def plot_roll(W, X, colors, embed_dim, image_name):
fig, (ax1, ax2) = pyplot.subplots(ncols=2)
show_neighbor_graph(X[:, (0, 2)],
W,
ax=ax1,
vertex_colors=colors,
vertex_edgecolor='k',
edge_style='k-')
# show the embedding
D = pairwise_distances(X, metric='euclidean')
D[~W.astype(bool)] = 0
embed = isomap(D, embed_dim)
scatterplot(embed, ax=ax2, c=colors, marker='o', edgecolor='k')
for ax in (ax1, ax2):
ax.tick_params(which='both',
bottom='off',
top='off',
left='off',
right='off',
labelbottom='off',
labelleft='off')
fig.tight_layout()
savefig(image_name)
def plot_roll(W, X, colors, embed_dim, image_name):
fig, (ax1,ax2) = pyplot.subplots(ncols=2)
show_neighbor_graph(X[:,(0,2)], W, ax=ax1, vertex_colors=colors,
vertex_edgecolor='k', edge_style='k-')
# show the embedding
D = pairwise_distances(X, metric='euclidean')
D[~W.astype(bool)] = 0
embed = isomap(D, embed_dim)
scatterplot(embed, ax=ax2, c=colors, marker='o', edgecolor='k')
for ax in (ax1,ax2):
ax.tick_params(which='both', bottom='off', top='off', left='off',
right='off', labelbottom='off', labelleft='off')
fig.tight_layout()
savefig(image_name)
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')
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')
fig, axes = pyplot.subplots(nrows=3, ncols=2)
fig.tight_layout() # spaces the subplots better
show_neighbor_graph(le_embed, corr, 'Laplacian Eigenmaps', ax=axes[0, 0])
show_neighbor_graph(lel_embed,
corr,
'Linear Laplacian Eigenmaps',
ax=axes[0, 1])
show_neighbor_graph(im_embed, corr, 'Isomap', ax=axes[1, 0])
show_neighbor_graph(lle_embed,
corr,
'Locally Linear Embedding',
ax=axes[1, 1])
show_neighbor_graph(sfa_embed,
corr,
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')()
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')()
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")
fig, axes = pyplot.subplots(nrows=3, ncols=2)
fig.tight_layout() # spaces the subplots better
show_neighbor_graph(le_embed, corr, "Laplacian Eigenmaps", ax=axes[0, 0])
show_neighbor_graph(lel_embed, corr, "Linear Laplacian Eigenmaps", ax=axes[0, 1])
show_neighbor_graph(im_embed, corr, "Isomap", ax=axes[1, 0])
show_neighbor_graph(lle_embed, corr, "Locally Linear Embedding", ax=axes[1, 1])
show_neighbor_graph(sfa_embed, corr, "Slow Features Embedding", ax=axes[2, 0])
pyplot.show()