def transform_rct2str(source, target_train, target_test):
covs_source = source['covs']
covs_target_train = target_train['covs']
covs_target_test = target_test['covs']
source_pow = {}
source_pow['covs'] = source['covs']
source_pow['labels'] = source['labels']
n = covs_source.shape[1]
disp_source = np.sum(
[distance_riemann(covi, np.eye(n))**2
for covi in covs_source]) / len(covs_source)
disp_target = np.sum(
[distance_riemann(covi, np.eye(n))**2
for covi in covs_target_train]) / len(covs_target_train)
p = np.sqrt(disp_target / disp_source)
target_pow_train = {}
target_pow_train['covs'] = np.stack(
[powm(covi, 1.0 / p) for covi in covs_target_train])
target_pow_train['labels'] = target_train['labels']
target_pow_test = {}
target_pow_test['covs'] = np.stack(
[powm(covi, 1.0 / p) for covi in covs_target_test])
target_pow_test['labels'] = target_test['labels']
return source_pow, target_pow_train, target_pow_test
def dim_reduction_nrmesup(X, P, labels, params):
K = X.shape[0]
nc = X.shape[1]
Sw = np.zeros((nc, nc))
Sb = np.zeros((nc, nc))
for i in range(K):
ci = labels[i]
for j in range(K):
Ci, Cj = X[i, :, :], X[j, :, :]
Sij = np.dot(invsqrtm(Ci), np.dot(Cj, invsqrtm(Ci)))
if (i != j) & (labels[j] == ci):
Sw = Sw + powm(logm(Sij), 2)
if (i != j) & (labels[j] != ci):
Sb = Sb + powm(logm(Sij), 2)
M = np.dot(np.linalg.inv(Sw), Sb)
g, U = np.linalg.eig(M)
idx = g.argsort()[::-1]
g = g[idx]
U = U[:, idx]
B, p = sp.linalg.polar(U)
W = B[:, :P]
return W
def power_means(C, p):
phi = 0.375/np.abs(p)
K = len(C)
n = C[0].shape[0]
w = np.ones(K)
w = w/(1.0*len(w))
G = np.sum([wk*powm(Ck, p) for (wk,Ck) in zip(w,C)], axis=0)
if p > 0:
X = invsqrtm(G)
else:
X = sqrtm(G)
zeta = 10e-10
test = 10*zeta
while test > zeta:
H = np.sum([wk*powm(np.dot(X, np.dot(powm(Ck, np.sign(p)), X.T)), np.abs(p)) for (wk,Ck) in zip(w,C)], axis=0)
X = np.dot(powm(H, -phi), X)
test = 1.0/np.sqrt(n) * np.linalg.norm(H - np.eye(n))
if p > 0:
P = np.dot(np.linalg.inv(X), np.linalg.inv(X.T))
else:
P = np.dot(X.T, X)
return P
def dim_reduction_nrmelandmark(X, P, labels, params):
K = X.shape[0]
nc = X.shape[1]
S = np.zeros((nc, nc))
M = mean_riemann(X)
for i in range(K):
Ci = X[i, :, :]
Sij = np.dot(invsqrtm(Ci), np.dot(M, invsqrtm(Ci)))
S = S + powm(logm(Sij), 2)
l, v = np.linalg.eig(S)
idx = l.argsort()[::-1]
l = l[idx]
v = v[:, idx]
W = v[:, :P]
return W
def dim_reduction_nrmeuns(X, P, labels, params):
K = X.shape[0]
nc = X.shape[1]
S = np.zeros((nc, nc))
for i in range(K):
for j in range(K):
if i != j:
Ci, Cj = X[i, :, :], X[j, :, :]
Sij = np.dot(invsqrtm(Ci), np.dot(Cj, invsqrtm(Ci)))
S = S + powm(logm(Sij), 2)
l, v = np.linalg.eig(S)
idx = l.argsort()[::-1]
l = l[idx]
v = v[:, idx]
W = v[:, :P]
return W
def test_powm():
"""Test matrix power"""
C = 2 * np.eye(3)
Ctrue = (2**0.5) * np.eye(3)
assert_array_almost_equal(powm(C, 0.5), Ctrue)
def test_powm():
"""Test matrix power"""
C = 2*np.eye(3)
Ctrue = (2**0.5)*np.eye(3)
assert_array_almost_equal(powm(C,0.5),Ctrue)
