def initialisation_gw(p, q, Cs, U, prior=0, nb_init=5, nb_dummies=1):
"""Initialisation of GW. From a barycenter, it gives a first shot for
the transport matrix
Parameters
----------
p: array of len (n_p)
weights of the source (positives !! with no dummies !!)
q: array of len (n_u)
weights of the target (unlabeled)
Cs: array of shape (n_p,n_p)
intra-source (P) cost matrix (!! no dummies !!)
U: array of shape (n_u,d_u)
U dataset
prior: percentage of positives on the dataset (s)
n_init: number of atoms on the barycenter
nb_dummies: number of dummy points, default: 1
(to avoid numerical instabilities of POT)
Returns
-------
list of numpy.array of shape (n_p+, n_u)
list of potentialtransport matrix initialisation
"""
if nb_init > 2:
res, _, _ = wass_bary_coarsening(nb_init,
np.array(U),
pt=np.ones(U.shape[0]) / (U.shape[0]))
else:
res, _, _ = wass_bary_coarsening(nb_init,
np.array(U),
pt=np.ones(U.shape[0]) / (U.shape[0]),
pb=[prior, 1 - prior])
idx = []
l_gamma = []
for i in range(nb_init):
idx = np.where(res[i, :] > 1e-5)[0]
gamma = np.zeros((len(p) + nb_dummies, len(q)))
Ct_0 = cdist(U.iloc[idx], U.iloc[idx])
gamma1 = gromov_wasserstein(Cs, Ct_0, p,
np.ones(Ct_0.shape[0]) / Ct_0.shape[0],
'square_loss')
gamma1 /= np.sum(gamma1)
for i in range(len(idx)):
gamma[:-nb_dummies, idx[i]] = gamma1[:, i]
l_gamma.append(gamma)
return l_gamma
def _compute_gw(pts_1, pts_2, wts_1, wts_2):
"""Normalize weights and compute OT matrix."""
# Normalize weights
p_1 = wts_1 / np.sum(wts_1)
p_2 = wts_2 / np.sum(wts_2)
# Normalized distance matrices
c_1 = _normalized_dist_mtx(pts_1, pts_1, metric='sqeuclidean')
c_2 = _normalized_dist_mtx(pts_2, pts_2, metric='sqeuclidean')
# Compute transport plan
return gromov_wasserstein(c_1, c_2, p_1, p_2, 'square_loss', log=True)
# Generate gaussian mixtures translated from each other
a, x, b, y = generate_data(n1, 0.7)
clf = KMeans(n_clusters=n_clust)
clf.fit(x)
idx = np.zeros(n_clust)
for i in range(n_clust):
d = clf.transform(x)[:, i]
idx[i] = np.argmin(d)
idx = idx.astype(int)
# Generate costs and transport plan
Cx, Cy = euclid_dist(x, x), euclid_dist(y, y)
if compute_balanced:
pi_b = gromov_wasserstein(Cx, Cy, a, b, loss_fun='square_loss')
plot_density_matching(pi_b, a, x, b, y, idx, alpha=1., linewidth=.5)
plt.legend()
plt.savefig(path + '/fig_matching_plan_balanced.png')
plt.show()
Cx, Cy = torch.from_numpy(Cx), torch.from_numpy(Cy)
rho_list = [0.1]
peps_list = [2, 1, 0, -1, -2, -3]
for rho in rho_list:
solver.rho = rho
pi = None
for p in peps_list:
eps = 10 ** p
solver.eps = eps
def g_wasserstein(x_src, x_tgt, C2):
N = x_src.shape[0]
C1 = GWmatrix(x_src)
M = gromov_wasserstein(C1, C2, np.ones(N), np.ones(N),
"square_loss") # epsilon=0.55,max_iter=100,tol=1e-4
return procrustes(np.dot(M, x_tgt), x_src)
a, b = a.cpu().data.numpy(), b.cpu().data.numpy()
pi = pi.cpu().data.numpy()
plot_density_matching(
pi,
a,
x,
b,
y,
Gx,
Gy,
titlename=f'UGW matching, ($\\rho$,$\epsilon$)={rho, eps}')
plt.legend()
plt.show()
if normalize_proba:
pi_b = gromov_wasserstein(Cx.cpu().numpy(),
Cy.cpu().numpy(),
a,
b,
loss_fun='square_loss')
plot_density_matching(pi_b,
a,
x,
b,
y,
Gx,
Gy,
titlename='GW matching')
plt.legend()
plt.show()
Gwg, logw = fused_gromov_wasserstein(M,
C1,
C2,
p,
q,
loss_fun='square_loss',
alpha=alpha,
verbose=True,
log=True)
ot.toc()
#%reload_ext WGW
Gg, log = gromov_wasserstein(C1,
C2,
p,
q,
loss_fun='square_loss',
verbose=True,
log=True)
##############################################################################
# Visualize transport matrices
# ---------
#%% visu OT matrix
cmap = 'Blues'
fs = 15
pl.figure(2, (13, 5))
pl.clf()
pl.subplot(1, 3, 1)
pl.imshow(Got, cmap=cmap, interpolation='nearest')
# for m in list_mass_pgw: # Compute partial GW plans, initialized with simulated annealing
# pi = a[:,None] * b[None,:]
# for eps in [10 ** e for e in [2., 1.5, 1]]: # Simulated annealing loop
# pi = entropic_partial_gromov_wasserstein(cx, cy, a, b, eps, m=m, G0=pi)
# pi = partial_gromov_wasserstein(cx, cy, a, b, m=m, G0=pi)
# cost = partial_gromov_wasserstein2(cx, cy, a, b, m=m, G0=pi)
# # Initialize with partial OT plan
# M = sp.spatial.distance.cdist(x, y)
# gam = partial_wasserstein(a, b, M, m=m)
# gam = partial_gromov_wasserstein(cx, cy, a, b, m=m, G0=gam)
# if partial_gromov_wasserstein2(cx, cy, a, b, m=m, G0=gam) < cost:
# pi = gam
# # Initialize with OT plan
# gam = emd(a, b, M)
# gam = partial_gromov_wasserstein(cx, cy, a, b, m=m, G0=gam)
# if partial_gromov_wasserstein2(cx, cy, a, b, m=m, G0=gam) < cost:
# pi = gam
#
# # Plot matchings between measures --> Partial GW
# plot_density_matching(pi, a, x, b, y, Gx, Gy, titlefile=f'PGW_mass{m:.3f}')
# plt.legend()
# plt.show()
if normalize_proba & compare_with_gw: # Plot the behaviour of GW as reference
pi = a[:, None] * b[None, :]
pi_gw = gromov_wasserstein(cx, cy, a, b, loss_fun='square_loss')
plot_density_matching(pi_gw, a, x, b, y, Gx, Gy, titlefile='GW')
plt.legend()
plt.show()