def example_random_graph_perspectives(N=100):
probs = [0.04, 0.05, 0.1, 0.2, 0.5, 1.0]
nums = [4, 5, 10, 20, 50, 100]
Ks = [1, 2, 3, 4, 5]
error = np.empty((len(Ks), len(probs)))
fig = plt.figure()
for i in range(len(probs)):
p = probs[i]
for j in range(len(Ks)):
K = Ks[j]
D = multigraph.binomial(N, p, K=K)
if K == 1: D = [D]
persp = perspective.Persp()
persp.fix_Q(number=K)
vis = MPSE(D, persp=persp)
vis.setup_visualization()
vis.initialize_X()
vis.initialize_Q()
vis.optimize_all(min_step=1e-8)
error[j, i] = max(vis.cost, 1e-6)
for i in range(len(Ks)):
plt.semilogy(error[i], label=f'K {Ks[i]}')
plt.ylabel('MDS stress')
plt.xlabel('average neighbors')
plt.xticks(range(len(nums)), nums)
plt.legend()
plt.tight_layout
plt.show()
def example_random_graph_2(N=100):
print('\n***mds.example_random_graph()***\n')
print('Here we explore the MDS embedding for a random binomial graph with'+\
'different edge probabilities.')
probs = [0.04, 0.05, 0.1, 0.2, 0.5, 1.0]
nums = [4, 5, 10, 20, 50, 100]
dims = [2, 3, 4, 5, 10, 20]
error = np.empty((len(dims), len(probs)))
fig = plt.figure()
for i in range(len(probs)):
p = probs[i]
D = multigraph.binomial(N, p)
for j in range(len(dims)):
dim = dims[j]
mds = MDS(D, dim=dim)
mds.initialize()
mds.stochastic(max_iters=100, approx=.3, lr=5)
mds.stochastic(max_iters=100, approx=.6, lr=10)
mds.stochastic(max_iters=100, approx=.9, lr=15)
mds.agd(min_step=1e-8)
error[j, i] = max(mds.cost, 1e-6)
for i in range(len(dims)):
plt.semilogy(error[i], label=f'dim {dims[i]}')
plt.ylabel('MDS stress')
plt.xlabel('average neighbors')
plt.xticks(range(len(nums)), nums)
plt.legend()
plt.tight_layout
plt.show()
def example_binomial(N=100, K=2):
for p in [0.05, 0.1, 0.5, 1.0]:
D = multigraph.binomial(N, p, K=K)
mv = MPSE(D, verbose=1)
mv.gd(plot=True, verbose=1)
mv.figureX()
mv.figureHY(edges=True)
plt.show()
def xyz():
X = np.load('raw/xyz.npy')
persp = perspective.Persp()
persp.fix_Q(number=3, special='standard')
D = multigraph.binomial(N=1000, p=.01, K=3)
mv = MPSE(D, persp=persp, verbose=1)
mv.setup_visualization()
mv.initialize_X(X)
mv.figureY(plot=True, title='', axis=False)
plt.show()
def example_binomial(N=100, K=2):
persp = perspective.Persp()
for p in [0.05, 0.1, 0.5, 1.0]:
D = multigraph.binomial(N, p, K=K)
mv = MPSE(D, persp=persp, verbose=1)
mv.setup_visualization(visualization='mds')
mv.initialize_Q()
mv.initialize_X()
mv.optimize_all(agd=True, max_iters=400, min_step=1e-8)
mv.figureX(plot=True)
mv.figureHY(edges=True)
plt.show()
def example_random_graph(N=100, dim=2):
print('\n***mds.example_random_graph()***\n')
print('Here we explore the MDS embedding for a random binomial graph with'+\
'different edge probabilities.')
fig, axes = plt.subplots(2, 3)
#[ax.set_axis_off() for ax in axes.ravel()]
plt.tight_layout()
for p, ax in zip([0.01, 0.02, 0.03, 0.05, 0.1, 1.0], axes.ravel()):
D = multigraph.binomial(N, p)
mds = MDS(D, dim=dim, verbose=1)
mds.initialize()
mds.stochastic(max_iters=100, approx=.6, lr=.5)
mds.agd(min_step=1e-6)
mds.figureX(ax=ax, edges=True)
ax.set_xlabel(f'ave. neighs. : {int(100*p)}')
ax.set_title(f'stress = {mds.cost:0.2e}')
ax.set_yticks([])
ax.set_xticks([])
plt.show()