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 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 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 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 lapeig_linear(X=None, W=None, L=None, num_vecs=None, k=None, eball=None):
if L is None:
if W is None:
W = neighbor_graph(X, k=k, epsilon=eball)
L = laplacian(W)
u, s, _ = np.linalg.svd(np.dot(X.T, X))
Fplus = np.linalg.pinv(np.dot(u, np.diag(np.sqrt(s))))
T = reduce(np.dot, (Fplus, X.T, L, X, Fplus.T))
L = 0.5 * (T + T.T)
return lapeig(L=L, num_vecs=num_vecs)
def lapeig_linear(X=None, W=None, L=None, num_vecs=None, k=None, eball=None):
if L is None:
if W is None:
W = neighbor_graph(X, k=k, epsilon=eball)
L = laplacian(W)
u, s, _ = np.linalg.svd(np.dot(X.T, X))
Fplus = np.linalg.pinv(np.dot(u, np.diag(np.sqrt(s))))
T = reduce(np.dot, (Fplus, X.T, L, X, Fplus.T))
L = 0.5 * (T + T.T)
return lapeig(L=L, num_vecs=num_vecs)
def evaluate_sensitivity(X, GT):
eps_values = np.linspace(0.2, 1.2, 50)
knn_values = np.arange(1, 7)
eps_method = lambda eps: neighbor_graph(X, epsilon=eps)
knn_method = lambda k: neighbor_graph(X, k=k, symmetrize=False)
errors, edges, conn = eval_method(knn_values, knn_method, GT)
one_cc = knn_values[len(conn) -
np.searchsorted(conn[::-1], 1, side='right')]
fig, axes = pyplot.subplots(nrows=2, ncols=2)
knn_err_ax, eps_err_ax = axes[0]
knn_edge_ax, eps_edge_ax = axes[1]
knn_err_ax.set_ylabel('Edge error %', fontsize=14)
knn_err_ax.plot(knn_values, errors * 100, 'k+-')
knn_err_ax.axvline(one_cc, color='k', linestyle='--')
knn_err_ax.set_ylim((-0.05, knn_err_ax.get_ylim()[1]))
knn_edge_ax.set_xlabel('$k$', fontsize=16)
knn_edge_ax.set_ylabel('Total edges', fontsize=14)
knn_edge_ax.plot(knn_values, edges, 'k+-')
knn_edge_ax.axvline(one_cc, color='k', linestyle='--')
errors, edges, conn = eval_method(eps_values, eps_method, GT)
one_cc = eps_values[len(conn) -
np.searchsorted(conn[::-1], 1, side='right')]
eps_err_ax.plot(eps_values, errors * 100, 'k+-')
eps_err_ax.axvline(one_cc, color='k', linestyle='--')
eps_err_ax.set_ylim((-0.1, eps_err_ax.get_ylim()[1]))
eps_edge_ax.set_xlabel('$\\epsilon$', fontsize=16)
eps_edge_ax.plot(eps_values, edges, 'k+-')
eps_edge_ax.axvline(one_cc, color='k', linestyle='--')
for ax in (knn_err_ax, knn_edge_ax):
start, end = ax.get_xlim()
ax.xaxis.set_ticks(np.arange(start, end + 1))
fig.tight_layout()
savefig('sensitivity.png')
def make_test_data(verify=True):
while True:
X, theta = swiss_roll(18, 500, radius=4.8, return_theta=True,
theta_noise=0, radius_noise=0)
GT = np.hstack((theta[:,None], X[:,1:2]))
GT -= GT.min(axis=0)
GT /= GT.max(axis=0)
if not verify:
break
# ensure our test_data fits our 1-NN assumption
W = neighbor_graph(X, k=1, symmetrize=False)
if error_ratio(W, GT) < 1e-10:
break
return X, GT
def evaluate_sensitivity(X, GT):
eps_values = np.linspace(0.2, 1.2, 50)
knn_values = np.arange(1,7)
eps_method = lambda eps: neighbor_graph(X, epsilon=eps)
knn_method = lambda k: neighbor_graph(X, k=k, symmetrize=False)
errors, edges, conn = eval_method(knn_values, knn_method, GT)
one_cc = knn_values[len(conn) - np.searchsorted(conn[::-1], 1, side='right')]
fig, axes = pyplot.subplots(nrows=2, ncols=2)
knn_err_ax, eps_err_ax = axes[0]
knn_edge_ax, eps_edge_ax = axes[1]
knn_err_ax.set_ylabel('Edge error %', fontsize=14)
knn_err_ax.plot(knn_values, errors*100, 'k+-')
knn_err_ax.axvline(one_cc, color='k', linestyle='--')
knn_err_ax.set_ylim((-0.05, knn_err_ax.get_ylim()[1]))
knn_edge_ax.set_xlabel('$k$', fontsize=16)
knn_edge_ax.set_ylabel('Total edges', fontsize=14)
knn_edge_ax.plot(knn_values, edges, 'k+-')
knn_edge_ax.axvline(one_cc, color='k', linestyle='--')
errors, edges, conn = eval_method(eps_values, eps_method, GT)
one_cc = eps_values[len(conn) - np.searchsorted(conn[::-1], 1, side='right')]
eps_err_ax.plot(eps_values, errors*100, 'k+-')
eps_err_ax.axvline(one_cc, color='k', linestyle='--')
eps_err_ax.set_ylim((-0.1, eps_err_ax.get_ylim()[1]))
eps_edge_ax.set_xlabel('$\\epsilon$', fontsize=16)
eps_edge_ax.plot(eps_values, edges, 'k+-')
eps_edge_ax.axvline(one_cc, color='k', linestyle='--')
for ax in (knn_err_ax, knn_edge_ax):
start,end = ax.get_xlim()
ax.xaxis.set_ticks(np.arange(start, end+1))
fig.tight_layout()
savefig('sensitivity.png')
def make_test_data(verify=True):
while True:
X, theta = swiss_roll(18,
500,
radius=4.8,
return_theta=True,
theta_noise=0,
radius_noise=0)
GT = np.hstack((theta[:, None], X[:, 1:2]))
GT -= GT.min(axis=0)
GT /= GT.max(axis=0)
if not verify:
break
# ensure our test_data fits our 1-NN assumption
W = neighbor_graph(X, k=1, symmetrize=False)
if error_ratio(W, GT) < 1e-10:
break
return X, GT
def show_skeleton_issue():
t = np.linspace(0,4,25)[:,None]
X = np.hstack((np.cos(t), np.random.uniform(-1,1,t.shape), np.sin(t)))
GT = np.hstack((t, X[:,1:2]))
W = neighbor_graph(X, k=1, symmetrize=False)
W = grow_trees(X, W, 2)
labels = join_CCs_simple(X, W)
# switch up the CC order for better contrast between groups
order = np.arange(labels.max()+1)
np.random.shuffle(order)
labels = order[labels]
show_neighbor_graph(GT, W, vertex_style=None, edge_style='k-')
ax = pyplot.gca()
for l,marker in zip(np.unique(labels), "osD^v><"):
scatterplot(GT[labels==l], marker, ax=ax, edgecolor='k', c='white')
ax.tick_params(which='both', bottom='off', top='off', left='off',
right='off', labelbottom='off', labelleft='off')
savefig('skeleton.png')
def show_skeleton_issue():
t = np.linspace(0, 4, 25)[:, None]
X = np.hstack((np.cos(t), np.random.uniform(-1, 1, t.shape), np.sin(t)))
GT = np.hstack((t, X[:, 1:2]))
W = neighbor_graph(X, k=1, symmetrize=False)
W = grow_trees(X, W, 2)
labels = join_CCs_simple(X, W)
# switch up the CC order for better contrast between groups
order = np.arange(labels.max() + 1)
np.random.shuffle(order)
labels = order[labels]
show_neighbor_graph(GT, W, vertex_style=None, edge_style='k-')
ax = pyplot.gca()
for l, marker in zip(np.unique(labels), "osD^v><"):
scatterplot(GT[labels == l], marker, ax=ax, edgecolor='k', c='white')
ax.tick_params(which='both',
bottom='off',
top='off',
left='off',
right='off',
labelbottom='off',
labelleft='off')
savefig('skeleton.png')
def manifold_spanning_graph(X, embed_dim, num_ccs=1, verbose=False):
W = neighbor_graph(X, k=1, symmetrize=True)
W = grow_trees(X, W, embed_dim, verbose=verbose)
CC_labels, angle_thresh = join_CCs(X, W, embed_dim, num_ccs=num_ccs,
verbose=verbose)
if num_ccs == 1:
W = flesh_out(X, W, embed_dim, CC_labels, angle_thresh=angle_thresh,
min_shortcircuit=embed_dim+1, verbose=verbose)
else:
n, labels = connected_components(W, directed=False, return_labels=True)
for i in xrange(n):
mask = labels==i
print 'CC', i, 'has size', np.count_nonzero(mask)
# This step is often counterproductive for >1 CC.
# idx = np.ix_(mask, mask)
# W[idx] = flesh_out(X[mask], W[idx], embed_dim, CC_labels[mask],
# angle_thresh=angle_thresh,
# min_shortcircuit=embed_dim+1,
# verbose=verbose)
return W
if __name__ == '__main__':
# simple usage example / visual test case
from matplotlib import pyplot
from viz import show_neighbor_graph
from util import Timer
from correspondence import Correspondence
from synthetic_data import cylinder
n = 300
knn = 5
out_dim = 2
X = cylinder(np.linspace(0, 4, n))
W = neighbor_graph(X=X, k=knn)
corr = Correspondence(matrix=W)
with Timer('LapEig'):
le_embed = lapeig(W=W, num_vecs=out_dim)
with Timer('Linear LapEig'):
# lapeig_linear returns a projector, not an embedding
lel_embed = np.dot(X, lapeig_linear(X=X, W=W, num_vecs=out_dim, k=knn))
with Timer('Isomap'):
im_embed = isomap(X=X, num_vecs=out_dim, k=knn)
with Timer('LLE'):
lle_embed = lle(X=X, num_vecs=out_dim, k=knn)
with Timer('SFA'):
sfa_embed = np.dot(X, slow_features(X=X, num_vecs=out_dim))
show_neighbor_graph(X, corr, 'Original space')
if __name__ == "__main__":
# simple usage example / visual test case
from matplotlib import pyplot
from viz import show_neighbor_graph
from util import Timer
from correspondence import Correspondence
from synthetic_data import cylinder
n = 300
knn = 5
out_dim = 2
X = cylinder(np.linspace(0, 4, n))
W = neighbor_graph(X=X, k=knn)
corr = Correspondence(matrix=W)
with Timer("LapEig"):
le_embed = lapeig(W=W, num_vecs=out_dim)
with Timer("Linear LapEig"):
# lapeig_linear returns a projector, not an embedding
lel_embed = np.dot(X, lapeig_linear(X=X, W=W, num_vecs=out_dim, k=knn))
with Timer("Isomap"):
im_embed = isomap(X=X, num_vecs=out_dim, k=knn)
with Timer("LLE"):
lle_embed = lle(X=X, num_vecs=out_dim, k=knn)
with Timer("SFA"):
sfa_embed = np.dot(X, slow_features(X=X, num_vecs=out_dim))
show_neighbor_graph(X, corr, "Original space")
t = np.linspace(0, 5, n)
if three_d:
X = swiss_roll(t, lambda A: np.sin(A)**2)
Y = np.vstack((np.sin(t)**2, t, np.zeros(n))).T
else:
X = spiral(t)
Y = X[:, (1, 0)] # swap x and y axes
return add_noise(X, 0.05), add_noise(Y, 0.05)
if __name__ == '__main__':
n = 500
d = 3
X, Y = gen_data(n, d == 3)
corr = Correspondence(matrix=np.eye(n))
Wx = neighbor_graph(X, k=5)
Wy = neighbor_graph(Y, k=5)
lin_aligners = (
('no alignment', lambda: TrivialAlignment(X, Y)),
('affine', lambda: Affine(X, Y, corr, d)),
('procrustes', lambda: Procrustes(X, Y, corr, d)),
('cca', lambda: CCA(X, Y, corr, d)),
('cca_v2', lambda: CCAv2(X, Y, d)),
('linear manifold', lambda: ManifoldLinear(X, Y, corr, d, Wx, Wy)),
('ctw', lambda: ctw(X, Y, d)[1]),
('manifold warping',
lambda: manifold_warping_linear(X, Y, d, Wx, Wy)[1]),
)
other_aligners = (
warp_inds[i] = P[j, 1]
return A[warp_inds]
def _bound_row(self):
P = self.pairs()
n = P.shape[0]
B = np.zeros((P[-1, 0] + 1, 2), dtype=np.int)
head = 0
while head < n:
i = P[head, 0]
tail = head + 1
while tail < n and P[tail, 0] == i:
tail += 1
B[i, :] = P[(head, tail - 1), 1]
head = tail
return B
if __name__ == '__main__':
# simple sanity-check tests
from neighborhood import neighbor_graph
from viz import show_neighbor_graph, pyplot
n = 500
data = np.random.uniform(-1, 1, (n, 2))
corr_k = Correspondence(matrix=neighbor_graph(data, k=3))
corr_eps = Correspondence(matrix=neighbor_graph(data, epsilon=0.01))
pyplot.subplot(1, 2, 1)
show_neighbor_graph(data, corr_k, 'kNN graph, k = 3')
pyplot.subplot(1, 2, 2)
show_neighbor_graph(data, corr_eps,
'$\epsilon$-ball graph, $\epsilon$ = 0.1')()
rf = r['load'](file)
dayExpr = pandas2ri.ri2py_dataframe(r['dayExpr'])
nightExpr = pandas2ri.ri2py_dataframe(r['nightExpr'])
X = dayExpr.as_matrix() # datWorm.iloc[:, 0:datWorm.shape[1]].as_matrix()
Y = nightExpr.as_matrix() # datFly.iloc[:, 0:datFly.shape[1]].as_matrix()
n = 17695
d = 3
X_normalized = preprocessing.normalize(X, norm='l2').T
Y_normalized = preprocessing.normalize(Y, norm='l2')[0:13, :].T
corr = Correspondence(
matrix=np.eye(n)) # Correspondence(matrix=corr.as_matrix())
Wx = neighbor_graph(X_normalized, k=5)
Wy = neighbor_graph(Y_normalized, k=5)
lin_aligners = (
('no alignment', lambda: TrivialAlignment(X_normalized, Y_normalized, d)),
# ('affine', lambda: Affine(X,Y,corr,d)),
# ('procrustes', lambda: Procrustes(X,Y,corr,d)),
('cca', lambda: CCA(X_normalized, Y_normalized, corr, d)),
# ('cca_v2', lambda: CCAv2(X,Y,d)),
('linear manifold',
lambda: ManifoldLinear(X_normalized, Y_normalized, corr, d, Wx, Wy)),
('ctw', lambda: ctw(X_normalized, Y_normalized, d)[1]),
('manifold warping',
lambda: manifold_warping_linear(X_normalized, Y_normalized, d, Wx, Wy)[1]
),
)
warp_inds[i] = P[j,1]
return A[warp_inds]
def _bound_row(self):
P = self.pairs()
n = P.shape[0]
B = np.zeros((P[-1,0]+1,2),dtype=np.int)
head = 0
while head < n:
i = P[head,0]
tail = head+1
while tail < n and P[tail,0] == i:
tail += 1
B[i,:] = P[(head,tail-1),1]
head = tail
return B
if __name__ == '__main__':
# simple sanity-check tests
from neighborhood import neighbor_graph
from viz import show_neighbor_graph, pyplot
n = 500
data = np.random.uniform(-1,1,(n,2))
corr_k = Correspondence(matrix=neighbor_graph(data,k=3))
corr_eps = Correspondence(matrix=neighbor_graph(data,epsilon=0.01))
pyplot.subplot(1,2,1)
show_neighbor_graph(data,corr_k,'kNN graph, k = 3')
pyplot.subplot(1,2,2)
show_neighbor_graph(data, corr_eps, '$\epsilon$-ball graph, $\epsilon$ = 0.1')()
t = np.linspace(0,5,n)
if three_d:
X = swiss_roll(t,lambda A: np.sin(A)**2)
Y = np.vstack((np.sin(t)**2,t,np.zeros(n))).T
else:
X = spiral(t)
Y = X[:,(1,0)] # swap x and y axes
return add_noise(X,0.05), add_noise(Y,0.05)
if __name__ == '__main__':
n = 500
d = 2
X,Y = gen_data(n, d==3)
corr = Correspondence(matrix=np.eye(n))
Wx = neighbor_graph(X,k=5)
Wy = neighbor_graph(Y,k=5)
lin_aligners = (
('no alignment', lambda: TrivialAlignment(X,Y)),
('affine', lambda: Affine(X,Y,corr,d)),
('procrustes', lambda: Procrustes(X,Y,corr,d)),
('cca', lambda: CCA(X,Y,corr,d)),
('cca_v2', lambda: CCAv2(X,Y,d)),
('linear manifold', lambda: ManifoldLinear(X,Y,corr,d,Wx,Wy)),
('ctw', lambda: ctw(X,Y,d)[1]),
('manifold warping', lambda: manifold_warping_linear(X,Y,d,Wx,Wy)[1]),
)
other_aligners = (
('dtw', lambda: (X, dtw(X,Y).warp(X))),