def _fit(self, X, y):
"""
Parameters
----------
X: list of 2d-arrays, (n_classes, n_dims, n_samples)
y: array, (n_classes)
"""
dic = [subspace_bases(_X, self.n_subdims) for _X in X]
# dic, (n_classes, n_dims, n_subdims)
dic = np.array(dic)
# all_bases, (n_dims, n_classes * n_subdims)
all_bases = np.hstack(dic)
# n_gds_dims
if 0.0 < self.n_gds_dims <= 1.0:
n_gds_dims = int(all_bases.shape[1] * self.n_gds_dims)
else:
n_gds_dims = self.n_gds_dims
# gds, (n_dims, n_gds_dims)
self.gds = subspace_bases(all_bases, n_gds_dims, higher=False)
dic = self._gds_projection(dic)
self.dic = dic
def _fit(self, X, y):
"""
Parameters
----------
X: list of 2d-arrays, (n_classes, n_dims, n_samples)
y: array, (n_classes)
"""
dic = [subspace_bases(_X, self.n_subdims) for _X in X]
# dic, (n_classes, n_dims, n_subdims)
dic = np.array(dic)
self.dic = dic
def _get_gramians(self, X):
"""
Parameters
----------
X: array, (n_dims, n_samples)
Returns
-------
G: array, (n_class, n_subdims, n_subdims)
gramian matricies of references of each class
"""
# bases, (n_dims, n_subdims)
bases = subspace_bases(X, self.test_n_subdims)
# grammians, (n_classes, n_subdims, n_subdims or greater)
dic = self.dic[:, :, :self.n_subdims]
gramians = np.dot(dic.transpose(0, 2, 1), bases)
return gramians
def _get_gramians(self, X):
"""
Parameters
----------
X: array, (n_dims, n_samples)
Returns
-------
G: array, (n_class, n_subdims, n_subdims)
gramian matricies of references of each class
"""
# bases, (n_dims, n_subdims)
bases = subspace_bases(X, self.n_subdims)
# bases, (n_gds_dims, n_subdims)
bases = self._gds_projection(bases)
# gramians, (n_classes, n_subdims, n_subdims)
gramians = np.dot(self.dic.transpose(0, 2, 1), bases)
return gramians
def _get_gramians(self, X):
"""
Parameters
----------
X: array, (n_dims, n_samples)
Returns
-------
G: array, (n_class, n_subdims, n_subdims)
gramian matricies of references of each class
"""
# K, (n_class * n_samples_train, n_samples)
K = rbf_kernel(self.train_stack_X, X)
# X_gds, (n_gds_dims, n_samples)
X_gds = np.dot(self.gds_coeff.T, K)
# input subspace bases
bases = subspace_bases(X_gds, self.n_subdims)
# grammians, (n_classes, n_subdims, n_subdims)
gramians = np.dot(self.dic.transpose(0, 2, 1), bases)
return gramians
def _fit(self, X, y):
"""
Parameters
----------
X: list of 2d-arrays, (n_classes, n_dims, n_samples)
y: array, (n_classes)
"""
# mapings, (n_classes * n_samples)
mappings = np.array([
i for i, _X in enumerate(X)
for _ in range(_X.shape[1])
])
# stack_X, (n_dims, n_classes * n_samples)
stack_X = np.hstack(X)
# K, (n_classes * n_samples, n_classes * n_samples)
K = rbf_kernel(stack_X, stack_X, self.sigma)
coeff = []
for i, _ in enumerate(X):
p = (mappings == i)
# clipping K(X[y==c], X[y==c])
# _K, (n_samples_i, n_samples_i)
_K = K[p][:, p]
_coeff, _ = dual_vectors(_K, self.n_subdims)
coeff.append(_coeff)
# coeff, (n_classes * n_samples, n_classes * n_subdims)
coeff = block_diag(*coeff)
# gramian, (n_classes * n_subdims, n_classes * n_subdims)
gramian = coeff.T @ K @ coeff
# n_gds_dims
if 0.0 < self.n_gds_dims <= 1.0:
n_gds_dims = int(gramian.shape[0] * self.n_gds_dims)
else:
n_gds_dims = self.n_gds_dims
# coefficients of `bases in feature space` to get GDS bases in feature space
# gds_coeff, (n_classes * n_subdims, n_gds_dims)
gds_coeff, _ = dual_vectors(gramian, n_gds_dims, higher=False)
# coefficients of `given data X in feature space` to get GDS bases in features space
# gds_coeff, (n_classes * n_samples, n_gds_dims)
gds_coeff = np.dot(coeff, gds_coeff)
# X_gds = (GDS bases in feature space).T @ (X_stacked in feature space)
# projection coefficients of GDS in feature space.
# this vectors have finite dimension, such as n_gds_dims,
# and these vectors can treat as linear feature.
# X_gds, (n_gds_dims, n_classes * n_samples)
X_gds = np.dot(gds_coeff.T, K)
# X_gds, (n_classes, n_gds_dims, n_samples)
X_gds = [X_gds[:, mappings == i] for i, _ in enumerate(X)]
# dic, (n_classes, n_dims, n_subdims)
dic = [subspace_bases(_X, self.n_subdims) for _X in X_gds]
dic = np.array(dic)
self.train_stack_X = stack_X
self.mappings = mappings
self.gds_coeff = gds_coeff
self.dic = dic
