def example_disk_dimensions(N=100):
print('\n***mds.example_disk_dimensions()***\n')
dims = range(1, 11)
stress = []
for dim in dims:
Y = misc.disk(N, dim)
D = distances.compute(Y)
mds = MDS(D, dim, verbose=1, label=f'dimension : {dim}')
mds.initialize_Y()
mds.optimize(algorithm='agd', max_iters=300)
stress.append(mds.ncost)
fig = plt.figure()
plt.semilogy(dims, stress)
plt.xlabel('dimension')
plt.ylabel('stress')
plt.title('Normalized MDS stress for various dimensions')
plt.show()
def example_disk_noisy(N=100, dim=2):
print('\n***mds.example_disk_noisy()***\n')
noise_levels = [0.001, 0.005, 0.01, 0.03, 0.07, 0.1, 0.15, 0.2, 0.7, 1.0]
stress = []
Y = misc.disk(N, dim)
D = distances.compute(Y)
for noise in noise_levels:
D_noisy = distances.add_noise(D, noise)
mds = MDS(D_noisy, dim, verbose=1, title=f'noise : {noise:0.2f}')
mds.initialize()
mds.optimize(algorithm='agd', max_iters=300, verbose=1)
stress.append(mds.ncost)
fig = plt.figure()
plt.loglog(noise_levels, stress, '.-')
plt.xlabel('noise level')
plt.ylabel('stress')
plt.title('Normalized MDS stress for various noise levels')
plt.show()
def embeddability_noise(ax=None):
print('\n**mds.embeddability_noise()')
N = 50
ncost = []
noise_list = [0] + 10**np.arange(-2, 1, 0.5)
X = misc.disk(N, 4)
DD = distances.compute(X)
for noise in noise_list:
D = DD * (1 + np.random.randn(N, N) * noise)
mds = MDS(D, dim=4, verbose=1)
mds.initialize()
mds.optimize()
ncost.append(mds.ncost)
if ax is None:
fig, ax = plt.subplots(1)
plot = True
else:
plot = False
ax.semilogx(noise_list, ncost)
if plot is True:
plt.show()
def embeddability_dims(ax=None):
print('\n**mds.embeddability_dims()')
N = 50
ncost = []
dims = list(range(2, 50, 5))
#XX = misc.disk(N,20)
XX = misc.box(N, 20)
for dim in dims:
X = XX[:, 0:dim]
D = multigraph.coord2dict(X, weights='relative')
mds = MDS(D, dim=2, verbose=1)
mds.initialize()
mds.optimize()
ncost.append(mds.ncost)
if ax is None:
fig, ax = plt.subplots(1)
plot = True
else:
plot = False
ax.plot(dims, ncost)
if plot is True:
plt.show()
def disk_compare(N=100, dim=2): ###
print('\n***mds.disk_compare()***')
X = misc.disk(N, 2)
labels = misc.labels(X)
plt.figure()
plt.scatter(X[:, 0], X[:, 1], c=labels)
plt.title('original data')
plt.draw()
plt.pause(0.1)
D = distances.compute(X)
mds = MDS(D, dim=dim, verbose=1, title='disk experiments', labels=labels)
mds.initialize()
mds.figureX(title='initial embedding')
title = 'full gradient & agd'
mds.optimize(algorithm='agd', verbose=2, label=title)
mds.figureX(title=title)
mds.figureH(title=title)
mds.forget()
title = 'approx gradient & gd'
mds.approximate(algorithm='gd', verbose=2, label=title)
mds.figureX(title=title)
mds.figureH(title=title)
mds.forget()
title = 'combine'
mds.approximate(algorithm='gd', verbose=2, label=title)
mds.optimize(verbose=2, label=title, max_iters=10)
mds.figureX(title=title)
mds.figureH(title=title)
plt.show()