def kmm(Xtrain, Xtest, sigma):
n_tr = len(Xtrain)
n_te = len(Xtest)
# calculate Kernel
print('Computing kernel for training data ...')
K_ns = sk.rbf_kernel(Xtrain, Xtrain, sigma)
# make it symmetric
K = 0.9 * (K_ns + K_ns.transpose())
# calculate kappa
print('Computing kernel for kappa ...')
kappa_r = sk.rbf_kernel(Xtrain, Xtest, sigma)
ones = numpy.ones(shape=(n_te, 1))
kappa = numpy.dot(kappa_r, ones)
kappa = -(float(n_tr) / float(n_te)) * kappa
# calculate eps
eps = (math.sqrt(n_tr) - 1) / math.sqrt(n_tr)
# constraints
A0 = numpy.ones(shape=(1, n_tr))
A1 = -numpy.ones(shape=(1, n_tr))
A = numpy.vstack([A0, A1, -numpy.eye(n_tr), numpy.eye(n_tr)])
b = numpy.array([[n_tr * (eps + 1), n_tr * (eps - 1)]])
b = numpy.vstack([b.T, -numpy.zeros(shape=(n_tr, 1)), numpy.ones(shape=(n_tr, 1)) * 1000])
print('Solving quadratic program for beta ...')
P = matrix(K, tc='d')
q = matrix(kappa, tc='d')
G = matrix(A, tc='d')
h = matrix(b, tc='d')
beta = solvers.qp(P, q, G, h)
return [i for i in beta['x']]
def _get_kernel(self, X, y=None):
if self.kernel == "rbf":
if y is None:
return rbf_kernel(X, X, gamma=self.gamma)
else:
return rbf_kernel(X, y, gamma=self.gamma)
elif self.kernel == "knn":
if self.nn_fit is None:
self.nn_fit = NearestNeighbors(self.n_neighbors).fit(X)
if y is None:
# Nearest neighbors returns a directed matrix.
dir_graph = self.nn_fit.kneighbors_graph(self.nn_fit._fit_X,
self.n_neighbors,
mode='connectivity')
# Making the matrix symmetric
un_graph = dir_graph + dir_graph.T
# Since it is a connectivity matrix, all values should be
# either 0 or 1
un_graph[un_graph > 1.0] = 1.0
return un_graph
else:
return self.nn_fit.kneighbors(y, return_distance=False)
else:
raise ValueError("%s is not a valid kernel. Only rbf and knn"
" are supported at this time" % self.kernel)
def _Gram(self, X):
if X is self.X:
if self.Gs_train is None:
kernel_scalar = rbf_kernel(self.X, gamma=self.gamma)[:, :,
newaxis,
newaxis]
delta = subtract(X.T[:, newaxis, :], self.X.T[:, :, newaxis])
self.Gs_train = asarray(transpose(
2 * self.gamma * kernel_scalar *
(2 * self.gamma * (delta[:, newaxis, :, :] *
delta[newaxis, :, :, :]).transpose(
(3, 2, 0, 1)) +
((self.p - 1) - 2 * self.gamma *
_norm_axis_0(delta)[:, :, newaxis, newaxis]**2) *
eye(self.p)[newaxis, newaxis, :, :]), (0, 2, 1, 3)
)).reshape((self.p * X.shape[0], self.p * self.X.shape[0]))
return self.Gs_train
kernel_scalar = rbf_kernel(X, self.X, gamma=self.gamma)[:, :,
newaxis,
newaxis]
delta = subtract(X.T[:, newaxis, :], self.X.T[:, :, newaxis])
return asarray(transpose(
2 * self.gamma * kernel_scalar *
(2 * self.gamma * (delta[:, newaxis, :, :] *
delta[newaxis, :, :, :]).transpose(
(3, 2, 0, 1)) +
((self.p - 1) - 2 * self.gamma *
_norm_axis_0(delta).T[:, :, newaxis, newaxis]**2) *
eye(self.p)[newaxis, newaxis, :, :]), (0, 2, 1, 3)
)).reshape((self.p * X.shape[0], self.p * self.X.shape[0]))
def hsic(x,y,sigma):
"""Compute HSIC between two random variables
Parameters
----------
x : array, shape(n_instances,1)
vector containing m observations of the first random variable
y : array, shape(n_instances,1)
vector containing m observations of the second random variable
sigma : scale parameter for Gaussian kernel
Returns
-------
hsic_value : float, HSIC value of the two input random variables
"""
# m is the number of observations here
m = len(x)
gamma = 1.0/(2*sigma**2)
k = rbf_kernel(x,x,gamma)
l = rbf_kernel(y,y,gamma)
for i in range(m):
k[i,i] = 0
l[i,i] = 0
h = np.eye(m)-1.0/m
hsic_value = (1.0/(m-1)**2)*np.trace(np.dot(np.dot(np.dot(k,h),l),h))
return hsic_value
def fit(self, X):
A = tools.kmeans_centroids(X, self.n_prototypes).cluster_centers_
self.W = rbf_kernel(A, A, gamma = 1./self.sigma2)
self.H = rbf_kernel(X, A, gamma = 1./self.sigma2)
self.W_dagger = np.linalg.pinv(self.W)
d_tilde = self.H.dot(self.W_dagger.dot(self.H.T.sum(axis=1)))
self.HtH = self.H.T.dot(self.H)
self.HtSH = (self.H.T * d_tilde).dot(self.H) - self.HtH.dot(self.W_dagger).dot(self.HtH.T)
self.n = X.shape[0]
def test_pairwise_kernels():
""" Test the pairwise_kernels helper function. """
def callable_rbf_kernel(x, y, **kwds):
""" Callable version of pairwise.rbf_kernel. """
K = rbf_kernel(np.atleast_2d(x), np.atleast_2d(y), **kwds)
return K
rng = np.random.RandomState(0)
X = rng.random_sample((5, 4))
Y = rng.random_sample((2, 4))
# Test with all metrics that should be in PAIRWISE_KERNEL_FUNCTIONS.
test_metrics = ["rbf", "sigmoid", "polynomial", "linear", "chi2",
"additive_chi2"]
for metric in test_metrics:
function = PAIRWISE_KERNEL_FUNCTIONS[metric]
# Test with Y=None
K1 = pairwise_kernels(X, metric=metric)
K2 = function(X)
assert_array_almost_equal(K1, K2)
# Test with Y=Y
K1 = pairwise_kernels(X, Y=Y, metric=metric)
K2 = function(X, Y=Y)
assert_array_almost_equal(K1, K2)
# Test with tuples as X and Y
X_tuples = tuple([tuple([v for v in row]) for row in X])
Y_tuples = tuple([tuple([v for v in row]) for row in Y])
K2 = pairwise_kernels(X_tuples, Y_tuples, metric=metric)
assert_array_almost_equal(K1, K2)
# Test with sparse X and Y
X_sparse = csr_matrix(X)
Y_sparse = csr_matrix(Y)
if metric in ["chi2", "additive_chi2"]:
# these don't support sparse matrices yet
assert_raises(ValueError, pairwise_kernels,
X_sparse, Y=Y_sparse, metric=metric)
continue
K1 = pairwise_kernels(X_sparse, Y=Y_sparse, metric=metric)
assert_array_almost_equal(K1, K2)
# Test with a callable function, with given keywords.
metric = callable_rbf_kernel
kwds = {}
kwds['gamma'] = 0.1
K1 = pairwise_kernels(X, Y=Y, metric=metric, **kwds)
K2 = rbf_kernel(X, Y=Y, **kwds)
assert_array_almost_equal(K1, K2)
# callable function, X=Y
K1 = pairwise_kernels(X, Y=X, metric=metric, **kwds)
K2 = rbf_kernel(X, Y=X, **kwds)
assert_array_almost_equal(K1, K2)
def compute_err(parameters):
X,k_train,USV_k_train,n_SR,method,gamma,seed,k = parameters
np.random.seed(seed)
idx_SR = subsampling(X,int(n_SR),method)
X_SR = X[idx_SR]
k_SR = rbf_kernel(X_SR,X_SR,gamma=gamma)
U_SR, S_SR, V_SR = np.linalg.svd(k_SR)
USV_k_SR = [U_SR, S_SR, V_SR]
k_train_SR = rbf_kernel(X,X_SR,gamma=gamma)
rel_err, USV_k_SR = rel_approx_error(k_train, USV_k_SR, idx_SR)
rel_acc = rel_approx_acc(k_train,USV_k_train,k_SR,USV_k_SR,idx_SR,k)
quan_err = quan_error(X,X_SR)
return [rel_err,quan_err,rel_acc]
def fit(self, X, y, unlabeled_data=None):
num_data = X.shape[0] + unlabeled_data.shape[0]
num_labeled = X.shape[0]
num_unlabeled = unlabeled_data.shape[0]
labeled = np.zeros((num_data,), dtype=np.float32)
labeled[0:num_labeled] = 1.0
if issparse(X):
self.X_ = vstack((util.cast_to_float32(X),
util.cast_to_float32(unlabeled_data)), format='csr')
else:
self.X_ = np.concatenate((util.cast_to_float32(X),
util.cast_to_float32(unlabeled_data)))
self.gamma = (
self.gamma if self.gamma is not None else 1.0 / X.shape[1])
self.kernel_params = {'gamma':self.gamma, 'degree':self.degree, 'coef0':self.coef0}
kernel_matrix = pairwise_kernels(self.X_, metric=self.kernel,
filter_params=True, **self.kernel_params)
A = np.dot(np.diag(labeled), kernel_matrix)
if self.nu2 != 0:
if self.kernel == 'rbf':
laplacian_kernel_matrix = kernel_matrix
else:
laplacian_kernel_matrix = rbf_kernel(self.X_, gamma=self.gamma)
laplacian_x_kernel = np.dot(graph_laplacian(
laplacian_kernel_matrix, normed=self.normalize_laplacian), kernel_matrix)
A += self.nu2 * laplacian_x_kernel
y = np.concatenate((y, -np.ones((num_unlabeled,), dtype=np.float32)),
axis=0)
super(LapRLSC, self).fit(A, y, class_for_unlabeled=-1)
def __init__(self, *args, **kwargs):
super(QUIRE, self).__init__(*args, **kwargs)
self.Uindex = [idx for idx, _ in self.dataset.get_unlabeled_entries()]
self.Lindex = [idx for idx in range(len(self.dataset)) if idx not in self.Uindex]
self.lmbda = kwargs.pop("lambda", 1.0)
X, self.y = zip(*self.dataset.get_entries())
self.y = list(self.y)
self.kernel = kwargs.pop("kernel", "rbf")
if self.kernel == "rbf":
self.K = rbf_kernel(X=X, Y=X, gamma=kwargs.pop("gamma", 1.0))
elif self.kernel == "poly":
self.K = polynomial_kernel(
X=X, Y=X, coef0=kwargs.pop("coef0", 1), degree=kwargs.pop("degree", 3), gamma=kwargs.pop("gamma", 1.0)
)
elif self.kernel == "linear":
self.K = linear_kernel(X=X, Y=X)
elif hasattr(self.kernel, "__call__"):
self.K = self.kernel(X=np.array(X), Y=np.array(X))
else:
raise NotImplementedError
if not isinstance(self.K, np.ndarray):
raise TypeError("K should be an ndarray")
if self.K.shape != (len(X), len(X)):
raise ValueError("kernel should have size (%d, %d)" % (len(X), len(X)))
self.L = np.linalg.inv(self.K + self.lmbda * np.eye(len(X)))
def bourgain_embedding_matrix(distance_matrix):
"""Use Bourgain algorithm to embed the neural architectures based on their edit-distance.
Args:
distance_matrix: A matrix of edit-distances.
Returns:
A matrix of distances after embedding.
"""
distance_matrix = np.array(distance_matrix)
n = len(distance_matrix)
if n == 1:
return distance_matrix
np.random.seed(123)
distort_elements = []
r = range(n)
k = int(math.ceil(math.log(n) / math.log(2) - 1))
t = int(math.ceil(math.log(n)))
counter = 0
for i in range(0, k + 1):
for t in range(t):
s = np.random.choice(r, 2 ** i)
for j in r:
d = min([distance_matrix[j][s] for s in s])
counter += len(s)
if i == 0 and t == 0:
distort_elements.append([d])
else:
distort_elements[j].append(d)
return rbf_kernel(distort_elements, distort_elements)
def _apply_kernel(self, X, y=None):
"""Apply the selected kernel function to the data."""
if self.kernel == 'linear':
phi = linear_kernel(X, y)
elif self.kernel == 'rbf':
phi = rbf_kernel(X, y, gamma=self.gamma)
elif self.kernel == 'poly':
phi = polynomial_kernel(X, y, degree=self.degree)
elif callable(self.kernel):
phi = self.kernel(X, y)
if len(phi.shape) != 2:
raise ValueError(
"Custom kernel function did not return 2D matrix"
)
if phi.shape[0] != X.shape[0]:
raise ValueError(
"Custom kernel function did not return matrix with rows"
" equal to number of data points."""
)
else:
raise ValueError("Kernel selection is invalid.")
phi = phi.T
if self.bias_used:
phi = np.hstack((np.ones((phi.shape[0], 1)), phi))
return phi
def test_svc_decision_function():
"""
Test SVC's decision_function
Sanity check, test that decision_function implemented in python
returns the same as the one in libsvm
"""
# multi class:
clf = svm.SVC(kernel="linear", C=0.1).fit(iris.data, iris.target)
dec = np.dot(iris.data, clf.coef_.T) + clf.intercept_
assert_array_almost_equal(dec, clf.decision_function(iris.data))
# binary:
clf.fit(X, Y)
dec = np.dot(X, clf.coef_.T) + clf.intercept_
prediction = clf.predict(X)
assert_array_almost_equal(dec.ravel(), clf.decision_function(X))
assert_array_almost_equal(prediction, clf.classes_[(clf.decision_function(X) > 0).astype(np.int)])
expected = np.array([-1.0, -0.66, -1.0, 0.66, 1.0, 1.0])
assert_array_almost_equal(clf.decision_function(X), expected, 2)
# kernel binary:
clf = svm.SVC(kernel="rbf", gamma=1)
clf.fit(X, Y)
rbfs = rbf_kernel(X, clf.support_vectors_, gamma=clf.gamma)
dec = np.dot(rbfs, clf.dual_coef_.T) + clf.intercept_
assert_array_almost_equal(dec.ravel(), clf.decision_function(X))
def test_nystroem_approximation():
# some basic tests
rnd = np.random.RandomState(0)
X = rnd.uniform(size=(10, 4))
# With n_components = n_samples this is exact
X_transformed = Nystroem(n_components=X.shape[0]).fit_transform(X)
K = rbf_kernel(X)
assert_array_almost_equal(np.dot(X_transformed, X_transformed.T), K)
trans = Nystroem(n_components=2, random_state=rnd)
X_transformed = trans.fit(X).transform(X)
assert_equal(X_transformed.shape, (X.shape[0], 2))
# test callable kernel
linear_kernel = lambda X, Y: np.dot(X, Y.T)
trans = Nystroem(n_components=2, kernel=linear_kernel, random_state=rnd)
X_transformed = trans.fit(X).transform(X)
assert_equal(X_transformed.shape, (X.shape[0], 2))
# test that available kernels fit and transform
kernels_available = kernel_metrics()
for kern in kernels_available:
trans = Nystroem(n_components=2, kernel=kern, random_state=rnd)
X_transformed = trans.fit(X).transform(X)
assert_equal(X_transformed.shape, (X.shape[0], 2))
def cartesian_affinities(data, distance = 2.0, sigma = 1.0):
"""
Computes affinities between points using euclidean distance, and
sets to 0 all affinities for which the points are further than a certain
threshold apart.
Parameters
----------
data : array, shape (N, M)
N instances of M-dimensional data.
distance : float
Distance threshold, above which all affinities are set to 0.
sigma : float
Sigma used to compute affinities.
Returns
-------
A : array, shape (N, N)
Symmetric affinity matrix.
"""
A = pairwise.rbf_kernel(data, data, gamma = (1.0 / (2 * (sigma ** 2))))
if (distance > 0.0):
distances = pairwise.pairwise_distances(data)
A[np.where(distances > distance)] = 0.0
return A
def test_decision_function():
# Test decision_function
# Sanity check, test that decision_function implemented in python
# returns the same as the one in libsvm
# multi class:
clf = svm.SVC(kernel='linear', C=0.1,
decision_function_shape='ovo').fit(iris.data, iris.target)
dec = np.dot(iris.data, clf.coef_.T) + clf.intercept_
assert_array_almost_equal(dec, clf.decision_function(iris.data))
# binary:
clf.fit(X, Y)
dec = np.dot(X, clf.coef_.T) + clf.intercept_
prediction = clf.predict(X)
assert_array_almost_equal(dec.ravel(), clf.decision_function(X))
assert_array_almost_equal(
prediction,
clf.classes_[(clf.decision_function(X) > 0).astype(np.int)])
expected = np.array([-1., -0.66, -1., 0.66, 1., 1.])
assert_array_almost_equal(clf.decision_function(X), expected, 2)
# kernel binary:
clf = svm.SVC(kernel='rbf', gamma=1, decision_function_shape='ovo')
clf.fit(X, Y)
rbfs = rbf_kernel(X, clf.support_vectors_, gamma=clf.gamma)
dec = np.dot(rbfs, clf.dual_coef_.T) + clf.intercept_
assert_array_almost_equal(dec.ravel(), clf.decision_function(X))
def test_spectral_embedding_callable_affinity(seed=36):
# Test spectral embedding with callable affinity
gamma = 0.9
kern = rbf_kernel(S, gamma=gamma)
se_callable = SpectralEmbedding(
n_components=2,
affinity=(lambda x: rbf_kernel(x, gamma=gamma)),
gamma=gamma,
random_state=np.random.RandomState(seed),
)
se_rbf = SpectralEmbedding(n_components=2, affinity="rbf", gamma=gamma, random_state=np.random.RandomState(seed))
embed_rbf = se_rbf.fit_transform(S)
embed_callable = se_callable.fit_transform(S)
assert_array_almost_equal(se_callable.affinity_matrix_, se_rbf.affinity_matrix_)
assert_array_almost_equal(kern, se_rbf.affinity_matrix_)
assert_true(_check_with_col_sign_flipping(embed_rbf, embed_callable, 0.05))
def _apply_kernel(self, x, y):
"""Apply the selected kernel function to the data."""
if self.kernel == 'linear':
phi = linear_kernel(x, y)
elif self.kernel == 'rbf':
phi = rbf_kernel(x, y, self.coef1)
elif self.kernel == 'poly':
phi = polynomial_kernel(x, y, self.degree, self.coef1, self.coef0)
elif callable(self.kernel):
phi = self.kernel(x, y)
if len(phi.shape) != 2:
raise ValueError(
"Custom kernel function did not return 2D matrix"
)
if phi.shape[0] != x.shape[0]:
raise ValueError(
"Custom kernel function did not return matrix with rows"
" equal to number of data points."""
)
else:
raise ValueError("Kernel selection is invalid.")
if self.bias_used:
phi = np.append(phi, np.ones((phi.shape[0], 1)), axis=1)
return phi
def predict(X,y,gamma):
K = rbf_kernel(X.reshape(-1,1),X.reshape(-1,1),gamma)
pred = (K * y[:, None]).sum(axis=0) / K.sum(axis=0)
return pred
def fit(self, X, y, L):
"""Fit the model according to the given training data.
Prameters
---------
X : array-like, shpae = [n_samples, n_features]
Training data.
y : array-like, shpae = [n_samples]
Target values (unlabeled points are marked as 0).
L : array-like, shpae = [n_samples, n_samples]
Graph Laplacian.
"""
labeled = y != 0
y_labeled = y[labeled]
n_samples, n_features = X.shape
n_labeled_samples = y_labeled.size
I = sp.eye(n_samples)
J = sp.diags(labeled.astype(np.float64))
K = rbf_kernel(X, gamma=self.gamma_k)
M = J @ K \
+ self.gamma_a * n_labeled_samples * I \
+ self.gamma_i * n_labeled_samples / n_samples**2 * L**self.p @ K
# Train a classifer
self.dual_coef_ = LA.solve(M, y)
return self
def _get_affinity_matrix(self, X, Y=None):
"""Calculate the affinity matrix from data
Parameters
----------
X : array-like, shape (n_samples, n_features)
Training vector, where n_samples in the number of samples
and n_features is the number of features.
If affinity is "precomputed"
X : array-like, shape (n_samples, n_samples),
Interpret X as precomputed adjacency graph computed from
samples.
Returns
-------
affinity_matrix, shape (n_samples, n_samples)
"""
if self.affinity == 'precomputed':
self.affinity_matrix_ = X
print( type( self.affinity_matrix_))
return self.affinity_matrix_
# nearest_neigh kept for backward compatibility
if self.affinity == 'nearest_neighbors':
if sparse.issparse(X):
warnings.warn("Nearest neighbors affinity currently does "
"not support sparse input, falling back to "
"rbf affinity")
self.affinity = "rbf"
else:
self.n_neighbors_ = (self.n_neighbors
if self.n_neighbors is not None
else max(int(X.shape[0] / 10), 1))
self.affinity_matrix_ = kneighbors_graph(X, self.n_neighbors_)
# currently only symmetric affinity_matrix supported
self.affinity_matrix_ = 0.5 * (self.affinity_matrix_ +
self.affinity_matrix_.T)
return self.affinity_matrix_
if self.affinity == 'radius_neighbors':
if self.neighbors_radius is None:
self.neighbors_radius_ = np.sqrt(X.shape[1])
# to put another defaault value, like diam(X)/sqrt(dimensions)/10
else:
self.neighbors_radius_ = self.neighbors_radius
self.gamma_ = (self.gamma
if self.gamma is not None else 1.0 / X.shape[1])
self.affinity_matrix_ = radius_neighbors_graph(X, self.neighbors_radius_, mode='distance')
self.affinity_matrix_.data **= 2
self.affinity_matrix_.data /= -self.neighbors_radius_**2
self.affinity_matrix_.data = np.exp( self.affinity_matrix_.data, self.affinity_matrix_.data )
return self.affinity_matrix_
if self.affinity == 'rbf':
self.gamma_ = (self.gamma
if self.gamma is not None else 1.0 / X.shape[1])
self.affinity_matrix_ = rbf_kernel(X, gamma=self.gamma_)
return self.affinity_matrix_
self.affinity_matrix_ = self.affinity(X)
return self.affinity_matrix_
def __kernel_definition__(self):
if self.Kf == 'rbf':
return lambda X,Y : rbf_kernel(X,Y,self.rbf_gamma)
if self.Kf == 'poly':
return lambda X,Y : polynomial_kernel(X, Y, degree=self.poly_deg, gamma=None, coef0=self.poly_coeff)
if self.Kf == None or self.Kf == 'linear':
return lambda X,Y : linear_kernel(X,Y)
def calculate_affinities(data, neighborhood, sigma):
"""
Calculates pairwise affinities for the data.
Parameters
----------
data : array, shape (N, M)
Matrix of M-dimensional data points.
neighborhood : float
L2 distance threshold for computing affinities, anything outside of this
threshold is set to 0.
sigma : float
Sigma value for computing affinities.
Returns
-------
affinities : array, shape (N, N)
Pairwise affinities for all data points.
"""
affinities = pairwise.rbf_kernel(data, data, gamma = (1.0 / (2 * sigma * sigma)))
distances = pairwise.pairwise_distances(data)
# affinities and distances are the same dimensionality: (N, N)
affinities[np.where(distances > neighborhood)] = 0.0
return affinities
def test_spectral_embedding_deterministic():
# Test that Spectral Embedding is deterministic
random_state = np.random.RandomState(36)
data = random_state.randn(10, 30)
sims = rbf_kernel(data)
embedding_1 = spectral_embedding(sims)
embedding_2 = spectral_embedding(sims)
assert_array_almost_equal(embedding_1, embedding_2)
def test_pairwise_kernels_callable():
# Test the pairwise_kernels helper function
# with a callable function, with given keywords.
rng = np.random.RandomState(0)
X = rng.random_sample((5, 4))
Y = rng.random_sample((2, 4))
metric = callable_rbf_kernel
kwds = {'gamma': 0.1}
K1 = pairwise_kernels(X, Y=Y, metric=metric, **kwds)
K2 = rbf_kernel(X, Y=Y, **kwds)
assert_array_almost_equal(K1, K2)
# callable function, X=Y
K1 = pairwise_kernels(X, Y=X, metric=metric, **kwds)
K2 = rbf_kernel(X, Y=X, **kwds)
assert_array_almost_equal(K1, K2)
def test_laplacian_eigenmap_deterministic():
# Test that laplacian eigenmap is deterministic
random_state = np.random.RandomState(36)
data = random_state.randn(10, 30)
sims = rbf_kernel(data)
embedding_1 = laplacian_eigenmap(sims)
embedding_2 = laplacian_eigenmap(sims)
assert_array_almost_equal(embedding_1, embedding_2)
def test_spectral_embeding_import():
random_state = np.random.RandomState(36)
data = random_state.randn(10, 30)
sims = rbf_kernel(data)
assert_warns_message(DeprecationWarning, "spectral_embedding is deprecated",
spectral_embedding, sims)
assert_warns_message(DeprecationWarning, "SpectralEmbedding is deprecated",
SpectralEmbedding)
def decision_function(self, X):
if self.kernel == 'linear':
f = np.dot(X, self._w) + self._b
elif self.kernel == 'rbf':
## rbf_kernel returns array of shape (n_samples_X, n_samples_Y)
assert self._ya.shape == (len(self._X), 1)
f = np.sum(np.multiply(rbf_kernel(self._X, X), self._ya), axis=0) + self._b
f = np.squeeze(np.array(f))
return f
def test_spectral_embedding_precomputed_affinity(seed=36):
# Test spectral embedding with precomputed kernel
gamma = 1.0
se_precomp = SpectralEmbedding(n_components=2, affinity="precomputed", random_state=np.random.RandomState(seed))
se_rbf = SpectralEmbedding(n_components=2, affinity="rbf", gamma=gamma, random_state=np.random.RandomState(seed))
embed_precomp = se_precomp.fit_transform(rbf_kernel(S, gamma=gamma))
embed_rbf = se_rbf.fit_transform(S)
assert_array_almost_equal(se_precomp.affinity_matrix_, se_rbf.affinity_matrix_)
assert_true(_check_with_col_sign_flipping(embed_precomp, embed_rbf, 0.05))
def fit(self, X, y):
t = time() # get labels for test data
# build the graph result is the affinity matrix
if self.kernel is 'dbscan' or self.kernel is None:
affinity_matrix = self.dbscan(X, self.eps, self.minPts)
# it is possible to use other kernels -> as parameter
elif self.kernel is 'rbf':
affinity_matrix = rbf_kernel(X, X, gamma=self.gamma)
elif self.kernel is 'knn':
affinity_matrix = NearestNeighbors(self.naighbors).fit(X).kneighbors_graph(X, self.naighbors).toarray()
else:
raise
print( "praph(%s) time %2.3fms"%(self.kernel, (time() - t) *1000))
if affinity_matrix.max() == 0 :
print("no affinity matrix found")
return y
degree_martix = np.diag(affinity_matrix.sum(axis=0))
affinity_matrix = np.matrix(affinity_matrix)
try:
inserve_degree_matrix = np.linalg.inv(degree_martix)
except np.linalg.linalg.LinAlgError as err:
if 'Singular matrix' in err.args:
# use a pseudo inverse if it's not possible to make a normal of the degree matrix
inserve_degree_matrix = np.linalg.pinv(degree_martix)
else:
raise
matrix = inserve_degree_matrix * affinity_matrix
# split labels in different vectors to calculate the propagation for the separate label
labels = np.unique(y)
labels = [x for x in labels if x != self.unlabeledValue]
# init the yn1 and y0
y0 = [[1 if (x == l) else 0 for x in y] for l in labels]
yn1 = y0
# function to set the probability to 1 if it was labeled in the source
toOrgLabels = np.vectorize(lambda x, y : 1 if y == 1 else x , otypes=[np.int0])
# function to set the index's of the source labeled
toOrgLabelsIndex = np.vectorize(lambda x, y, z : z if y == 1 else x , otypes=[np.int0])
lastLabels = np.argmax(y0, axis=0)
while True:
yn1 = yn1 * matrix
#first matrix to labels
ynLablesIndex = np.argmax(yn1, axis=0)
# row-normalize
yn1 /= yn1.max()
yn1 = toOrgLabels(yn1, y0)
for x in y0:
ynLablesIndex = toOrgLabelsIndex(ynLablesIndex, x, y0.index(x))
#second original labels to result
if np.array_equiv(ynLablesIndex, lastLabels):
break
lastLabels = ynLablesIndex
# result is the index of the labels -> cast index to the given labels
toLabeles = np.vectorize(lambda x : labels[x])
return np.array(toLabeles(lastLabels))[0]
def cls(mkl):
for data in datasets:
print "####################"
print '# ',data
print "####################"
# consider labels with more than 2%
t = 0.02
datadir = '../data/'
km_dir = datadir + data + "/"
if data == 'Fingerprint':
kernels = ['PPKr', 'NB','CP2','NI','LB','CPC','RLB','LC','LI','CPK','RLI','CSC']
km_list = []
y = np.loadtxt(km_dir+"y.txt",ndmin=2)
p = np.sum(y==1,0)/float(y.shape[0])
y = y[:,p>t]
for k in kernels:
km_f = datadir + data + ("/%s.txt" % k)
km_list.append(center(normalize_km(np.loadtxt(km_f))))
pred_f = "../ovkr_result/pred/%s_cvpred_%s.npy" % (data, mkl)
pred = ovkr_mkl(km_list, y, mkl, 5, data,data)
np.save(pred_f, pred)
elif data in image_datasets:
y = np.loadtxt(km_dir+"y.txt",ndmin=2)
p = np.sum(y==1,0)/float(y.shape[0])
y = y[:,p>t]
linear_km_list = []
for i in range(1,16):
name = 'kernel_linear_%d.txt' % i
km_f = km_dir+name
km = np.loadtxt(km_f)
# normalize input kernel !!!!!!!!
linear_km_list.append(center(normalize_km(km)))
pred_f = "../ovkr_result/pred/%s_cvpred_%s.npy" % (data, mkl)
pred = ovkr_mkl(linear_km_list, y, mkl, 5, data,data)
np.save(pred_f, pred)
else:
rbf_km_list = []
gammas = [2**-13,2**-11,2**-9,2**-7,2**-5,2**-3,2**-1,2**1,2**3]
X = np.loadtxt(km_dir+"/x.txt")
scaler = preprocessing.StandardScaler().fit(X)
X = scaler.transform(X)
X = preprocessing.normalize(X)
y = np.loadtxt(km_dir+"y.txt")
p = np.sum(y==1,0)/float(y.shape[0])
y = y[:,p>t]
for gamma in gammas:
km = rbf_kernel(X, gamma=gamma)
# normalize input kernel !!!!!!!!
rbf_km_list.append(center(km))
pred_f = "../ovkr_result/pred/%s_cvpred_%s.npy" % (data, mkl)
pred = ovkr_mkl(rbf_km_list, y, mkl, 5, data,data)
np.save(pred_f, pred)
def test_svr_predict():
# Test SVR's decision_function
# Sanity check, test that predict implemented in python
# returns the same as the one in libsvm
X = iris.data
y = iris.target
# linear kernel
reg = svm.SVR(kernel='linear', C=0.1).fit(X, y)
dec = np.dot(X, reg.coef_.T) + reg.intercept_
assert_array_almost_equal(dec.ravel(), reg.predict(X).ravel())
# rbf kernel
reg = svm.SVR(kernel='rbf', gamma=1).fit(X, y)
rbfs = rbf_kernel(X, reg.support_vectors_, gamma=reg.gamma)
dec = np.dot(rbfs, reg.dual_coef_.T) + reg.intercept_
assert_array_almost_equal(dec.ravel(), reg.predict(X).ravel())
def test_average_dist(self) : # 3 samples a = [1, 3] b = [0, 4] c = [2, 5] samples = np.array([a, b, c]) dist = al.average_distance(samples) avg_a = (rbf_kernel([a], [b])[0][0] + rbf_kernel([a], [c])[0][0])/2 avg_b = (rbf_kernel([b], [a])[0][0] + rbf_kernel([b], [c])[0][0])/2 avg_c = (rbf_kernel([c], [a])[0][0] + rbf_kernel([c], [b])[0][0])/2 self.assertAlmostEqual(dist[0],avg_a) self.assertAlmostEqual(dist[1],avg_b) self.assertAlmostEqual(dist[2],avg_c)
def test_kernel(self):
# compute kernel with special rbf kernel
# compute kernel with sklearn kernel
# compute kernel between sparse_data_ and sparse_data
# compute_kernel between sparse_data and data
# compute kernel between sparse_data and random_data
# compute_kernel between data and random_data
# sklearn_kernel_first = rbf_kernel(self.data, self.data, self.gamma)
# sklearn_kernel_verylittle = rbf_kernel(self.data_verylittle, self.data_verylittle)
for name_pair, pair in self.pairs_data.items():
data_norm = self.norm_data[name_pair]
gamma = self.gamma_data[name_pair]
sklearn_kernel = rbf_kernel(pair, pair, gamma=gamma)
special_kernel = special_rbf_kernel(pair,
pair,
gamma=gamma,
norm_X=data_norm,
norm_Y=data_norm.T,
exp_outside=False)
special_kernel_flag = special_rbf_kernel(pair,
pair,
gamma=gamma,
norm_X=data_norm,
norm_Y=data_norm.T,
exp_outside=True)
special_kernel[special_kernel < 1e-12] = 0
special_kernel_flag[special_kernel_flag < 1e-12] = 0
sklearn_kernel[sklearn_kernel < 1e-12] = 0
equality = np.allclose(sklearn_kernel, special_kernel)
equality_flag = np.allclose(sklearn_kernel, special_kernel_flag)
delta = np.linalg.norm(special_kernel - sklearn_kernel)
delta_flag = np.linalg.norm(special_kernel_flag - sklearn_kernel)
print("Delta flag: {}; delta: {}".format(delta_flag, delta))
self.assertTrue(delta_flag < delta)
self.assertTrue(equality, msg=name_pair)
self.assertTrue(equality_flag, msg=name_pair)
def get_kernel_matrix(X1, X2=None, kernel='rbf',gamma = 1, degree = 3, coef0=1):
#Obtain N1xN2 kernel matrix from N1xM and N2xM data matrices
if kernel == 'rbf':
K = pairwise.rbf_kernel(X1,X2,gamma = gamma);
elif kernel == 'poly':
K = pairwise.polynomial_kernel(X1,X2,degree = degree, gamma = gamma,
coef0 = coef0);
elif kernel == 'linear':
K = pairwise.linear_kernel(X1,X2);
elif kernel == 'laplacian':
K = pairwise.laplacian_kernel(X1,X2,gamma = gamma);
elif kernel == 'chi2':
K = pairwise.chi2_kernel(X1,X2,gamma = gamma);
elif kernel == 'additive_chi2':
K = pairwise.additive_chi2_kernel(X1,X2);
elif kernel == 'sigmoid':
K = pairwise.sigmoid_kernel(X1,X2,gamma = gamma,coef0 = coef0);
else:
print('[Error] Unknown kernel');
K = None;
return K;
def test_fastfood():
"""test that Fastfood fast approximates kernel on random data"""
# compute exact kernel
gamma = 10.
kernel = rbf_kernel(X, Y, gamma=gamma)
sigma = np.sqrt(1 / (2 * gamma))
# approximate kernel mapping
ff_transform = Fastfood(sigma, n_components=1000, random_state=42)
pars = ff_transform.fit(X)
X_trans = pars.transform(X)
Y_trans = ff_transform.transform(Y)
# print X_trans, Y_trans
kernel_approx = np.dot(X_trans, Y_trans.T)
print('approximation:', kernel_approx[:5, :5])
print('true kernel:', kernel[:5, :5])
assert_array_almost_equal(kernel, kernel_approx, decimal=1)
def _kernel(data, centers):
"""
Euclidean distance from each point to each cluster center.
Parameters
----------
data : 2d array (N x Q)
Data to be analyzed. There are N data points.
centers : 2d array (C x Q)
Cluster centers. There are C clusters, with Q features.
Returns
-------
dist : 2d array (C x N)
Euclidean distance from each point, to each cluster center.
See Also
--------
scipy.spatial.distance.cdist
"""
return rbf_kernel(data, centers, gamma=0.01).T
def __kernel_definition__(self):
"""Select the kernel function
Returns
-------
kernel : a callable relative to selected kernel
"""
if hasattr(self.kernel, '__call__'):
return self.kernel
if self.kernel == 'rbf' or self.kernel == None:
return lambda X, Y: rbf_kernel(X, Y, self.rbf_gamma)
if self.kernel == 'poly':
return lambda X, Y: polynomial_kernel(X,
Y,
degree=self.degree,
gamma=self.rbf_gamma,
coef0=self.coef0)
if self.kernel == 'linear':
return lambda X, Y: linear_kernel(X, Y)
if self.kernel == 'precomputed':
return lambda X, Y: X
def test_spectral_embedding_unnormalized():
# Test that spectral_embedding is also processing unnormalized laplacian
# correctly
random_state = np.random.RandomState(36)
data = random_state.randn(10, 30)
sims = rbf_kernel(data)
n_components = 8
embedding_1 = spectral_embedding(sims,
norm_laplacian=False,
n_components=n_components,
drop_first=False)
# Verify using manual computation with dense eigh
laplacian, dd = sparse.csgraph.laplacian(sims,
normed=False,
return_diag=True)
_, diffusion_map = eigh(laplacian)
embedding_2 = diffusion_map.T[:n_components] * dd
embedding_2 = _deterministic_vector_sign_flip(embedding_2).T
assert_array_almost_equal(embedding_1, embedding_2)
def similarity_regression(X, y, n_neighbors=None):
"""
Calculates similarity based on labels using X (data) y (labels)
this considers X, by use knn first and then a distance metric - in this setting
we will use the rbf kernel for similarity.
Then if X is "far" in the knn sense we will set to 0
we can determine "distance" based on clusters? that is if we build
a cluster around this obs, which other observations are closest.
"""
from sklearn.neighbors import NearestNeighbors
if n_neighbors is None:
n_neighbors = max(int(X.shape[0] * 0.05)+1, 2)
# use NerestNeighbors to determine closest obs
y_ = np.array(y).reshape(-1,1)
nbrs = NearestNeighbors(n_neighbors=n_neighbors, algorithm='auto').fit(y_)
return np.multiply(nbrs.kneighbors_graph(y_).toarray(), rbf_kernel(X, gamma=1))
def MAO_lambda_Diversity(idx, yp, ssc_method="none", lam=0.6):
# MAO lambda: trade-off between uncertainty and diversity
K = rbf_kernel(active.xunlab, gamma=active.gamma) #provisional kernel
Sidx = np.zeros(query_points, dtype=type(idx[0]))
for j in np.arange(query_points):
# Add the first point, and remove it from pool
Sidx[j] = idx[0]
idx = idx[1:]
# Compute distances (kernel matrix)
# Distances between selected samples (Sidx) and the rest (idx)
Kdist = np.abs(K[Sidx[0:j + 1], :][:, idx])
# Obtain the minimum distance for each column
Kdist = Kdist.min(axis=0)
# Trade-off between AL algorithm and Diversity
if ssc_method == "ssc":
heuristic = yp[idx, -1] * lam + Kdist * (1 - lam)
elif ssc_method == "none":
heuristic = yp[idx] * lam + Kdist * (1 - lam)
idx = idx[heuristic.argsort()] # axis=0
# Move selected samples from unlabeled set to labeled set
return active.updateLabels(Sidx)
def kernel(x, k=0):
n = len(x)
# create matrices A, D and L
A = rbf_kernel(x, gamma=0.55)
A[np.arange(n), np.arange(n)] = 0
D = np.diag(A.sum(axis=0)**(-0.5))
L = D @ A @ D
# find eigenpairs and take the k biggest ones
l, v = eig(L)
i = np.flip(l.argsort())
k = k or find_gap(l[i])
i = i[:k]
# create new, normalised representation of data points
x_ = v[:, i]
n = norm(x_, axis=1, keepdims=True)
x_ = x_ / n
k = linear_kernel(x_)
return k
def transform(self, X):
nt = X.shape[0]
if self._kernel_type == 'rbf':
K = rbf_kernel(X, self._X, gamma=self._gamma)
elif self._kernel_type == 'poly':
K = polynomial_kernel(X,
self._X,
degree=self._degree,
coef0=self._coef0)
elif self._kernel_type == 'linear':
K = linear_kernel(X, self._X)
if self._centred == True:
"""
YOUR CODE
"""
K1 = (K - 1. / self._n * np.ones((nt, self._n)).dot(self._K))
K2 = np.eye(self._n) - 1. / self._n * np.ones((self._n, self._n))
Ko = K1.dot(K2)
else:
Ko = K
return Ko
def _rbf_kernel(self, data_validation, data_training):
"""Radial basis function
Parameters
----------
data_validation : ndarray
Validation data
data_training : ndarray
Training data
Returns
-------
kernel : ndarray
Kernel similarity matrix
"""
if isinstance(self.gamma, str):
gamma = 1 / data_training.shape[1]
else:
gamma = self.gamma
return rbf_kernel(data_validation, data_training, gamma)
def get_RBF(A, s=1.):
""" Compute radial basis function kernel.
Parameters:
A -- Feature matrix.
s -- Scale parameter (positive float, 1.0 by default).
Return:
K -- Radial basis function kernel matrix.
"""
from sklearn.metrics.pairwise import euclidean_distances, rbf_kernel
from sklearn.preprocessing import scale
A = scale(A)
dist_matrix = euclidean_distances(A, A, None, squared=True)
dist_vector = dist_matrix[np.nonzero(np.tril(dist_matrix))]
dist_median = np.median(dist_vector)
K = rbf_kernel(A, None, dist_median * s)
return K
def extract_batch(self, inp, idx_i, idx_j, batch_X):
if self.cached_rawbatch is None or self.cached_rawbatch.shape[
0] < batch_X.shape[0]:
self.cached_rawbatch = np.zeros((batch_X.shape[0], len(self.fext)),
self.fext.dtype)
rawbatch = self.cached_rawbatch
else:
rawbatch = self.cached_rawbatch[:idx_i.shape[0]]
self.fext.extract_batch(inp, idx_i, idx_j, rawbatch)
Xscaled = rawbatch.astype(np.float64)
Xscaled -= self.mean
Xscaled /= self.std
if self.kernel == 'poly':
K_y = fast_poly_kernel(Xscaled, self.basis,
degree=self.degree).astype(self.dtype)
else:
K_y = rbf_kernel(Xscaled, self.basis,
gamma=self.gamma).astype(self.dtype)
batch_X[:] = self.phi_map.dot(K_y.T).T
def Gram_Matrix(Kernel, X_set, Degree, Gamma):
print("Computing Gram Matrix...")
Gram = np.zeros(shape=(X_set.shape[0], X_set.shape[0]))
for i in range(0, (X_set.shape[0])):
for j in range(0, (X_set.shape[0])):
if Kernel == 'poly':
Gram[i, j] = polynomial_kernel(X_set[i], X_set[j], Degree)
elif Kernel == 'rbf':
Gram[i, j] = rbf_kernel(X_set[i], X_set[j], Gamma)
elif Kernel == 'linear':
Gram[i, j] = polynomial_kernel(X_set[i],
X_set[j],
Degree,
coef0=0)
#Use following instruction to fix Gram matrix symmetric problem
Gram = np.maximum(Gram, Gram.transpose())
#Use following instruction to fix CPLEX Error 5002 (objective is not convex)
if set_kernel == 'poly' or set_kernel == 'rbf':
Gram = Gram + np.identity(Gram.shape[1])
print("Done")
return Gram
def choose_article(self, selected_user, article_pool, time): rbf_row=rbf_kernel(self.user_features[selected_user].reshape(1,-1), self.user_features) neighbors=np.argsort(rbf_row)[0][self.user_num-self.k:] #neighbors=self.neighbors[selected_user] neighbors=list(set(neighbors)&set(self.served_users)) if (len(neighbors)==0): self.user_cluster_features[selected_user]=self.user_features[selected_user] else: if (len(neighbors)==1): weights=[1] else: weights=rbf_row[0][neighbors]/np.sum(rbf_row[0][neighbors]) self.user_cluster_features[selected_user]=np.average(self.user_features[neighbors], weights=weights, axis=0) mean=np.dot(self.artificial_article_features[article_pool], self.user_cluster_features[selected_user]) temp1=np.dot(self.artificial_article_features[article_pool], np.linalg.inv(self.cluster_cor_matrix[selected_user])) temp2=np.sum(temp1*self.artificial_article_features[article_pool], axis=1)*np.log(time+1) var=np.sqrt(temp2) pta=mean+self.alpha*var article_picked=np.argmax(pta) article_picked=article_pool[article_picked] return article_picked, neighbors
def load_data(self, X, y, gamma=None, docalkernel=False, savefile=None, testfile=None, dobin=False):
self.X = X
if dobin:
bins = [-1.0, -0.67, -0.33, 0, 0.33, 0.67, 1.0]
# bins = [-1.0, 0, 1.0]
binned = np.digitize(self.X, bins )
self.X=np.array([bins[binned[i, j] - 1] for i in range(np.shape(self.X)[0]) for j in range(np.shape(self.X)[1])]).reshape(np.shape(self.X))
self.y = y
if testfile is not None:
dat2 = load_svmlight_file(testfile)
self.testX = dat2[0].todense()
if dobin:
bins = [-1.0, -0.67, -0.33, 0, 0.33, 0.67, 1.0]
binned = np.digitize(self.testX, bins)
self.testX = np.array([bins[binned[i, j] - 1] for i in range(np.shape(self.testX)[0]) for j in range(np.shape(self.testX)[1])]).reshape(np.shape(self.testX))
self.testy = dat2[1]
# print np.shape(self.X)
self.gamma = gamma
self.kernel = rbf_kernel(self.X, gamma=gamma)
def lalign_kernel(X, y, kernel="rbf", alpha=2, sigma=5):
# X: np array of shape (n_samples, n_features) where n_pos is the nb of positives per samples
# returns E_(x,x')~p (kernel(y, y') * ||f(x) - f(x')||_2**alpha)
from sklearn.metrics import pairwise_distances
from sklearn.metrics.pairwise import rbf_kernel
if kernel == "rbf":
kernel = lambda y1, y2: rbf_kernel(y1, y2, gamma=1. / (2 * sigma**2))
else:
assert hasattr(kernel, '__call__'), 'kernel must be a callable'
if len(X.shape) == 3:
# Merges the first 2 dimensions
y = y.reshape(y.shape[0] * y.shape[1], -1)
X = X.reshape(X.shape[0] * X.shape[1], -1)
assert len(y) == len(X)
weights = kernel(y, y) # (n_samples, n_samples)
weights = (1 - np.eye(len(weights))) * weights
weights /= weights.sum(axis=1)
dist_matrix = pairwise_distances(
X / np.linalg.norm(X, 2, axis=1, keepdims=True),
metric='euclidean')**alpha
dist = (dist_matrix * weights).sum() / weights.sum()
return dist
def prepare(self, X, y, gamma=0.7, δ_p=1e-6, δ_n=1e-6):
'''
compute extra information for gaussian kernel method
Parameters:
X(np.array): 2D matrix containing the whole dataset, rows are samples, columns are variables
y(np.array): 1D array containing the labels of the whole dataset
kernel(bool): a switch that determines if parameters for kenerl method will be computed
gamma(float): a constant used in the rbf kernel, check sklearn.metrics.pairwise.rbf_kernel
δ_p/δ_n (float): regularization terms that ensures the S++ of the kernel covaiance matrix F
'''
X_p, y_p, w_p, X_n, y_n, w_n = super().prepare(X, y)
self.gamma = gamma
self.m_p = len(y_p)
self.m_n = len(y_n)
self.J_p = np.zeros((self.m_p + self.m_n, self.m_p + self.m_n))
self.J_p[0:self.m_p, 0:self.m_p] = 1 / np.sqrt(
self.m_p) * (np.identity(self.m_p) - 1 / self.m_p * np.ones(
(self.m_p, self.m_p)))
self.J_n = np.zeros((self.m_p + self.m_n, self.m_p + self.m_n))
self.J_n[self.m_p:, self.m_p:] = 1 / np.sqrt(
self.m_n) * (np.identity(self.m_n) - 1 / self.m_n * np.ones(
(self.m_n, self.m_n)))
self.g_p = np.zeros(self.m_p + self.m_n)
self.g_p[0:self.m_p] = 1 / self.m_p * np.ones(self.m_p)
self.g_n = np.zeros(self.m_p + self.m_n)
self.g_n[self.m_p:] = 1 / self.m_n * np.ones(self.m_n)
self.X_combine = np.append(X_p, X_n, axis=0)
self.G = rbf_kernel(X=self.X_combine,
Y=self.X_combine,
gamma=self.gamma)
self.F_p = self.G @ self.J_p @ self.J_p.T @ self.G + δ_p * self.G
self.F_n = self.G @ self.J_n @ self.J_n.T @ self.G + δ_n * self.G
self.F_p_sqrt = np.real(sqrtm(self.F_p))
self.F_n_sqrt = np.real(sqrtm(self.F_n))
# set up varaibles for cvxpy
self.α_kernel = cp.Variable(shape=(len(self.G), 1))
def _build_kernel(x, kernel, gamma=None):
if kernel in {'pearson', 'spearman'}:
if kernel == 'spearman':
x = np.apply_along_axis(rankdata, 1, x)
return np.corrcoef(x)
if kernel in {'cosine', 'normalized_angle'}:
x = 1 - squareform(pdist(x, metric='cosine'))
if kernel == 'normalized_angle':
x = 1 - np.arccos(x, x) / np.pi
return x
if kernel == 'gaussian':
if gamma is None:
gamma = 1 / x.shape[1]
return rbf_kernel(x, gamma=gamma)
if callable(kernel):
return kernel(x)
raise ValueError("Unknown kernel '{0}'.".format(kernel))
def bourgain_embedding_matrix(distance_matrix):
distance_matrix = np.array(distance_matrix)
n = len(distance_matrix)
if n == 1:
return distance_matrix
np.random.seed(123)
distort_elements = []
r = range(n)
k = int(math.ceil(math.log(n) / math.log(2) - 1))
t = int(math.ceil(math.log(n)))
counter = 0
for i in range(0, k + 1):
for t in range(t):
s = np.random.choice(r, 2**i)
for j in r:
d = min([distance_matrix[j][s] for s in s])
counter += len(s)
if i == 0 and t == 0:
distort_elements.append([d])
else:
distort_elements[j].append(d)
return rbf_kernel(distort_elements, distort_elements)
def estimate_density(self, X):
model = self.model
if self.algo == 'kde':
# model : kde scikit-learn
self.density = np.exp(model.score_samples(X))
elif self.algo == 'mom-kde':
# model : list of kdes scikit-learn
z = []
for k in range(len(model)):
kde_k = model[k]
z.append(np.exp(kde_k.score_samples(X)))
self.density = np.median(z, axis=0)
elif self.algo == 'rkde':
# model : weights vector w
n_samples, d = self.X_data.shape
m = X.shape[0]
K_plot = np.zeros((m, n_samples))
for i_d in range(d):
temp_xpos = X[:, i_d].reshape((-1, 1))
temp_x = self.X_data[:, i_d].reshape((-1, 1))
K_plot = K_plot + (np.dot(np.ones((m, 1)), temp_x.T) -
np.dot(temp_xpos, np.ones(
(1, n_samples))))**2
K_plot = kde_lib.gaussian_kernel(K_plot, self.bandwidth, d)
z = np.dot(K_plot, model)
self.density = z
elif self.algo == 'spkde':
# model : weights vector a
d = self.X_data.shape[1]
gamma = 1. / (2 * (self.bandwidth**2))
GG = rbf_kernel(self.X_data, X, gamma=gamma) * (
2 * np.pi * self.bandwidth**2)**(-d / 2.)
z = np.zeros((X.shape[0]))
for j in range(X.shape[0]):
for i in range(len(model)):
z[j] += model[i] * GG[i, j]
self.density = z
else:
print('no algo specified')
def gradForm2(Data, W, w, gamma, K1=None):
# gradient of L= 1/2N (k(x1,x2)-cos(Wx1)cos(Wx2))
import numpy as np
from sklearn.metrics import pairwise
Nexp = np.shape(W)[1]
Ndata, Nfeat = np.shape(Data)
if K1 is None:
K1 = pairwise.rbf_kernel(Data, gamma=gamma)
C = np.zeros((Nfeat, Ndata))
B = np.zeros((Nfeat, Ndata))
for i in range(Ndata):
X = np.tile(Data[i, ], (Ndata, 1))
K = K1[i, :]
K = K[:, np.newaxis]
#
c1 = np.outer(
np.cos(np.dot(Data, w)) * K, np.sin(np.dot(Data[i, ], w)))
c2 = np.outer(
np.sin(np.dot(Data, w)) * K, np.cos(np.dot(Data[i, ], w)))
C[:, i] = np.squeeze((np.dot((X.T), c1) + np.dot((Data.T), c2)))
#
AK = np.dot(np.cos(np.dot(Data[i, ], W)), np.cos(np.dot(Data, W)).T)
AK = AK[:, np.newaxis]
#
b1 = np.outer(
np.cos(np.dot(Data, w)) * AK, np.sin(np.dot(Data[i, ], w)))
b2 = np.outer(
np.sin(np.dot(Data, w)) * AK, np.cos(np.dot(Data[i, ], w)))
B[:, i] = np.squeeze((np.dot((X.T), b1) + np.dot((Data.T), b2)))
#
L = (1.0 / Ndata**2) * (np.sum(C, axis=1) -
(2.0 / Nexp) * np.sum(B, axis=1))
L = L[:, np.newaxis]
return L
def Lossfunction(Data, W, gamma, K=None, w=None):
import numpy as np
from sklearn.metrics import pairwise
if w is None:
W = W
else:
W = np.concatenate((W, w), axis=1)
Nexp = np.shape(W)[1]
Ndata, Nfeat = np.shape(Data)
# if kernel is not provided
if K is None:
K = pairwise.rbf_kernel(Data, gamma=gamma)
Phi = np.cos(np.dot(Data, W))
AK = (2.0 / Nexp) * np.dot(Phi, Phi.T)
L = np.sum((K - AK)**2) / Ndata**2
# L= np.linalg.norm(K-AK)/np.linalg.norm(K)
return L
def kernel_matrix(X, sigma, kernel, pkDegree, c0):
print("Calculating Kernel matrix")
# Value of sigma is very important, and objective of research.Here default value.
# Get dimensions of square distance Matrix N
N = X.shape[0]
# Initialise with zeros Kernel matrix
K = np.zeros((N, N))
if kernel == 'gaussian':
gamma = 0.5 / sigma**2
K = rbf_kernel(X, gamma=gamma)
elif kernel == 'laplacian':
gamma = 1 / sigma
K = laplacian_kernel(X, gamma=gamma)
elif kernel == 'linear':
K = linear_kernel(X)
elif kernel == 'polynomial':
K = polynomial_kernel(X, gamma=sigma, degree=pkDegree, coef0=c0)
return K
def GP(seq_length=30, num_samples=28*5*100, num_signals=1, scale=0.1, kernel='rbf', **kwargs):
# the shape of the samples is num_samples x seq_length x num_signals
samples = np.empty(shape=(num_samples, seq_length, num_signals))
#T = np.arange(seq_length)/seq_length # note, between 0 and 1
T = np.arange(seq_length) # note, not between 0 and 1
if kernel == 'periodic':
cov = periodic_kernel(T)
elif kernel =='rbf':
cov = rbf_kernel(T.reshape(-1, 1), gamma=scale)
else:
raise NotImplementedError
# scale the covariance
cov *= 0.2
# define the distribution
mu = np.zeros(seq_length)
print(np.linalg.det(cov))
distribution = multivariate_normal(mean=np.zeros(cov.shape[0]), cov=cov)
pdf = distribution.logpdf
# now generate samples
for i in range(num_signals):
samples[:, :, i] = distribution.rvs(size=num_samples)
return samples, pdf
def updating_weight(j, weights, X, u, v, m, variances, nominator):
"""
j: weight vector dimension to update
weights: weights vector
X: data sample
u: fuzzy membership degree
v: centroid
m: constant
"""
denominator = 0.0
quantile = np.divide(1, variances[j])
for i in range(v.shape[0]):
k_sum = 0
for k in range(X.shape[0]):
kernel = rbf_kernel(X[k, j].reshape(-1, 1),
v[i, j].reshape(-1, 1),
gamma=quantile)
k_sum += np.multiply(np.power(u[i, k], m),
np.multiply(2, 1 - kernel))
denominator += k_sum
return nominator / denominator
def updating_centroid(i, j, u, X, m, v, variances):
"""
i: cluster position
k: sample position
u: fuzzy membership degree
X: data sample
m: constant
v: centroid
"""
nominators = []
denominators = []
quantile = np.divide(1, variances[j])
for k in range(X.shape[0]):
kernel = rbf_kernel(X[k, j].reshape(-1, 1),
v[i, j].reshape(-1, 1),
gamma=quantile)
nominators.append(
np.multiply(np.multiply(np.power(u[i, k], m), kernel), X[k, j]))
denominators.append(np.multiply(np.power(u[i, k], m), kernel))
nominators = np.array(nominators)
denominators = np.array(denominators)
return nominators.sum() / denominators.sum()
def UPDATE_PROBABILITY_PARTIAL(R, X_train, s):
R = np.array(R)
temp = R
C_pie = rbf_kernel(X_train, X_train[R, :])
k_pie = int(s / 2)
ui_m, s, vt = linalg.svd(C_pie, full_matrices=False)
new_K = (ui_m[:, 0:k_pie]).dot(np.diag(1 / np.sqrt(s[0:k_pie]))).dot(
vt[0:k_pie, :])
C_nys = new_K
E = C_pie - C_nys
temp_p = np.zeros((X_train.shape[0], 1)).reshape(-1, 1)
for j in range(X_train.shape[0]):
if j in temp:
temp_p[j] = 0
else:
temp_p[j] = np.linalg.norm(E[j], ord=2)
P = np.square(temp_p / np.sqrt(np.sum(np.square(temp_p))))
return P