def plot_canonical_roll(X, GT):
# manifold space
fig = pyplot.figure(figsize=(8,5))
scatterplot(GT, c=GT[:,0], edgecolor='k', s=20, marker='o', fig=fig)
ax = pyplot.gca()
pyplot.setp(ax.get_xticklabels(), visible=False)
pyplot.setp(ax.get_yticklabels(), visible=False)
ax.set_xlabel('$\\theta$', labelpad=15, size=20)
ax.set_ylabel('$r$', labelpad=20, rotation=0, size=20)
ax.set_xlim((-0.02, 1.02))
ax.set_ylim((-0.02, 1.02))
savefig('swiss_roll_flat.png')
# input space
pyplot.figure()
scatterplot(X, c=GT[:,0], edgecolor='k', s=20, marker='o')
ax = pyplot.gca()
pyplot.setp(ax.get_xticklabels(), visible=False)
pyplot.setp(ax.get_yticklabels(), visible=False)
pyplot.setp(ax.get_zticklabels(), visible=False)
ax.set_xlabel('$x$', labelpad=15, size=20)
ax.set_ylabel('$z$', labelpad=20, rotation=0, size=20)
ax.set_zlabel('$y$', labelpad=20, rotation=0, size=20)
ax.view_init(elev=6, azim=265)
ax.autoscale_view(True, True, True)
savefig('swiss_roll.png')
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_canonical_roll(X, GT):
# manifold space
fig = pyplot.figure(figsize=(8, 5))
scatterplot(GT, c=GT[:, 0], edgecolor='k', s=20, marker='o', fig=fig)
ax = pyplot.gca()
pyplot.setp(ax.get_xticklabels(), visible=False)
pyplot.setp(ax.get_yticklabels(), visible=False)
ax.set_xlabel('$\\theta$', labelpad=15, size=20)
ax.set_ylabel('$r$', labelpad=20, rotation=0, size=20)
ax.set_xlim((-0.02, 1.02))
ax.set_ylim((-0.02, 1.02))
savefig('swiss_roll_flat.png')
# input space
pyplot.figure()
scatterplot(X, c=GT[:, 0], edgecolor='k', s=20, marker='o')
ax = pyplot.gca()
pyplot.setp(ax.get_xticklabels(), visible=False)
pyplot.setp(ax.get_yticklabels(), visible=False)
pyplot.setp(ax.get_zticklabels(), visible=False)
ax.set_xlabel('$x$', labelpad=15, size=20)
ax.set_ylabel('$z$', labelpad=20, rotation=0, size=20)
ax.set_zlabel('$y$', labelpad=20, rotation=0, size=20)
ax.view_init(elev=6, azim=265)
ax.autoscale_view(True, True, True)
savefig('swiss_roll.png')
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')