def transform_org2talmon(source, target_train, target_test):
covs_source = source['covs']
covs_target_train = target_train['covs']
covs_target_test = target_test['covs']
M_source = mean_riemann(covs_source)
M_target_train = mean_riemann(covs_target_train)
M = geodesic_riemann(M_source, M_target_train, alpha=0.5)
Gamma = ParallelTransport(reference_old=M_source, reference_new=M)
covs_source_transp = Gamma.fit_transform(covs_source)
Gamma = ParallelTransport(reference_old=M_target_train, reference_new=M)
covs_target_train_transp = Gamma.fit_transform(covs_target_train)
covs_target_test_transp = Gamma.transform(covs_target_test)
source_talmon = {}
source_talmon['labels'] = source['labels']
source_talmon['covs'] = covs_source_transp
target_talmon_train = {}
target_talmon_train['labels'] = target_train['labels']
target_talmon_train['covs'] = covs_target_train_transp
target_talmon_test = {}
target_talmon_test['labels'] = target_test['labels']
target_talmon_test['covs'] = covs_target_test_transp
return source_talmon, target_talmon_train, target_talmon_test
def transform_org2talmon_p300(source, target_train, target_test):
covs_source = source['covs']
covs_target_train = target_train['covs']
covs_target_test = target_test['covs']
weights = np.ones(len(source['labels']))
weights[source['labels'] == 2] = 5
M_source = mean_riemann(covs_source, sample_weight=weights)
weights = np.ones(len(target_train['labels']))
weights[target_train['labels'] == 2] = 5
M_target_train = mean_riemann(covs_target_train, sample_weight=weights)
M = geodesic_riemann(M_source, M_target_train, alpha=0.5)
Gamma = ParallelTransport(reference_old=M_source, reference_new=M)
covs_source_transp = Gamma.fit_transform(covs_source)
Gamma = ParallelTransport(reference_old=M_target_train, reference_new=M)
covs_target_train_transp = Gamma.fit_transform(covs_target_train)
covs_target_test_transp = Gamma.transform(covs_target_test)
source_talmon = {}
source_talmon['labels'] = source['labels']
source_talmon['covs'] = covs_source_transp
target_talmon_train = {}
target_talmon_train['labels'] = target_train['labels']
target_talmon_train['covs'] = covs_target_train_transp
target_talmon_test = {}
target_talmon_test['labels'] = target_test['labels']
target_talmon_test['covs'] = covs_target_test_transp
return source_talmon, target_talmon_train, target_talmon_test
def transform_org2opt(source, target_train, target_test):
target_opt_train = {}
target_opt_test = {}
target_opt_train['labels'] = target_train['labels']
target_opt_test['labels'] = target_test['labels']
# get cost matrix
Cs = source['covs']
ys = source['labels']
Ct_train = target_train['covs']
Ct_test = target_test['covs']
M = np.zeros((len(Cs), len(Ct_train)))
for i, Cs_i in enumerate(Cs):
for j, Ct_j in enumerate(Ct_train):
M[i, j] = distance_riemann(Cs_i, Ct_j)**2
# get the transportation plan
mu_s = distribution_estimation_uniform(Cs)
mu_t = distribution_estimation_uniform(Ct_train)
gamma = sinkhorn_lpl1_mm(mu_s, ys, mu_t, M, reg=1.0)
# transport the target matrices (train)
Ct_train_transported = np.zeros(Ct_train.shape)
for j in range(len(Ct_train_transported)):
Ct_train_transported[j] = mean_riemann(Cs, sample_weight=gamma[:, j])
target_opt_train['covs'] = Ct_train_transported
# transport the target matrices (test)
D = np.zeros((len(Ct_test), len(Ct_train)))
for k, Ct_k in enumerate(Ct_test):
for l, Ct_l in enumerate(Ct_train):
D[k, l] = distance_riemann(Ct_k, Ct_l)**2
idx = np.argmin(D, axis=1) # nearest neighbour to each target test matrix
Ct_test_transported = np.zeros(Ct_test.shape)
for i in range(len(Ct_test)):
j = idx[i]
Ci = Ct_test[i]
Ri = Ct_train[j]
Rf = Ct_train_transported[j]
Ri_sqrt = sqrtm(Ri)
Ri_invsqrt = invsqrtm(Ri)
Li = logm(np.dot(Ri_invsqrt, np.dot(Ci, Ri_invsqrt)))
eta_i = np.dot(Ri_sqrt, np.dot(Li, Ri_sqrt))
Ri_Rf = geodesic_riemann(Rf, Ri, alpha=0.5)
Ri_inv = np.linalg.inv(Ri)
eta_f = np.dot(Ri_inv, np.dot(eta_i, Ri_inv))
eta_f = np.dot(Ri_Rf, np.dot(eta_f, Ri_Rf))
Rf_sqrt = sqrtm(Rf)
Rf_invsqrt = invsqrtm(Rf)
Ef = expm(np.dot(Rf_invsqrt, np.dot(eta_f, Rf_invsqrt)))
Ct_test_transported[i] = np.dot(Rf_sqrt, np.dot(Ef, Rf_sqrt))
target_opt_test['covs'] = Ct_test_transported
return source, target_opt_train, target_opt_test