def objective(K, y, alpha, lamda, beta, w):
"""Objective function for lasso kernel learning."""
obj = .5 * sum(squared_norm(
alpha[j].dot(K[j].T.dot(w)) - y[j]) for j in range(len(K)))
obj += lamda * np.abs(w).sum()
obj += beta * sum(squared_norm(a) for a in alpha)
return obj
def _f(x, _Z_0, Z_0, loss_res, nabla_con, nabla_pen, loss_func, S, C):
_Z_0, A = _Z_0(x[0], x[1], Z_0, loss_res, nabla_con, nabla_pen)
loss_res = loss_gen(loss_func, S, _Z_0) - C
# loss_res_A = loss_gen(loss_func, S, A) - C
# return squared_norm(loss_res) + squared_norm(loss_res - loss_res_A)
return squared_norm(loss_res) + squared_norm(_Z_0 - A) / (S.shape[1] *
S.shape[2])
def objective_admm(K, y, alpha, lamda, beta, w, w1, w2):
"""Objective function for lasso kernel learning."""
obj = .5 * sum(squared_norm(
np.dot(alpha[j], K[j].T.dot(w)) - y[j]) for j in range(len(K)))
obj += lamda * np.abs(w1).sum()
obj += beta * squared_norm(w2)
return obj
def objective(K, y, alpha, lamda, beta, w):
"""Objective function for lasso kernel learning."""
obj = .5 * sum(
squared_norm(alpha[j].dot(K[j].T.dot(w)) - y[j])
for j in range(len(K)))
obj += lamda * np.abs(w).sum()
obj += beta * sum(squared_norm(a) for a in alpha)
return obj
def test_norm_squared_norm():
X = np.random.RandomState(42).randn(50, 63)
X *= 100 # check stability
X += 200
assert_almost_equal(np.linalg.norm(X.ravel()), norm(X))
assert_almost_equal(norm(X)**2, squared_norm(X), decimal=6)
assert_almost_equal(np.linalg.norm(X), np.sqrt(squared_norm(X)), decimal=6)
def test_norm_squared_norm():
X = np.random.RandomState(42).randn(50, 63)
X *= 100 # check stability
X += 200
assert_almost_equal(np.linalg.norm(X.ravel()), norm(X))
assert_almost_equal(norm(X) ** 2, squared_norm(X), decimal=6)
assert_almost_equal(np.linalg.norm(X), np.sqrt(squared_norm(X)), decimal=6)
def objective_admm(K, y, alpha, lamda, beta, w, w1, w2):
"""Objective function for lasso kernel learning."""
obj = .5 * sum(
squared_norm(np.dot(alpha[j], K[j].T.dot(w)) - y[j])
for j in range(len(K)))
obj += lamda * np.abs(w1).sum()
obj += beta * squared_norm(w2)
return obj
def _fit_projected_gradient(X, W, H, tol, max_iter, nls_max_iter, alpha,
l1_ratio):
gradW = (np.dot(W, np.dot(H, H.T)) -
safe_sparse_dot(X, H.T, dense_output=True))
gradH = (np.dot(np.dot(W.T, W), H) -
safe_sparse_dot(W.T, X, dense_output=True))
init_grad = squared_norm(gradW) + squared_norm(gradH.T)
# max(0.001, tol) to force alternating minimizations of W and H
tolW = max(0.001, tol) * np.sqrt(init_grad)
tolH = tolW
for n_iter in range(1, max_iter + 1):
# stopping condition as discussed in paper
proj_grad_W = squared_norm(gradW * np.logical_or(gradW < 0, W > 0))
proj_grad_H = squared_norm(gradH * np.logical_or(gradH < 0, H > 0))
if (proj_grad_W + proj_grad_H) / init_grad < tol**2:
break
# update W
Wt, gradWt, iterW = _nls_subproblem(X.T,
H.T,
W.T,
tolW,
nls_max_iter,
alpha=alpha,
l1_ratio=l1_ratio)
W, gradW = Wt.T, gradWt.T
if iterW == 1:
tolW = 0.1 * tolW
# update H
H, gradH, iterH = _nls_subproblem(X,
W,
H,
tolH,
nls_max_iter,
alpha=alpha,
l1_ratio=l1_ratio)
if iterH == 1:
tolH = 0.1 * tolH
H[H == 0] = 0 # fix up negative zeros
if n_iter == max_iter:
Wt, _, _ = _nls_subproblem(X.T,
H.T,
W.T,
tolW,
nls_max_iter,
alpha=alpha,
l1_ratio=l1_ratio)
W = Wt.T
return W, H, n_iter
def _fit_projected_gradient(X, W, H, tol, max_iter, nls_max_iter, alpha,
l1_ratio, sparseness, beta, eta):
"""Compute Non-negative Matrix Factorization (NMF) with Projected Gradient
References
----------
C.-J. Lin. Projected gradient methods for non-negative matrix
factorization. Neural Computation, 19(2007), 2756-2779.
http://www.csie.ntu.edu.tw/~cjlin/nmf/
P. Hoyer. Non-negative Matrix Factorization with Sparseness Constraints.
Journal of Machine Learning Research 2004.
"""
gradW = (np.dot(W, np.dot(H, H.T)) -
safe_sparse_dot(X, H.T, dense_output=True))
gradH = (np.dot(np.dot(W.T, W), H) -
safe_sparse_dot(W.T, X, dense_output=True))
init_grad = squared_norm(gradW) + squared_norm(gradH.T)
# max(0.001, tol) to force alternating minimizations of W and H
tolW = max(0.001, tol) * np.sqrt(init_grad)
tolH = tolW
for n_iter in range(1, max_iter + 1):
# stopping condition
# as discussed in paper
proj_grad_W = squared_norm(gradW * np.logical_or(gradW < 0, W > 0))
proj_grad_H = squared_norm(gradH * np.logical_or(gradH < 0, H > 0))
if (proj_grad_W + proj_grad_H) / init_grad < tol**2:
break
# update W
W, gradW, iterW = _update_projected_gradient_w(X, W, H, tolW,
nls_max_iter, alpha,
l1_ratio, sparseness,
"L2", beta, eta)
if iterW == 1:
tolW = 0.1 * tolW
# update H
H, gradH, iterH = _update_projected_gradient_h(X, W, H, tolH,
nls_max_iter, alpha,
l1_ratio, sparseness,
"L1", beta, eta)
if iterH == 1:
tolH = 0.1 * tolH
H[H == 0] = 0 # fix up negative zeros
if n_iter == max_iter:
W, _, _ = _update_projected_gradient_w(X, W, H, tol, nls_max_iter,
alpha, l1_ratio, sparseness,
"L2", beta, eta)
return W, H, n_iter
def test_norm_squared_norm():
X = np.random.RandomState(42).randn(50, 63)
X *= 100 # check stability
X += 200
assert_almost_equal(np.linalg.norm(X.ravel()), norm(X))
assert_almost_equal(norm(X)**2, squared_norm(X), decimal=6)
assert_almost_equal(np.linalg.norm(X), np.sqrt(squared_norm(X)), decimal=6)
# Check the warning with an int array and np.dot potential overflow
assert_warns_message(
UserWarning, 'Array type is integer, np.dot may '
'overflow. Data should be float type to avoid this issue',
squared_norm, X.astype(int))
def test_norm_squared_norm():
X = np.random.RandomState(42).randn(50, 63)
X *= 100 # check stability
X += 200
assert_almost_equal(np.linalg.norm(X.ravel()), norm(X))
assert_almost_equal(norm(X) ** 2, squared_norm(X), decimal=6)
assert_almost_equal(np.linalg.norm(X), np.sqrt(squared_norm(X)), decimal=6)
# Check the warning with an int array and np.dot potential overflow
assert_warns_message(
UserWarning, 'Array type is integer, np.dot may '
'overflow. Data should be float type to avoid this issue',
squared_norm, X.astype(int))
def _objective_func(self, w):
bias, wf = self._split_coefficents(w)
l_plus, xv_plus, l_minus, xv_minus = self._counter.calculate(wf) # pylint: disable=unused-variable
xw = self._xw
val = 0.5 * squared_norm(wf)
if self._has_time:
val += 0.5 * self._regr_penalty * squared_norm(self.y_compressed - bias
- xw.compress(self.regr_mask, axis=0))
val += 0.5 * self._rank_penalty * numexpr.evaluate(
'sum(xw * ((l_plus + l_minus) * xw - xv_plus - xv_minus - 2 * (l_minus - l_plus)) + l_minus)')
return val
def _objective_func(self, w):
bias, wf = self._split_coefficents(w)
l_plus, xv_plus, l_minus, xv_minus = self._counter.calculate(wf)
xw = self._xw
val = 0.5 * squared_norm(wf)
if self._has_time:
val += 0.5 * self._regr_penalty * squared_norm(self.y_compressed - bias
- xw.compress(self.regr_mask, axis=0))
val += 0.5 * self._rank_penalty * numexpr.evaluate(
'sum(xw * ((l_plus + l_minus) * xw - xv_plus - xv_minus - 2 * (l_minus - l_plus)) + l_minus)')
return val
def _beta_divergence(X, W, H, square_root=False):
"""Compute the beta-divergence of X and dot(W, H).
Parameters
----------
X : float or array-like, shape (n_samples, n_features)
W : float or dense array-like, shape (n_samples, n_components)
H : float or dense array-like, shape (n_components, n_features)
square_root : boolean, default False
If True, return np.sqrt(2 * res)
Returns
-------
res : float
Beta divergence of X and np.dot(X, H)
"""
if not sp.issparse(X):
X = np.atleast_2d(X)
W = np.atleast_2d(W)
H = np.atleast_2d(H)
# Avoid the creation of the dense np.dot(W, H) if X is sparse.
if sp.issparse(X):
norm_X = np.dot(X.data, X.data)
norm_WH = trace_dot(np.dot(np.dot(W.T, W), H), H)
cross_prod = trace_dot((X * H.T), W)
res = (norm_X + norm_WH - 2. * cross_prod) / 2
else:
res = squared_norm(X - np.dot(W, H)) / 2
if square_root:
return np.sqrt(res * 2)
else:
return res
def _beta_divergence_dense(X, W, H, beta):
"""Compute the beta-divergence of X and W.H for dense array only.
Used as a reference for testing nmf._beta_divergence.
"""
WH = np.dot(W, H)
if beta == 2:
return squared_norm(X - WH) / 2
WH_Xnonzero = WH[X != 0]
X_nonzero = X[X != 0]
np.maximum(WH_Xnonzero, 1e-9, out=WH_Xnonzero)
if beta == 1:
res = np.sum(X_nonzero * np.log(X_nonzero / WH_Xnonzero))
res += WH.sum() - X.sum()
elif beta == 0:
div = X_nonzero / WH_Xnonzero
res = np.sum(div) - X.size - np.sum(np.log(div))
else:
res = (X_nonzero**beta).sum()
res += (beta - 1) * (WH**beta).sum()
res -= beta * (X_nonzero * (WH_Xnonzero**(beta - 1))).sum()
res /= beta * (beta - 1)
return res
def loss(self, w):
"""Compute negative partial log-likelihood
Parameters
----------
w : array, shape = [n_features]
Estimate of coefficients
Returns
-------
loss : float
Average negative partial log-likelihood
"""
xw = numpy.dot(self.x, w)
at_risk = numpy.empty(self.x.shape[0])
for i in range(self.x.shape[0]):
idx = self.time >= self.time[i]
at_risk[i] = logsumexp(xw[idx])
loss = numpy.mean(self.event * (xw - at_risk))
if self.alpha > 0:
loss -= 0.5 * self.alpha * squared_norm(w)
return -loss
def _update_center(self, X):
"""
Fix Label, Weight, Update Center
"""
centers_old = self.cluster_centers_.copy()
if self.cluster_method == 'k-means':
cluster_center = kmeans_center
elif self.cluster_method == 'k-median':
cluster_center = kmedian_center
else:
raise ValueError('cluster_method must be kmeans or kmedian')
# Choose data belong to cluster k and
# Update cluster center with it mean
for k in range(self.n_clusters):
mask = self.labels_ == k
self.cluster_centers_[k] = cluster_center(X[mask])
# check cluster is empty
if np.isnan(self.cluster_centers_).any():
raise ValueError('Cluster must have at least one member')
center_shift_total = squared_norm(self.cluster_centers_ - centers_old)
return center_shift_total
def choose_alpha(alpha,
x,
S,
n_samples,
beta,
lamda,
gamma,
theta=.99,
max_iter=1000):
"""Choose alpha for backtracking.
References
----------
Salzo S. (2017). https://doi.org/10.1137/16M1073741
"""
eps = .5
partial_J = partial(_J,
x,
beta=beta,
lamda=lamda,
gamma=gamma,
S=S,
n_samples=n_samples)
partial_f = partial(_f, n_samples=n_samples, S=S)
gradient_ = _gradient(x, S, n_samples)
for i in range(max_iter):
iter_diff = partial_J(alpha=alpha) - x
obj_diff = partial_f(K=partial_J(alpha=alpha)) - partial_f(K=x)
if obj_diff - _scalar_product_3d(iter_diff, gradient_) <= theta / (
gamma * alpha) * squared_norm(iter_diff) + 1e-16:
return alpha
alpha *= eps
return alpha
def _beta_divergence_dense(X, W, H, beta):
"""Compute the beta-divergence of X and W.H for dense array only.
Used as a reference for testing nmf._beta_divergence.
"""
if isinstance(X, numbers.Number):
W = np.array([[W]])
H = np.array([[H]])
X = np.array([[X]])
WH = np.dot(W, H)
if beta == 2:
return squared_norm(X - WH) / 2
WH_Xnonzero = WH[X != 0]
X_nonzero = X[X != 0]
np.maximum(WH_Xnonzero, 1e-9, out=WH_Xnonzero)
if beta == 1:
res = np.sum(X_nonzero * np.log(X_nonzero / WH_Xnonzero))
res += WH.sum() - X.sum()
elif beta == 0:
div = X_nonzero / WH_Xnonzero
res = np.sum(div) - X.size - np.sum(np.log(div))
else:
res = (X_nonzero ** beta).sum()
res += (beta - 1) * (WH ** beta).sum()
res -= beta * (X_nonzero * (WH_Xnonzero ** (beta - 1))).sum()
res /= beta * (beta - 1)
return res
def _solve_weight_vector(similarities, grouping_matrix, delta):
"""Solve for the weight vector of the similarities, used for
_solve_omega and _solve_pi
Parameters
----------
similarities : np.ndarray (n_similarities,
(n_features * (n_features - 1) /2)
similarity matrices
grouping_matrix : np.ndarray (n_features, n_communities)
delta : float
Returns
-------
weights : np.ndarray (1, n_similarities)
"""
# do some type check
if np.any(similarities < 0):
raise ValueError('similarities contain invalid values (< 0)')
if delta <= 0:
raise ValueError('delta value of {0} not allowed, '
'needs to be >=0'.format(delta))
sigma = np.dot(grouping_matrix, grouping_matrix.T)
n_similarities = len(similarities)
# preallocate vector
a = np.zeros(n_similarities)
for i in range(n_similarities):
a[i] = squared_norm(squareform(similarities[i]) - sigma)
# solve for weight
weight = simplex_projection(a / (2 * delta))
return np.atleast_2d(weight)
def _fit(self, X):
"""Fit the LatentTimeMatrixDecomposition model to X.
Parameters
----------
X : ndarray, shape (n_time, n_samples, n_features), or
(n_samples, n_features, n_time)
Matrix to decompose.
"""
self.precision_, self.latent_, self.n_iter_ = latent_time_matrix_decomposition(
X,
alpha=self.alpha,
tau=self.tau,
rho=self.rho,
beta=self.beta,
eta=self.eta,
mode=self.mode,
tol=self.tol,
rtol=self.rtol,
psi=self.psi,
phi=self.phi,
max_iter=self.max_iter,
verbose=self.verbose,
return_n_iter=True,
return_history=False,
update_rho_options=self.update_rho_options,
compute_objective=self.compute_objective,
)
self.reconstruction_err_ = squared_norm(X - self.get_observed_precision())
return self
def kmeans(X, k):
samples = X.shape[0]
best_inertia = None
best_labels = None
x_squared_norms = row_norms(X, squared=True)
seeds = random_state.permutation(samples)[:k]
centers = X[seeds]
centers = centers.toarray()
distances = numpy.zeros(shape=(X.shape[0], ), dtype=X.dtype)
# Iterations
for i in range(100):
centers_old = centers.copy()
labels, inertia = assign_labels(X, x_squared_norms, centers, distances,
samples)
centers = maximization(X, labels, distances, centers, samples)
if best_inertia is None or inertia < best_inertia:
best_labels = labels.copy()
best_inertia = inertia
center_shift = squared_norm(centers_old - centers)
if center_shift > 0:
best_labels, best_inertia = assign_labels(X, x_squared_norms, centers,
distances, samples)
return best_labels
def nlog_likelihood(self, w):
"""Compute negative partial log-likelihood
Parameters
----------
w : array, shape = (n_features,)
Estimate of coefficients
Returns
-------
loss : float
Average negative partial log-likelihood
"""
time = self.time
n_samples = self.x.shape[0]
xw = numpy.dot(self.x, w)
loss = 0
risk_set = 0
k = 0
for i in range(n_samples):
ti = time[i]
while k < n_samples and ti == time[k]:
risk_set += numpy.exp(xw[k])
k += 1
if self.event[i]:
loss -= (xw[i] - numpy.log(risk_set)) / n_samples
# add regularization term to log-likelihood
return loss + self.alpha * squared_norm(w) / (2. * n_samples)
def objectiveFLGL(emp_cov, K, R, T, H, U, mu, eta, rho):
res = -fast_logdet(R) + np.sum(R * emp_cov)
res += rho / 2. * squared_norm(R - T + U + np.linalg.multi_dot(
(K.T, linalg.pinvh(H), K)))
res += mu * l1_od_norm(H)
res += eta * l1_od_norm(T)
return res
def objective(S, R, Z_0, Z_1, Z_2, W_0, W_1, W_2, alpha, tau, beta, eta, psi, phi):
"""Objective for latent variable time-varying matrix decomposition."""
obj = squared_norm(S - R)
obj += alpha * sum(map(l1_od_norm, Z_0))
obj += tau * sum(map(partial(np.linalg.norm, ord="nuc"), W_0))
obj += beta * sum(map(psi, Z_2 - Z_1))
obj += eta * sum(map(phi, W_2 - W_1))
return obj
def _objective_func(self, w):
self._update_constraints(w)
l_plus, xv_plus, l_minus, xv_minus = self._counter.calculate(w)
x = self._counter.x
xs = numpy.dot(x, w)
val = 0.5 * squared_norm(w)
if self._has_time:
val += 0.5 * self._regr_penalty * squared_norm(
self.y_compressed - xs.compress(self.regr_mask, axis=0))
val += 0.5 * self._rank_penalty * numexpr.evaluate(
'sum(xs * ((l_plus + l_minus) * xs - xv_plus - xv_minus - 2 * (l_minus - l_plus)) + l_minus)'
)
return val
def test_loss_gradients_hessp_intercept(base_loss, sample_weight,
l2_reg_strength, X_sparse):
"""Test that loss and gradient handle intercept correctly."""
loss = LinearModelLoss(base_loss=base_loss(), fit_intercept=False)
loss_inter = LinearModelLoss(base_loss=base_loss(), fit_intercept=True)
n_samples, n_features = 10, 5
X, y, coef = random_X_y_coef(linear_model_loss=loss,
n_samples=n_samples,
n_features=n_features,
seed=42)
X[:, -1] = 1 # make last column of 1 to mimic intercept term
X_inter = X[:, :
-1] # exclude intercept column as it is added automatically by loss_inter
if X_sparse:
X = sparse.csr_matrix(X)
if sample_weight == "range":
sample_weight = np.linspace(1, y.shape[0], num=y.shape[0])
l, g = loss.loss_gradient(coef,
X,
y,
sample_weight=sample_weight,
l2_reg_strength=l2_reg_strength)
_, hessp = loss.gradient_hessian_product(coef,
X,
y,
sample_weight=sample_weight,
l2_reg_strength=l2_reg_strength)
l_inter, g_inter = loss_inter.loss_gradient(
coef,
X_inter,
y,
sample_weight=sample_weight,
l2_reg_strength=l2_reg_strength)
_, hessp_inter = loss_inter.gradient_hessian_product(
coef,
X_inter,
y,
sample_weight=sample_weight,
l2_reg_strength=l2_reg_strength)
# Note, that intercept gets no L2 penalty.
assert l == pytest.approx(l_inter +
0.5 * l2_reg_strength * squared_norm(coef.T[-1]))
g_inter_corrected = g_inter
g_inter_corrected.T[-1] += l2_reg_strength * coef.T[-1]
assert_allclose(g, g_inter_corrected)
s = np.random.RandomState(42).randn(*coef.shape)
h = hessp(s)
h_inter = hessp_inter(s)
h_inter_corrected = h_inter
h_inter_corrected.T[-1] += l2_reg_strength * s.T[-1]
assert_allclose(h, h_inter_corrected)
def norm(x):
"""Dot product-based Euclidean norm implementation
See: http://fseoane.net/blog/2011/computing-the-vector-norm/
Parameters
----------
x : array-like
Vector for which to compute the norm
"""
return sqrt(squared_norm(x))
def _kmeans_spark(X, n_clusters, max_iter=300, worker_nums=10, init='k-means++', random_state=None, tol=1e-4):
from pyspark import SparkContext, SparkConf
conf = SparkConf().setAppName('K-Means_Spark').setMaster('local[%d]'%worker_nums)
sc = SparkContext(conf=conf)
data = sc.parallelize(X)
data.cache()
random_state = check_random_state(random_state)
best_labels, best_inertia, best_centers = None, None, None
x_squared_norms = row_norms(X, squared=True)
# x_squared_norms = data.map(lambda x: (x*x).sum(axis=0)).collect()
# x_squared_norms = np.array(x_squared_norms, dtype='float64')
centers = _init_centroids(X, n_clusters, init, random_state, x_squared_norms=x_squared_norms)
bs = X.shape[0]/worker_nums
data_temp = []
for i in range(worker_nums-1):
data_temp.append(X[i*bs:(i+1)*bs])
data_temp.append(X[(worker_nums-1)*bs:])
data_temp = np.array(data_temp, dtype='float64')
data_temp = sc.parallelize(data_temp)
data_temp.cache()
for i in range(max_iter):
centers_old = centers.copy()
all_distances = data_temp.map(lambda x: euclidean_distances(centers, x, squared=True)).collect()
temp_all_distances = all_distances[0]
for i in range(1, worker_nums):
temp_all_distances = np.hstack((temp_all_distances, all_distances[i]))
all_distances = temp_all_distances
# all_distances = data.map(lambda x: euclidean_distances(centers, x, squared=True)).collect()
# # reshape, from (1, n_samples, k) to (k, n_samples)
# all_distances = np.asarray(all_distances, dtype="float64").T[0]
# Assignment, also called E-step of EM
labels, inertia = _labels_inertia(X, x_squared_norms, centers, all_distances=all_distances)
# re-computation of the centroids, also called M-step of EM
centers = _centers(X, labels, n_clusters)
if best_inertia is None or inertia < best_inertia:
best_labels = labels.copy()
best_centers = centers.copy()
best_inertia = inertia
shift = squared_norm(centers_old - centers)
if shift <= tol:
break
return best_centers, best_labels, best_inertia
def fit(self, X):
self.n_samples = X.shape[0]
self.n_features = X.shape[1]
if self.balanced:
self.cluster_size = int(self.n_samples / self.n_clusters)
# Place k centroids randomly.
centers = self.init_centers(X)
best_labels, best_inertia, best_centers = None, None, None
for i in range(self.max_iterations):
centers_old = centers.copy()
# Get labels and inertia.
if not self.balanced:
labels, inertia = self.get_labels_and_inertia(X, centers)
else:
labels, inertia = self.get_labels_and_inertia_extended(
X, centers)
# Move the centers to the mean of the points assigned to it.
centers = self.move_to_mean(X, labels)
print("Iteration {:2d}, inertia {:.3f}".format(i, inertia))
# Update the labels and centers if the inertia is the minimum.
if best_inertia is None or inertia < best_inertia:
best_labels = labels.copy()
best_centers = centers.copy()
best_inertia = inertia
# Check if the centers move.
center_shift_total = squared_norm(centers_old - centers)
print("center shift {:f}".format(center_shift_total))
if center_shift_total == 0:
print("Converged at iteration {:d}: center shift {:f}".format(
i, center_shift_total))
break
# For the case it stops due to the max iterations
if center_shift_total > 0:
if not self.balanced:
best_labels, best_inertia = self.get_labels_and_inertia(
X, best_centers)
else:
best_labels, best_inertia = self.get_labels_and_inertia_extended(
X, best_centers)
# Convert array to list for grading purpose.
list_best_centers = []
for centroid in best_centers:
list_best_centers.append(list(centroid))
return list(best_labels), list_best_centers
def _fit_projected_gradient(X, W, H, tol, max_iter, nls_max_iter, alpha,
l1_ratio):
gradW = (np.dot(W, np.dot(H, H.T)) -
safe_sparse_dot(X, H.T, dense_output=True))
gradH = (np.dot(np.dot(W.T, W), H) -
safe_sparse_dot(W.T, X, dense_output=True))
init_grad = squared_norm(gradW) + squared_norm(gradH.T)
# max(0.001, tol) to force alternating minimizations of W and H
tolW = max(0.001, tol) * np.sqrt(init_grad)
tolH = tolW
for n_iter in range(1, max_iter + 1):
# stopping condition as discussed in paper
proj_grad_W = squared_norm(gradW * np.logical_or(gradW < 0, W > 0))
proj_grad_H = squared_norm(gradH * np.logical_or(gradH < 0, H > 0))
if (proj_grad_W + proj_grad_H) / init_grad < tol ** 2:
break
# update W
Wt, gradWt, iterW = _nls_subproblem(X.T, H.T, W.T, tolW, nls_max_iter,
alpha=alpha, l1_ratio=l1_ratio)
W, gradW = Wt.T, gradWt.T
if iterW == 1:
tolW = 0.1 * tolW
# update H
H, gradH, iterH = _nls_subproblem(X, W, H, tolH, nls_max_iter,
alpha=alpha, l1_ratio=l1_ratio)
if iterH == 1:
tolH = 0.1 * tolH
H[H == 0] = 0 # fix up negative zeros
if n_iter == max_iter:
Wt, _, _ = _nls_subproblem(X.T, H.T, W.T, tolW, nls_max_iter,
alpha=alpha, l1_ratio=l1_ratio)
W = Wt.T
return W, H, n_iter
def _compute_RMSETOTAL(D, A, Ft, P, O, S, R):
fD = 0
numElementsD = 0
fA = 0
numElementsA = 0
baselineSum = sum([norm(mat) for mat in D]) + sum([norm(mat) for mat in A])
for i, Di in enumerate(D):
PiSiFt = P[i] @ S[i] @ Ft
fD += squared_norm(Di - PiSiFt) / (squared_norm(Di))
# numElementsD += Di.size
for i, Ai in enumerate(A):
OiRiFt = O[i] @ R[i] @ Ft
fA += squared_norm(Ai - OiRiFt) / (squared_norm(Ai))
# numElementsA += Ai.size
answer = (fD + fA) #/(numElementsD+numElementsA)
return math.sqrt(answer), math.sqrt(fA) #/numElementsA)
def _compute_RMSETOTAL(D, A, F, P, O):
fD = 0
numElementsD = 0
fA = 0
numElementsA = 0
for i, Di in enumerate(D):
PiF = dot(P[i], F)
fD += squared_norm(Di - PiF)
# numElementsD += Di.size
numElementsD += squared_norm(Di)
for i, Ai in enumerate(A):
OiF = dot(O[i], F)
fA += squared_norm(Ai - OiF)
# numElementsA += Ai.size
numElementsA += squared_norm(Ai)
answer = (fD + fA) / (numElementsD + numElementsA)
return answer, fA / numElementsA
def _kmeans_single_lloyd(X, n_clusters, max_iter=300, init='k-means||',
verbose=False, x_squared_norms=None,
random_state=None, tol=1e-4,
precompute_distances=True,
oversampling_factor=2,
init_max_iter=None):
centers = k_init(X, n_clusters, init=init,
oversampling_factor=oversampling_factor,
random_state=random_state, max_iter=init_max_iter)
dt = X.dtype
X = X.astype(np.float32)
P = X.shape[1]
for i in range(max_iter):
t0 = tic()
centers = centers.astype('f4')
labels, distances = pairwise_distances_argmin_min(
X, centers, metric='euclidean', metric_kwargs={"squared": True}
)
labels = labels.astype(np.int32)
distances = distances.astype(np.float32)
r = da.atop(_centers_dense, 'ij',
X, 'ij',
labels, 'i',
n_clusters, None,
distances, 'i',
adjust_chunks={"i": n_clusters, "j": P},
dtype='f8')
new_centers = da.from_delayed(
sum(r.to_delayed().flatten()),
(n_clusters, P),
X.dtype
)
counts = da.bincount(labels, minlength=n_clusters)
new_centers = new_centers / counts[:, None]
new_centers, = compute(new_centers)
# Convergence check
shift = squared_norm(centers - new_centers)
t1 = tic()
logger.info("Lloyd loop %2d. Shift: %0.4f [%.2f s]", i, shift, t1 - t0)
if shift < tol:
break
centers = new_centers
if shift > 1e-7:
labels, distances = pairwise_distances_argmin_min(X, centers)
inertia = distances.astype(dt).sum()
centers = centers.astype(dt)
labels = labels.astype(np.int64)
return labels, inertia, centers, i + 1
def _multinomial_loss_and_gradient(w, X, Y, alpha, sample_weight, xStd, standardization):
# print("coefficients = " + str(w))
_, n_features = X.shape
_, n_classes = Y.shape
n_samples = np.sum(sample_weight)
sample_weight = sample_weight[:, np.newaxis]
fit_intercept = (w.size == n_classes * (n_features + 1))
grad = np.zeros((n_classes, n_features + bool(fit_intercept)))
# Calculate loss value
w = w.reshape(n_classes, -1)
if fit_intercept:
intercept = w[:, -1]
w = w[:, :-1]
else:
intercept = 0
p = safe_sparse_dot(X, w.T) + intercept
p -= logsumexp(p, axis=1)[:, np.newaxis]
if standardization:
l2reg = 0.5 * alpha * squared_norm(w)
l2reg_grad = alpha * w
else:
_w = w / xStd
l2reg = 0.5 * alpha * squared_norm(_w)
l2reg_grad = alpha * _w / xStd
loss = -(sample_weight * Y * p).sum() / n_samples + l2reg
# print("loss = " + str(loss))
diff = sample_weight * (np.exp(p) - Y)
grad[:, :n_features] = safe_sparse_dot(diff.T, X) / n_samples
grad[:, :n_features] += l2reg_grad
# print("grad = " + str(grad))
if fit_intercept:
grad[:, -1] = diff.sum(axis=0) / n_samples
return loss, grad.ravel()
def logistic_loss(w, X, Y, alpha):
"""
Implementation of the logistic loss function when Y is a probability
distribution.
loss = -SUM_i SUM_k y_ik * log(P[yi == k]) + alpha * ||w||^2
"""
n_classes = Y.shape[1]
n_features = X.shape[1]
intercept = 0
if n_classes > 2:
fit_intercept = w.size == (n_classes * (n_features + 1))
w = w.reshape(n_classes, -1)
if fit_intercept:
intercept = w[:, -1]
w = w[:, :-1]
else:
fit_intercept = w.size == (n_features + 1)
if fit_intercept:
intercept = w[-1]
w = w[:-1]
z = safe_sparse_dot(X, w.T) + intercept
if n_classes == 2:
# in the binary case, simply compute the logistic function
p = np.vstack([log_logistic(-z), log_logistic(z)]).T
else:
# compute the logistic function for each class and normalize
denom = expit(z)
denom = denom.sum(axis=1).reshape((denom.shape[0], -1))
p = log_logistic(z)
loss = -(Y * p).sum()
loss += np.log(denom).sum() # Y.sum() = 1
loss += 0.5 * alpha * squared_norm(w)
return loss
loss = -(Y * p).sum() + 0.5 * alpha * squared_norm(w)
return loss
def _multinomial_loss(w, X, Y, alpha, sample_weight):
"""Computes multinomial loss and class probabilities.
Parameters
----------
w : ndarray, shape (n_classes * n_features,) or (n_classes * (n_features +
1),)
Coefficient vector.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
Y : ndarray, shape (n_samples, n_classes)
Transformed labels according to the output of LabelBinarizer.
alpha : float
Regularization parameter. alpha is equal to 1 / C.
sample_weight : ndarray, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
loss : float
Multinomial loss.
p : ndarray, shape (n_samples, n_classes)
Estimated class probabilities.
w : ndarray, shape (n_classes, n_features)
Reshaped param vector excluding intercept terms.
"""
n_classes = Y.shape[1]
n_features = X.shape[1]
fit_intercept = w.size == (n_classes * (n_features + 1))
w = w.reshape(n_classes, -1)
sample_weight = sample_weight[:, np.newaxis]
if fit_intercept:
intercept = w[:, -1]
w = w[:, :-1]
else:
intercept = 0
p = safe_sparse_dot(X, w.T)
p += intercept
p -= logsumexp(p, axis=1)[:, np.newaxis]
loss = -(sample_weight * Y * p).sum()
loss += 0.5 * alpha * squared_norm(w)
p = np.exp(p, p)
return loss, p, w
def _update_center(self, X):
"""
Fix Weights and Labels, Update Centers
"""
centers_old = self.cluster_centers_.copy()
# choose data belong to cluster k
# and update cluster center with it mean
for k in range(self.n_clusters):
mask = self.labels_ == k
self.cluster_centers_[k] = np.mean(X[mask], axis=0)
center_shift_total = squared_norm(self.cluster_centers_ - centers_old)
return center_shift_total
def _multinomial_loss(w, X, Y, alpha, sample_weight):
"""Computes multinomial loss and class probabilities.
Parameters
----------
w : ndarray, shape (n_classes * n_features,) or (n_classes * (n_features +
1),)
Coefficient vector.
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Training data.
Y : ndarray, shape (n_samples, n_classes)
Transformed labels according to the output of LabelBinarizer.
alpha : float
Regularization parameter. alpha is equal to 1 / C.
sample_weight : ndarray, shape (n_samples,) optional
Array of weights that are assigned to individual samples.
If not provided, then each sample is given unit weight.
Returns
-------
loss : float
Multinomial loss.
p : ndarray, shape (n_samples, n_classes)
Estimated class probabilities.
w : ndarray, shape (n_classes, n_features)
Reshaped param vector excluding intercept terms.
"""
n_classes = Y.shape[1]
n_features = X.shape[1]
fit_intercept = w.size == (n_classes * (n_features + 1))
w = w.reshape(n_classes, -1)
sample_weight = sample_weight[:, np.newaxis]
if fit_intercept:
intercept = w[:, -1]
w = w[:, :-1]
else:
intercept = 0
p = safe_sparse_dot(X, w.T)
p += intercept
p -= logsumexp(p, axis=1)[:, np.newaxis]
loss = -(sample_weight * Y * p).sum()
loss += 0.5 * alpha * squared_norm(w)
p = np.exp(p, p)
return loss, p, w
def _objective_func(self, beta_bias):
bias, beta = self._split_coefficents(beta_bias)
Kw = self._Kw
val = 0.5 * numpy.dot(beta, Kw)
if self._has_time:
val += 0.5 * self._regr_penalty * squared_norm(self.y_compressed - bias
- Kw.compress(self.regr_mask, axis=0))
l_plus, xv_plus, l_minus, xv_minus = self._counter.calculate(beta)
val += 0.5 * self._rank_penalty * numexpr.evaluate(
'sum(Kw * ((l_plus + l_minus) * Kw - xv_plus - xv_minus - 2 * (l_minus - l_plus)) + l_minus)')
return val
def kmeansopt(data, k ,rng, T = 50 , method = 'kmeans' , tol = 1e-4 ):
centroids = []
lable = []
if(method == 'kmeans++'):
centroids = optimize_centroids(data, centroids , k ,rng )
else:
centroids = ramdon_centroids(data, centroids , k ,rng)
# print("inital centroids")
# print(centroids)
old_centroids = []
# result_dict = {}
Iteration = 0
clusters = [[] for i in range(k)]
# while(Iteration < T and not compare(old_centroids , centroids)):
while(Iteration < T ):
clusters = [[] for i in range(k)]
clusters,lable= euclidean(data, centroids, clusters)
# print(" The %d times cluster" % Iteration)
# print(clusters)
# recalculate centriods from exist cluster
index = 0
old_centroids = list(centroids);
# print(Iteration)
for cluster in clusters:
centroids[index] = np.mean(cluster, axis = 0).tolist()
index += 1
# for num in range(0,len(clusters)):
# for ld in clusters[num]:
# result_dict[str(ld)] = num
# print(centroids)
centroids_matrix = np.matrix(centroids)
# print(centroids_matrix)
# print(old_centroids)
old_centroids_matrix = np.matrix(old_centroids)
# print(old_centroids_matrix)
shift = squared_norm(old_centroids_matrix - centroids_matrix)
if shift <= tol:
# print("Already Coverage , break")
break
Iteration += 1 # End of innerLoop
return clusters, centroids, lable
def temp_log_loss(w, X, Y, alpha):
n_classes = Y.shape[1]
w = w.reshape(n_classes, -1)
intercept = w[:, -1]
w = w[:, :-1]
z = safe_sparse_dot(X, w.T) + intercept
denom = expit(z)
#print denom
#print denom.sum()
denom = denom.sum(axis=1).reshape((denom.shape[0], -1))
#print denom
p = log_logistic(z)
loss = - (Y * p).sum()
loss += np.log(denom).sum()
loss += 0.5 * alpha * squared_norm(w)
return loss
def _multinomial_loss(w, X, Y, alpha):
sample_weight = np.ones(len(Y))
n_classes = Y.shape[1]
n_features = X.shape[1]
fit_intercept = w.size == (n_classes * (n_features + 1))
w = w.reshape(n_classes, -1)
sample_weight = sample_weight[:, np.newaxis]
if fit_intercept:
intercept = w[:, -1]
w = w[:, :-1]
else:
intercept = 0
p = safe_sparse_dot(X, w.T)
p += intercept
p -= logsumexp(p, axis=1)[:, np.newaxis]
loss = -(sample_weight * Y * p).sum()
loss += 0.5 * alpha * squared_norm(w)
p = np.exp(p, p)
return loss, p, w
def _kmeans_single(X, n_clusters, max_iter=300, init='k-means++', random_state=None, tol=1e-4):
random_state = check_random_state(random_state)
best_labels, best_inertia, best_centers = None, None, None
# init
x_squared_norms = row_norms(X, squared=True)
centers = _init_centroids(X, n_clusters, init, random_state, x_squared_norms=x_squared_norms)
# distances = np.zeros(shape=(X.shape[0],), dtype=np.float64)
# iterations
for i in range(max_iter):
centers_old = centers.copy()
# Assignment, also called E-step of EM
labels, inertia = _labels_inertia(X, x_squared_norms, centers)
# re-computation of the centroids, also called M-step of EM
centers = _centers(X, labels, n_clusters)
if best_inertia is None or inertia < best_inertia:
best_labels = labels.copy()
best_centers = centers.copy()
best_inertia = inertia
shift = squared_norm(centers_old - centers)
if shift <= tol:
break
if shift > 0:
# rerun E-step in case of non-convergence so that predicted labels
# match cluster centers
best_labels, best_inertia = \
_labels_inertia(X, x_squared_norms, best_centers)
return best_centers, best_labels, best_inertia
def enet_kernel_learning(
K, y, lamda=0.01, beta=0.01, gamma='auto', max_iter=100, verbose=0,
tol=1e-4, return_n_iter=True):
"""Elastic Net kernel learning.
Solve the following problem via alternating minimisation:
min sum_{i=1}^p 1/2 ||alpha_i * w * K_i - y_i||^2 + lamda ||w||_1 +
+ beta||w||_2^2
"""
n_patients = len(K)
n_kernels = len(K[0])
coef = np.ones(n_kernels)
alpha = [np.zeros(K[j].shape[2]) for j in range(n_patients)]
# KKT = [K[j].T.dot(K[j]) for j in range(len(K))]
# print(KKT[0].shape)
if gamma == 'auto':
lipschitz_constant = np.array([
sum(np.linalg.norm(K_j[i].dot(K_j[i].T))
for i in range(K_j.shape[0]))
for K_j in K])
gamma = 1. / (lipschitz_constant)
objective_new = 0
for iteration_ in range(max_iter):
w_old = coef.copy()
alpha_old = [a.copy() for a in alpha]
objective_old = objective_new
# update w
A = [K[j].dot(alpha[j]) for j in range(n_patients)]
alpha_coef_K = [alpha[j].dot(K[j].T.dot(coef))
for j in range(n_patients)]
gradient = sum((alpha_coef_K[j] - y[j]).dot(A[j].T)
for j in range(n_patients))
# gradient_2 = coef.dot(sum(
# np.dot(K[j].dot(alpha[j]), K[j].dot(alpha[j]).T)
# for j in range(len(K)))) - sum(
# y[j].dot(K[j].dot(alpha[j]).T) for j in range(len(K)))
# gradient = coef.dot(sum(
# alpha[j].dot(KKT[j].dot(alpha[j])) for j in range(len(K)))) - sum(
# y[j].dot(K[j].dot(alpha[j]).T) for j in range(len(K)))
# gradient += 2 * beta * coef
coef = soft_thresholding(coef - gamma * gradient, lamda=lamda * gamma)
# update alpha
# for j in range(len(K)):
# alpha[j] = _solve_cholesky_kernel(
# K[j].T.dot(coef), y[j][..., None], lamda).ravel()
A = [K[j].T.dot(coef) for j in range(n_patients)]
alpha_coef_K = [alpha[j].dot(K[j].T.dot(coef))
for j in range(n_patients)]
gradient = [(alpha_coef_K[j] - y[j]).dot(A[j].T) + 2 * beta * alpha[j]
for j in range(n_patients)]
alpha = [alpha[j] - gamma * gradient[j] for j in range(n_patients)]
objective_new = objective(K, y, alpha, lamda, beta, coef)
objective_difference = abs(objective_new - objective_old)
snorm = np.sqrt(squared_norm(coef - w_old) + sum(
squared_norm(a - a_old) for a, a_old in zip(alpha, alpha_old)))
obj = objective(K, y, alpha, lamda, beta, coef)
if verbose and iteration_ % 10 == 0:
print("obj: %.4f, snorm: %.4f" % (obj, snorm))
if snorm < tol and objective_difference < tol:
break
if np.isnan(snorm) or np.isnan(objective_difference):
raise ValueError('assdgg')
else:
warnings.warn("Objective did not converge.")
return_list = [alpha, coef]
if return_n_iter:
return_list.append(iteration_)
return return_list
def objective_admm2(x, y, alpha, lamda, beta, w1):
"""Objective function for lasso kernel learning."""
obj = .5 * sum(squared_norm(x[j] - y[j]) for j in range(len(x)))
obj += lamda * np.abs(w1).sum()
obj += beta * sum(squared_norm(a) for a in alpha)
return obj
def _spherical_kmeans_single_lloyd(X, n_clusters, max_iter=300,
init='k-means++', verbose=False,
x_squared_norms=None,
random_state=None, tol=1e-4,
precompute_distances=True):
'''
Modified from sklearn.cluster.k_means_.k_means_single_lloyd.
'''
random_state = check_random_state(random_state)
best_labels, best_inertia, best_centers = None, None, None
# init
centers = _init_centroids(X, n_clusters, init, random_state=random_state,
x_squared_norms=x_squared_norms)
if verbose:
print("Initialization complete")
# Allocate memory to store the distances for each sample to its
# closer center for reallocation in case of ties
distances = np.zeros(shape=(X.shape[0],), dtype=X.dtype)
# iterations
for i in range(max_iter):
centers_old = centers.copy()
# labels assignment
# TODO: _labels_inertia should be done with cosine distance
# since ||a - b|| = 2(1 - cos(a,b)) when a,b are unit normalized
# this doesn't really matter.
labels, inertia = \
_labels_inertia(X, x_squared_norms, centers,
precompute_distances=precompute_distances,
distances=distances)
# computation of the means
if sp.issparse(X):
centers = _k_means._centers_sparse(X, labels, n_clusters,
distances)
else:
centers = _k_means._centers_dense(X, labels, n_clusters, distances)
# l2-normalize centers (this is the main contibution here)
centers = normalize(centers)
if verbose:
print("Iteration %2d, inertia %.3f" % (i, inertia))
if best_inertia is None or inertia < best_inertia:
best_labels = labels.copy()
best_centers = centers.copy()
best_inertia = inertia
center_shift_total = squared_norm(centers_old - centers)
if center_shift_total <= tol:
if verbose:
print("Converged at iteration %d: "
"center shift %e within tolerance %e"
% (i, center_shift_total, tol))
break
if center_shift_total > 0:
# rerun E-step in case of non-convergence so that predicted labels
# match cluster centers
best_labels, best_inertia = \
_labels_inertia(X, x_squared_norms, best_centers,
precompute_distances=precompute_distances,
distances=distances)
return best_labels, best_inertia, best_centers, i + 1
def enet_kernel_learning_admm(
K, y, lamda=0.01, beta=0.01, rho=1., max_iter=100, verbose=0, rtol=1e-4,
tol=1e-4, return_n_iter=True, update_rho_options=None):
"""Elastic Net kernel learning.
Solve the following problem via ADMM:
min sum_{i=1}^p 1/2 ||alpha_i * w * K_i - y_i||^2 + lamda ||w||_1 +
+ beta||w||_2^2
"""
n_patients = len(K)
n_kernels = len(K[0])
coef = np.ones(n_kernels)
u_1 = np.zeros(n_kernels)
u_2 = np.zeros(n_kernels)
w_1 = np.zeros(n_kernels)
w_2 = np.zeros(n_kernels)
w_1_old = w_1.copy()
w_2_old = w_2.copy()
checks = []
for iteration_ in range(max_iter):
# update alpha
# solve (AtA + 2I)^-1 (Aty) with A = wK
A = [K[j].T.dot(coef) for j in range(n_patients)]
KK = [A[j].dot(A[j].T) for j in range(n_patients)]
yy = [y[j].dot(A[j]) for j in range(n_patients)]
alpha = [_solve_cholesky_kernel(
KK[j], yy[j][..., None], 2).ravel() for j in range(n_patients)]
# alpha = [_solve_cholesky_kernel(
# K_dot_coef[j], y[j][..., None], 0).ravel() for j in range(n_patients)]
w_1 = soft_thresholding(coef + u_1, lamda / rho)
w_2 = prox_laplacian(coef + u_2, beta / rho)
# equivalent to alpha_dot_K
# solve (sum(AtA) + 2*rho I)^-1 (sum(Aty) + rho(w1+w2-u1-u2))
# with A = K * alpha
A = [K[j].dot(alpha[j]) for j in range(n_patients)]
KK = sum(A[j].dot(A[j].T) for j in range(n_patients))
yy = sum(y[j].dot(A[j].T) for j in range(n_patients))
yy += rho * (w_1 + w_2 - u_1 - u_2)
coef = _solve_cholesky_kernel(KK, yy[..., None], 2 * rho).ravel()
# update residuals
u_1 += coef - w_1
u_2 += coef - w_2
# diagnostics, reporting, termination checks
rnorm = np.sqrt(squared_norm(coef - w_1) + squared_norm(coef - w_2))
snorm = rho * np.sqrt(
squared_norm(w_1 - w_1_old) + squared_norm(w_2 - w_2_old))
obj = objective_admm(K, y, alpha, lamda, beta, coef, w_1, w_2)
check = convergence(
obj=obj, rnorm=rnorm, snorm=snorm,
e_pri=np.sqrt(2 * coef.size) * tol + rtol * max(
np.sqrt(squared_norm(coef) + squared_norm(coef)),
np.sqrt(squared_norm(w_1) + squared_norm(w_2))),
e_dual=np.sqrt(2 * coef.size) * tol + rtol * rho * (
np.sqrt(squared_norm(u_1) + squared_norm(u_2))))
w_1_old = w_1.copy()
w_2_old = w_2.copy()
if verbose:
print("obj: %.4f, rnorm: %.4f, snorm: %.4f,"
"eps_pri: %.4f, eps_dual: %.4f" % check)
checks.append(check)
if check.rnorm <= check.e_pri and check.snorm <= check.e_dual and iteration_ > 1:
break
rho_new = update_rho(rho, rnorm, snorm, iteration=iteration_,
**(update_rho_options or {}))
# scaled dual variables should be also rescaled
u_1 *= rho / rho_new
u_2 *= rho / rho_new
rho = rho_new
else:
warnings.warn("Objective did not converge.")
return_list = [alpha, coef]
if return_n_iter:
return_list.append(iteration_)
return return_list
def _norm(x):
"""Dot product-based Euclidean norm implementation
See: http://fseoane.net/blog/2011/computing-the-vector-norm/
"""
return np.sqrt(squared_norm(x))
def matrix_factorization(X, H=None, n_components=None,
init=None, update_H=True,
tol=1e-4, max_iter=200, alpha=0.01,
beta=0.02):
n_samples, n_features = X.shape
if n_components is None:
n_components = n_features
# check W and H, or initialize them
if not update_H:
W = np.zeros((n_samples, n_components))
else:
W, H = _initialize_nmf(X, n_components, init=init, eps=1e-6)
print W
print H
n_iter = 0
e_before = 0
for step in xrange(max_iter):
n_iter = step + 1
print n_iter
xs, ys = X.nonzero() # the x index and y index of nonzero
W_temp = W
ER = X - np.dot(W,H) # the error matrix
for i in xrange(n_samples):
for k in xrange(n_components):
sum = 0
for j in ys[xs==i]:
sum += ER[i][j] * H[k][j]
t = W[i][k] + alpha * (sum - beta * W[i][k])
if t < 0:
a = alpha
for l in xrange(10):
a /= 2
t = W[i][k] + a * (sum - beta * W[i][k])
if t >= 0:
break
if t < 0:
t = W[i][k]
W[i][k] = t
if update_H:
for j in xrange(n_features):
for k in xrange(n_components):
sum = 0
for i in xs[ys==j]:
sum += ER[i][j] * W_temp[i][k]
t = H[k][j] + alpha * (sum - beta * H[k][j])
if t < 0:
a = alpha
for l in xrange(10):
a /= 2
t = H[k][j] + a * (sum - beta * H[k][j])
if t >= 0:
break
if t < 0:
t = H[k][j]
H[k][j] = t
E = (X - np.dot(W,H)) * (X>0)
e = squared_norm(E) + beta * ( squared_norm(W) + squared_norm(H) )
# if step > 0:
# if abs(e/e_before - 1) < tol:
# break
# e_before = e
print e
if e < tol:
break
if n_iter == max_iter:
print ("Maximum number of iteration %d reached. Increase it to"
" improve convergence." % max_iter)
return W, H, n_iter
def norm(x):
return sqrt(squared_norm(x))
b = pd.DataFrame(temp)
print b
b0 = b.fillna(0)
X = np.array(b0)
# print X.mean()
# print (X[X>0]).mean()
# X[X==0] = (X[X>0]).mean()
# print X
# U, S, V = randomized_svd(X, 20)
U, S, V = svds(sparse.csr_matrix(X), k=50, maxiter=2000)
S = vector_to_diagonal(S)
print X
print U
print S
print V
recon= pd.DataFrame(np.dot(U,np.dot(S,V)),b0.index,b0.columns)
recon[recon<1] = 1
recon[recon>5] = 5
# recon.to_csv('svdrecon.csv')
print recon
d = (t0 - recon) * (t0>0)
# d.to_csv('svdd.csv')
d.fillna(0,inplace = True)
print squared_norm(d)
def _objective_func(self, w):
z = self.Aw.shape[0] + squared_norm(self.AXw) - 2. * self.AXw.sum()
val = 0.5 * squared_norm(w) + 0.5 * self.alpha * z
return val
def enet_kernel_learning_admm2(
K, y, lamda=0.01, beta=0.01, rho=1., max_iter=100, verbose=0, rtol=1e-4,
tol=1e-4, return_n_iter=True, update_rho_options=None):
"""Elastic Net kernel learning.
Solve the following problem via ADMM:
min sum_{i=1}^p 1/2 ||y_i - alpha_i * sum_{k=1}^{n_k} w_k * K_{ik}||^2
+ lamda ||w||_1 + beta sum_{j=1}^{c_i}||alpha_j||_2^2
"""
n_patients = len(K)
n_kernels = len(K[0])
coef = np.ones(n_kernels)
alpha = [np.zeros(K[j].shape[2]) for j in range(n_patients)]
u = [np.zeros(K[j].shape[1]) for j in range(n_patients)]
u_1 = np.zeros(n_kernels)
w_1 = np.zeros(n_kernels)
x_old = [np.zeros(K[0].shape[1]) for j in range(n_patients)]
w_1_old = w_1.copy()
# w_2_old = w_2.copy()
checks = []
for iteration_ in range(max_iter):
# update x
A = [K[j].T.dot(coef) for j in range(n_patients)]
x = [prox_laplacian(y[j] + rho * (A[j].T.dot(alpha[j]) - u[j]), rho / 2.)
for j in range(n_patients)]
# update alpha
# solve (AtA + 2I)^-1 (Aty) with A = wK
KK = [rho * A[j].dot(A[j].T) for j in range(n_patients)]
yy = [rho * A[j].dot(x[j] + u[j]) for j in range(n_patients)]
alpha = [_solve_cholesky_kernel(
KK[j], yy[j][..., None], 2 * beta).ravel() for j in range(n_patients)]
# equivalent to alpha_dot_K
# solve (sum(AtA) + 2*rho I)^-1 (sum(Aty) + rho(w1+w2-u1-u2))
# with A = K * alpha
A = [K[j].dot(alpha[j]) for j in range(n_patients)]
KK = sum(A[j].dot(A[j].T) for j in range(n_patients))
yy = sum(A[j].dot(x[j] + u[j]) for j in range(n_patients))
yy += w_1 - u_1
coef = _solve_cholesky_kernel(KK, yy[..., None], 1).ravel()
w_1 = soft_thresholding(coef + u_1, lamda / rho)
# w_2 = prox_laplacian(coef + u_2, beta / rho)
# update residuals
alpha_coef_K = [
alpha[j].dot(K[j].T.dot(coef)) for j in range(n_patients)]
residuals = [x[j] - alpha_coef_K[j] for j in range(n_patients)]
u = [u[j] + residuals[j] for j in range(n_patients)]
u_1 += coef - w_1
# diagnostics, reporting, termination checks
rnorm = np.sqrt(
squared_norm(coef - w_1) +
sum(squared_norm(residuals[j]) for j in range(n_patients)))
snorm = rho * np.sqrt(
squared_norm(w_1 - w_1_old) +
sum(squared_norm(x[j] - x_old[j]) for j in range(n_patients)))
obj = objective_admm2(x, y, alpha, lamda, beta, w_1)
check = convergence(
obj=obj, rnorm=rnorm, snorm=snorm,
e_pri=np.sqrt(coef.size + sum(
x[j].size for j in range(n_patients))) * tol + rtol * max(
np.sqrt(squared_norm(coef) + sum(squared_norm(
alpha_coef_K[j]) for j in range(n_patients))),
np.sqrt(squared_norm(w_1) + sum(squared_norm(
x[j]) for j in range(n_patients)))),
e_dual=np.sqrt(coef.size + sum(
x[j].size for j in range(n_patients))) * tol + rtol * rho * (
np.sqrt(squared_norm(u_1) + sum(squared_norm(
u[j]) for j in range(n_patients)))))
w_1_old = w_1.copy()
x_old = [x[j].copy() for j in range(n_patients)]
if verbose:
print("obj: %.4f, rnorm: %.4f, snorm: %.4f,"
"eps_pri: %.4f, eps_dual: %.4f" % check)
checks.append(check)
if check.rnorm <= check.e_pri and check.snorm <= check.e_dual and iteration_ > 1:
break
rho_new = update_rho(rho, rnorm, snorm, iteration=iteration_,
**(update_rho_options or {}))
# scaled dual variables should be also rescaled
u = [u[j] * (rho / rho_new) for j in range(n_patients)]
u_1 *= rho / rho_new
rho = rho_new
else:
warnings.warn("Objective did not converge.")
return_list = [alpha, coef]
if return_n_iter:
return_list.append(iteration_)
return return_list
def _objective_func(self, w):
val = 0.5 * squared_norm(w) + 0.5 * self.alpha * squared_norm(self.L)
return val