, precomputed=True, k=5, symmetrize=True)
knn_err[i] = error_ratio(W, GT, return_tuple=True)
W = neighbor_graph(D, precomputed=True, epsilon=1.0)
eps_err[i] = error_ratio(W, GT, return_tuple=True)
W = hacky_b_matching(D, 5)
bma_err[i] = error_ratio(W, GT, return_tuple=True)
W = manifold_spanning_graph(X, 2)
msg_err[i] = error_ratio(W, GT, return_tuple=True)
errors = np.hstack(
(knn_err[:, :1], eps_err[:, :1], bma_err[:, :1], msg_err[:, :1]))
edges = np.hstack(
(knn_err[:, 1:], eps_err[:, 1:], bma_err[:, 1:], msg_err[:, 1:]))
labels = ('$k$-nearest', '$\\epsilon$-close', '$b$-matching', 'MSG')
pyplot.figure(figsize=(5, 6))
ax = pyplot.gca()
ax.boxplot(errors, widths=0.75)
ax.set_xticklabels(labels, fontsize=12)
ymin, ymax = pyplot.ylim()
pyplot.ylim((ymin - 1, ymax))
savefig('average_error.png')
pyplot.figure(figsize=(5, 6))
ax = pyplot.gca()
ax.boxplot(edges, widths=0.75)
ax.set_xticklabels(labels, fontsize=12)
savefig('average_edges.png')
def compute_Ws(X, num_ccs):
with Timer('Calculating pairwise distances...'):
D = pairwise_distances(X, metric='sqeuclidean')
np.save('mnist_D.npy', D)
# k-nn
with Timer('Calculating knn graph...'):
for k in xrange(1, 10):
Wknn = neighbor_graph(D, precomputed=True, k=k, symmetrize=True)
n = connected_components(Wknn, directed=False, return_labels=False)
if n <= num_ccs:
break
else:
assert False, 'k too low'
np.save('mnist_Wknn.npy', Wknn)
print 'knn (k=%d)' % k
# b-matching
with Timer('Calculating b-matching graph...'):
# using 8 decimal places kills the disk
Wbma = hacky_b_matching(D, k, fmt='%.1f')
np.save('mnist_Wbma.npy', Wbma)
# msg
with Timer('Calculating MSG graph...'):
Wmsg = manifold_spanning_graph(X, 2, num_ccs=num_ccs)
np.save('mnist_Wmsg.npy', Wmsg)
return D, Wknn, Wbma, Wmsg
def swiss_roll_experiment():
embed_dim = 2
X, GT = make_test_data(verify=True)
plot_canonical_roll(X, GT)
evaluate_sensitivity(X, GT)
# kNN
D = pairwise_distances(X, metric='sqeuclidean')
for k in xrange(3, 10):
Wknn = neighbor_graph(D, precomputed=True, k=k, symmetrize=True)
n = connected_components(Wknn, directed=False, return_labels=False)
if n == 1:
break
else:
assert False, 'k too low'
print 'k:', k, 'error:', error_ratio(Wknn, GT)
plot_roll(Wknn, X, GT[:, 0], embed_dim, 'swiss_knn_result.png')
# eball
for eps in np.linspace(0.4, 1.2, 50):
Weps = neighbor_graph(D,
precomputed=True,
epsilon=eps,
symmetrize=False)
n = connected_components(Weps, directed=False, return_labels=False)
if n == 1:
break
else:
assert False, 'eps too low'
print 'eps:', eps, 'error:', error_ratio(Weps, GT)
plot_roll(Weps, X, GT[:, 0], embed_dim, 'swiss_eps_result.png')
# b-matching
for b in xrange(3, 10):
Wbma = hacky_b_matching(D, b)
n = connected_components(Wbma, directed=False, return_labels=False)
if n == 1:
break
else:
assert False, 'b too low'
print 'b:', b, 'error:', error_ratio(Wbma, GT)
plot_roll(Wbma, X, GT[:, 0], embed_dim, 'swiss_bma_result.png')
# MSG
Wmsg = manifold_spanning_graph(X, embed_dim)
print 'MSG error:', error_ratio(Wmsg, GT)
plot_roll(Wmsg, X, GT[:, 0], embed_dim, 'swiss_msg_result.png')
def swiss_roll_experiment():
embed_dim = 2
X, GT = make_test_data(verify=True)
plot_canonical_roll(X, GT)
evaluate_sensitivity(X, GT)
# kNN
D = pairwise_distances(X, metric='sqeuclidean')
for k in xrange(3,10):
Wknn = neighbor_graph(D, precomputed=True, k=k, symmetrize=True)
n = connected_components(Wknn, directed=False, return_labels=False)
if n == 1:
break
else:
assert False, 'k too low'
print 'k:', k, 'error:', error_ratio(Wknn, GT)
plot_roll(Wknn, X, GT[:,0], embed_dim, 'swiss_knn_result.png')
# eball
for eps in np.linspace(0.4, 1.2, 50):
Weps = neighbor_graph(D, precomputed=True, epsilon=eps, symmetrize=False)
n = connected_components(Weps, directed=False, return_labels=False)
if n == 1:
break
else:
assert False, 'eps too low'
print 'eps:', eps, 'error:', error_ratio(Weps, GT)
plot_roll(Weps, X, GT[:,0], embed_dim, 'swiss_eps_result.png')
# b-matching
for b in xrange(3,10):
Wbma = hacky_b_matching(D, b)
n = connected_components(Wbma, directed=False, return_labels=False)
if n == 1:
break
else:
assert False, 'b too low'
print 'b:', b, 'error:', error_ratio(Wbma, GT)
plot_roll(Wbma, X, GT[:,0], embed_dim, 'swiss_bma_result.png')
# MSG
Wmsg = manifold_spanning_graph(X, embed_dim)
print 'MSG error:', error_ratio(Wmsg, GT)
plot_roll(Wmsg, X, GT[:,0], embed_dim, 'swiss_msg_result.png')