def ksvd(Y, D, X, n_cycles=1, verbose=True):
n_atoms = D.shape[1]
n_features, n_samples = Y.shape
unused_atoms = []
R = Y - fast_dot(D, X)
for c in range(n_cycles):
for k in range(n_atoms):
if verbose:
sys.stdout.write("\r" + "k-svd..." + ":%3.2f%%" % ((k / float(n_atoms)) * 100))
sys.stdout.flush()
# find all the datapoints that use the kth atom
omega_k = X[k, :] != 0
if not np.any(omega_k):
unused_atoms.append(k)
continue
# the residual due to all the other atoms but k
Rk = R[:, omega_k] + np.outer(D[:, k], X[k, omega_k])
U, S, V = randomized_svd(Rk, n_components=1, n_iter=10, flip_sign=False)
D[:, k] = U[:, 0]
X[k, omega_k] = V[0, :] * S[0]
# update the residual
R[:, omega_k] = Rk - np.outer(D[:, k], X[k, omega_k])
print ""
return D, X, unused_atoms
def approx_ksvd(Y, D, X, n_cycles=1, verbose=True):
# the approximate KSVD algorithm
n_atoms = D.shape[1]
n_features, n_samples = Y.shape
unused_atoms = []
R = Y - fast_dot(D, X)
for c in range(n_cycles):
for k in range(n_atoms):
if verbose:
sys.stdout.write("\r" + "k-svd..." + ":%3.2f%%" % ((k / float(n_atoms)) * 100))
sys.stdout.flush()
# find all the datapoints that use the kth atom
omega_k = X[k, :] != 0
if not np.any(omega_k):
# print "this atom is not used"
unused_atoms.append(k)
continue
Rk = R[:, omega_k] + np.outer(D[:, k], X[k, omega_k])
# update of D[:,k]
D[:, k] = np.dot(Rk, X[k, omega_k])
D[:, k] = normalize(D[:, k])
# update of X[:,k]
X[k, omega_k] = np.dot(Rk.T, D[:, k])
# update the residual
R[:, omega_k] = Rk - np.outer(D[:, k], X[k, omega_k])
print ""
return D, X, unused_atoms
def approx_ksvd(Y, D, X, n_cycles=1, verbose=True):
# the approximate KSVD algorithm
n_atoms = D.shape[1]
n_features, n_samples = Y.shape
unused_atoms = []
R = Y - fast_dot(D, X)
for c in range(n_cycles):
for k in range(n_atoms):
if verbose:
sys.stdout.write("\r" + "k-svd..." + ":%3.2f%%" % ((k / float(n_atoms)) * 100))
sys.stdout.flush()
# find all the datapoints that use the kth atom
omega_k = X[k, :] != 0
if not np.any(omega_k):
# print "this atom is not used"
unused_atoms.append(k)
continue
Rk = R[:, omega_k] + np.outer(D[:, k], X[k, omega_k])
# update of D[:,k]
D[:, k] = np.dot(Rk, X[k, omega_k])
D[:, k] = normalize(D[:, k])
# update of X[:,k]
X[k, omega_k] = np.dot(Rk.T, D[:, k])
# update the residual
R[:, omega_k] = Rk - np.outer(D[:, k], X[k, omega_k])
print ""
return D, X, unused_atoms
def ksvd(Y, D, X, n_cycles=1, verbose=True):
n_atoms = D.shape[1]
n_features, n_samples = Y.shape
unused_atoms = []
R = Y - fast_dot(D, X)
for c in range(n_cycles):
for k in range(n_atoms):
if verbose:
sys.stdout.write("\r" + "k-svd..." + ":%3.2f%%" % ((k / float(n_atoms)) * 100))
sys.stdout.flush()
# find all the datapoints that use the kth atom
omega_k = X[k, :] != 0
if not np.any(omega_k):
unused_atoms.append(k)
continue
# the residual due to all the other atoms but k
Rk = R[:, omega_k] + np.outer(D[:, k], X[k, omega_k])
U, S, V = randomized_svd(Rk, n_components=1, n_iter=10, flip_sign=False)
D[:, k] = U[:, 0]
X[k, omega_k] = V[0, :] * S[0]
# update the residual
R[:, omega_k] = Rk - np.outer(D[:, k], X[k, omega_k])
print ""
return D, X, unused_atoms
def nn_ksvd(Y, D, X, n_cycles=1, verbose=True):
# the non-negative variant
n_atoms = D.shape[1]
n_features, n_samples = Y.shape
unused_atoms = []
R = Y - fast_dot(D, X)
for k in range(n_atoms):
if verbose:
sys.stdout.write("\r" + "k-svd..." + ":%3.2f%%" %
((k / float(n_atoms)) * 100))
sys.stdout.flush()
# find all the datapoints that use the kth atom
omega_k = X[k, :] != 0
if not np.any(omega_k):
unused_atoms.append(k)
continue
# the residual due to all the other atoms but k
Rk = R[:, omega_k] + np.outer(D[:, k], X[k, omega_k])
try:
U, S, V = randomized_svd(Rk,
n_components=1,
n_iter=50,
flip_sign=False)
except:
warnings.warn('SVD error')
continue
d = U[:, 0]
x = V[0, :] * S[0]
# projection to the constraint set
d[d < 0] = 0
x[x < 0] = 0
dTd = np.dot(d, d)
xTx = np.dot(x, x)
if dTd <= np.finfo('float').eps or xTx <= np.finfo('float').eps:
continue
for j in range(n_cycles):
d = np.dot(Rk, x) / np.dot(x, x)
d[d < 0] = 0
x = np.dot(d.T, Rk) / np.dot(d, d)
x[x < 0] = 0
_norm = norm(d)
d = d / _norm
x = x * _norm
D[:, k] = d
X[k, omega_k] = x
# update the residual
R[:, omega_k] = Rk - np.outer(D[:, k], X[k, omega_k])
print ""
return D, X, unused_atoms
def nn_ksvd(Y, D, X, n_cycles=1, verbose=True):
# the non-negative variant
n_atoms = D.shape[1]
n_features, n_samples = Y.shape
unused_atoms = []
R = Y - fast_dot(D, X)
for k in range(n_atoms):
if verbose:
sys.stdout.write("\r" + "k-svd..." + ":%3.2f%%" % ((k / float(n_atoms)) * 100))
sys.stdout.flush()
# find all the datapoints that use the kth atom
omega_k = X[k, :] != 0
if not np.any(omega_k):
unused_atoms.append(k)
continue
# the residual due to all the other atoms but k
Rk = R[:, omega_k] + np.outer(D[:, k], X[k, omega_k])
try:
U, S, V = randomized_svd(Rk, n_components=1, n_iter=50, flip_sign=False)
except:
warnings.warn('SVD error')
continue
d = U[:, 0]
x = V[0, :] * S[0]
# projection to the constraint set
d[d < 0] = 0
x[x < 0] = 0
dTd = np.dot(d, d)
xTx = np.dot(x, x)
if dTd <= np.finfo('float').eps or xTx <= np.finfo('float').eps:
continue
for j in range(n_cycles):
d = np.dot(Rk, x) / np.dot(x, x)
d[d < 0] = 0
x = np.dot(d.T, Rk) / np.dot(d, d)
x[x < 0] = 0
_norm = norm(d)
d = d / _norm
x = x * _norm
D[:, k] = d
X[k, omega_k] = x
# update the residual
R[:, omega_k] = Rk - np.outer(D[:, k], X[k, omega_k])
print ""
return D, X, unused_atoms
def global_error(X, D, sparse_coder, n_class_atoms, n_jobs=1):
"""
computes the approximation error of the dataset to
each class-specific dictionary. The dataset is first encoded over the
joint dictionary.
"""
Z = sparse_coder(X, D)
n_samples = X.shape[1]
n_classes = len(n_class_atoms)
E = np.zeros((n_classes, n_samples))
if n_jobs > 1:
set_openblas_threads(n_jobs)
for c in range(n_classes):
c_idx = get_class_atoms(c, n_class_atoms)
E[c, :] = np.sum(np.power(fast_dot(D[:, c_idx], Z[c_idx, :]) - X, 2), axis=0)
if n_jobs > 1:
set_openblas_threads(1)
return E
def approx_error_proc(X, Z, D):
error = frobenius_squared(X - fast_dot(D, Z))
return error
def approx_error(D, Z, X, n_jobs=1):
"""computes the approximation error ||X-DZ||_{F}^{2} """
if n_jobs > 1:
set_openblas_threads(n_jobs)
error = frobenius_squared(X - fast_dot(D, Z))
return error
def approx_error_proc(X, Z, D):
error = frobenius_squared(X - fast_dot(D, Z))
return error
def approx_error(D, Z, X, n_jobs=1):
"""computes the approximation error ||X-DZ||_{F}^{2} """
if n_jobs > 1:
set_openblas_threads(n_jobs)
error = frobenius_squared(X - fast_dot(D, Z))
return error