def varying_view_number(N=100,runs=1):
"""\
Multiview-MDS experiment with varying number of views
"""
view_number = range(1,11)
print('*** test.varying_view_number() ***')
print(f' N : {N}')
print()
X = misc.disk(N,dim=3)
persp = perspective.Persp(dimX=3,dimY=2,family='linear',
restriction='orthogonal')
cost = []
for i in view_number:
persp.fix_Q(number=i,random='orthogonal')
Y = persp.compute_Y(X)
D = distances.compute(Y)
mv = multiview.Multiview(D,persp=persp)
mv.setup_visualization(visualization='mds')
mv.initialize_X(number=runs)
mv.optimize_X(algorithm='agd')
cost.append(mv.ncost)
print(f' {i:>2} : {mv.ncost:0.2e}')
print()
def mds_comparison():
max_iters = 100
save_frequency = 10
import misc, distances, mds
print('\n*** gd.mds_comparison() ***\n')
Y = misc.disk(30,2)
plt.figure()
plt.plot(Y[:,0],Y[:,1],'o')
plt.title('Original data')
plt.draw()
plt.pause(0.1)
D = distances.compute(Y)
vis = mds.MDS(D,dim=2,verbose=1)
vis.initialize_Y()
vis.optimize(algorithm='gd',max_iters=max_iters,save_cost=True,
learning_rate=0.01,from_scratch=True,
save_frequency=save_frequency,label='mds, lr=0.01',verbose=2)
vis.optimize(algorithm='gd',max_iters=max_iters,save_cost=True,
learning_rate=0.1,from_scratch=True,
save_frequency=save_frequency,label='mds, lr=0.05',verbose=2)
vis.optimize(algorithm='agd',max_iters=max_iters,save_cost=True,
from_scratch=True,save_frequency=save_frequency,verbose=2)
plt.show()
def agd_multiview_mds_standard(N=100,trials=3,runs=5):
"""\
Test convergence of adaptive gradient descent for multiview MDS with
standard projections, by solving a single multiview MDS problem using
multiple initial parameters.
"""
print('*** test.agd_multiview_mds_standard() ***')
print(f' N : {N}')
print()
for i in range(trials):
print(f' Trial # {i}')
print(' Normalized cost :')
X = misc.disk(N,dim=3)
persp = perspective.Persp()
persp.fix_Q(special='standard')
Y = persp.compute_Y(X)
D = distances.compute(Y)
mv = multiview.Multiview(D,persp=persp)
mv.setup_visualization(visualization='mds')
stress = []
for run in range(runs):
mv.initialize_X()
mv.optimize_X(algorithm='agd')
stress.append(mv.ncost)
print(f' {mv.ncost:0.2e}')
print()
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()
def example_approx(N=30, dim=2, batch_number=5):
print('\n***mds.example_disk_batch()***\n')
Y = misc.disk(N, dim)
labels = misc.labels(Y)
plt.figure()
plt.scatter(Y[:, 0], Y[:, 1], c=labels)
plt.title('Original data')
plt.draw()
plt.pause(0.1)
D = distances.compute(Y)
title = 'basic disk example using approximate gradient'
mds = MDS(D, dim=dim, verbose=1, title=title, labels=labels)
mds.initialize()
mds.approximate(verbose=2,
max_iters=200,
lr=0.1,
batch_number=batch_number,
algorithm='gd')
mds.figureX(title='Final embedding')
mds.figureH()
plt.show()
def compare_multiview_same(N=100,runs=1):
noise_levels = [0.0001,0.001,0.01,0.1,0.5]
stress = []
X = misc.disk(N,dim=2)
persp = perspective.Persp(dimX=2,dimY=2)
#persp.fix_Q(random='orthogonal',number=3)
persp.fix_Q(special='identity',number=3)
Y = persp.compute_Y(X)
D = distances.compute(Y)
persp1 = perspective.Persp(dimX=3,dimY=2)
persp1.fix_Q(special='standard',number=3)
persp2 = perspective.Persp(dimX=2,dimY=2)
persp2.fix_Q(special='identity',number=3)
persp3 = perspective.Persp(dimX=3,dimY=3)
persp3.fix_Q(special='identity',number=3)
cost = []; cost2 = []; cost3 = []; costm = []
for noise in noise_levels:
D_noisy = distances.add_noise(D,noise)
mv = Multiview(D_noisy,persp=persp1,verbose=1)
mv.setup_visualization(visualization='mds')
mv.initialize_X(number=1)
mv.optimize_X(algorithm='agd',max_iters=200)
cost.append(mv.ncost)
mv = Multiview(D_noisy,persp=persp2,verbose=1)
mv.setup_visualization(visualization='mds')
mv.initialize_X(number=runs)
mv.optimize_X(algorithm='agd',max_iters=200)
cost2.append(mv.ncost)
mv = Multiview(D_noisy,persp=persp3,verbose=1)
mv.setup_visualization(visualization='mds')
mv.initialize_X(number=1)
mv.optimize_X(algorithm='agd',max_iters=200)
cost3.append(mv.ncost)
mv = Multiview(D_noisy,persp=persp1,verbose=1)
mv.setup_visualization(visualization='mds')
mv.initialize_Q()
mv.initialize_X(number=1)
mv.optimize_all(algorithm='agd',max_iters=[30,20],rounds=40)
costm.append(mv.ncost)
fig = plt.figure()
plt.loglog(noise_levels,cost,linestyle='--',marker='o',
label='multi-perspective')
plt.loglog(noise_levels,cost2,linestyle='--',marker='o', label='combine 2')
plt.loglog(noise_levels,cost3,linestyle='--',marker='o', label='combine 3')
plt.loglog(noise_levels,costm,linestyle='--',marker='o', label='multi-all')
plt.legend()
plt.xlabel('noise level')
plt.ylabel('normalized stress')
plt.show()
def example_disk(N=100):
X = misc.disk(N,dim=3); labels=misc.labels(X)
persp = perspective.Persp()
persp.fix_Q(number=3,special='standard')
Y = persp.compute_Y(X)
D = distances.compute(Y)
mv = Multiview(D,persp=persp,verbose=1,labels=labels)
mv.setup_visualization(visualization='mds')
mv.initialize_X(verbose=1)
mv.optimize_X(batch_size=10,max_iters=50,verbose=1)
mv.figureX(save='hola')
mv.figureY()
mv.figureH()
plt.show()
def example_disk_Q(N=100):
X = misc.disk(N,dim=3)
persp = perspective.Persp()
Q_true = persp.generate_Q(number=3,special='standard')
Y_true = persp.compute_Y(X,Q=Q_true)
D = distances.compute(Y_true)
mv = Multiview(D,persp=persp,verbose=1)
mv.setup_visualization(visualization='mds')
mv.initialize_Q(random='orthogonal')
mv.initialize_X(X0=X)
mv.optimize_Q(verbose=2,batch_size=10)
mv.optimize_Q(verbose=2)
mv.figureH()
plt.show()
def example_disk_all(N=100):
X = misc.disk(N,dim=3); labels=misc.labels(X)
persp = perspective.Persp()
Q_true = persp.generate_Q(number=3,special='standard')
Y_true = persp.compute_Y(X,Q=Q_true)
D = distances.compute(Y_true)
mv = Multiview(D,persp=persp,verbose=1,labels=labels)
mv.setup_visualization(visualization='mds')
mv.initialize_Q()
mv.initialize_X()
mv.optimize_all(agd=True,batch_size=10)
mv.figureX(plot=True)
mv.figureY(plot=True)
mv.figureH()
plt.show()
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 noise_all(N=100):
noise_levels = [0.001,0.01,0.07,0.15,0.4]
stress = []
X = misc.disk(N,dim=3)
proj = perspective.Proj(dimX=2,dimY=2)
proj.set_params_list(special='identity',number=3)
Y = proj.project(X)
D = distances.compute(Y)
for noise in noise_levels:
D_noisy = distances.add_noise(D,noise)
mv = Multiview(D_noisy,persp=proj)
mv.setup_visualization(visualization='mds')
mv.initialize_X(verbose=1)
mv.optimize_X(algorithm='gd',learning_rate=1,max_iters=300,
verbose=1)
stress.append(mv.cost)
fig = plt.figure()
plt.semilogx(noise_levels,stress)
plt.show()
def embeddability_noise(ax=None):
print('\n**mds.embeddability_noise()')
N=50
ncost = []
noise_list = [0]+10**np.arange(-4,0,0.5)
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 example_disk(N=100,dim=2,**kwargs):
print('\n***mds.example_disk()***')
Y = misc.disk(N,dim); labels = misc.labels(Y)
plt.figure()
plt.scatter(Y[:,0],Y[:,1],c=labels)
plt.title('original data')
plt.draw()
plt.pause(0.1)
D = distances.compute(Y)
title = 'basic disk example'
mds = MDS(D,dim=dim,verbose=1,title=title,labels=labels)
mds.initialize()
mds.figureX(title='initial embedding')
mds.optimize(**kwargs)
mds.figureX(title='final embedding',labels=labels,edges=.2)
mds.figure(title='final embedding',labels=labels)
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 = distances.compute(X)
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 agd_mds_standard(N=100,dim=2,trials=3,runs=5):
"""\
test convergence of adaptive gradient descent for MDS problem, by solving
the MDS problems with multiple initial parameters.
"""
print('*** test.agd_mds_standard() ***')
print(f' N : {N}')
print(f' dim : {dim}')
print()
for i in range(trials):
print(f' Trial # {i}')
print(' Normalized cost :')
Y = misc.disk(N,dim)
D = distances.compute(Y)
vis = mds.MDS(D,dim=dim)
stress = []
for run in range(runs):
vis.initialize_Y()
vis.optimize(algorithm='agd')
stress.append(vis.ncost)
print(f' {vis.ncost:0.2e}')
print()
def noisy(N=100):
noise_levels = [0.0001, 0.001, 0.01, 0.1, 0.5]
stress = []
X = misc.disk(N, dim=3)
proj = perspective.Proj()
proj.set_params_list(special='standard')
Y = proj.project(X)
D = distances.compute(Y)
for noise in noise_levels:
D_noisy = distances.add_noise(D, noise)
stress_best = []
for i in range(3):
mv = Multiview(D_noisy, persp=proj, verbose=1)
mv.setup_visualization(visualization='mds')
mv.initialize_X()
mv.optimize_X(algorithm='agd')
stress_best.append(mv.normalized_cost)
stress.append(min(stress_best))
fig = plt.figure()
plt.loglog(noise_levels, stress, linestyle='--', marker='o')
plt.title('Normalized total stress')
plt.xlabel('noise level')
plt.ylabel('total stress')
plt.show()
