def _fit_full_daal4py(self, X, n_components):
n_samples, n_features = X.shape
# due to need to flip components, need to do full decomposition
self._fit_daal4py(X, min(n_samples, n_features))
U = self._transform_daal4py(X, whiten=True, check_X=False, scale_eigenvalues=True)
V = self.components_
U, V = svd_flip(U, V)
U = U.copy()
V = V.copy()
S = self.singular_values_.copy()
if n_components == 'mle':
n_components = \
_infer_dimension_(self.explained_variance_, n_samples, n_features)
elif 0 < n_components < 1.0:
n_components = _n_components_from_fraction(
self.explained_variance_ratio_, n_components)
# Compute noise covariance using Probabilistic PCA model
# The sigma2 maximum likelihood (cf. eq. 12.46)
if n_components < min(n_features, n_samples):
self.noise_variance_ = self.explained_variance_[n_components:].mean()
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = self.components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = self.explained_variance_[:n_components]
self.explained_variance_ratio_ = \
self.explained_variance_ratio_[:n_components]
self.singular_values_ = self.singular_values_[:n_components]
return U, S, V
def _fit_daal4py(self, X, n_components):
n_samples, n_features = X.shape
n_sf_min = min(n_samples, n_features)
_validate_n_components(n_components, n_samples, n_features)
if n_components == 'mle':
daal_n_components = n_features
elif n_components < 1:
daal_n_components = n_sf_min
else:
daal_n_components = n_components
fpType = getFPType(X)
centering_algo = daal4py.normalization_zscore(fptype=fpType,
doScale=False)
pca_alg = daal4py.pca(fptype=fpType,
method='svdDense',
normalization=centering_algo,
resultsToCompute='mean|variance|eigenvalue',
isDeterministic=True,
nComponents=daal_n_components)
pca_res = pca_alg.compute(X)
self.mean_ = pca_res.means.ravel()
variances_ = pca_res.variances.ravel()
components_ = pca_res.eigenvectors
explained_variance_ = pca_res.eigenvalues.ravel()
tot_var = explained_variance_.sum()
explained_variance_ratio_ = explained_variance_ / tot_var
if n_components == 'mle':
n_components = \
_infer_dimension_(explained_variance_, n_samples, n_features)
elif 0 < n_components < 1.0:
n_components = _n_components_from_fraction(
explained_variance_ratio_, n_components)
# Compute noise covariance using Probabilistic PCA model
# The sigma2 maximum likelihood (cf. eq. 12.46)
if n_components < n_sf_min:
if explained_variance_.shape[0] == n_sf_min:
self.noise_variance_ = explained_variance_[n_components:].mean(
)
else:
resid_var_ = variances_.sum()
resid_var_ -= explained_variance_[:n_components].sum()
self.noise_variance_ = resid_var_ / (n_sf_min - n_components)
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = explained_variance_[:n_components]
self.explained_variance_ratio_ = \
explained_variance_ratio_[:n_components]
self.singular_values_ = np.sqrt(
(n_samples - 1) * self.explained_variance_)
def test_infer_dim_3():
n, p = 100, 5
rng = np.random.RandomState(0)
X = rng.randn(n, p) * .1
X[:10] += np.array([3, 4, 5, 1, 2])
X[10:20] += np.array([6, 0, 7, 2, -1])
X[30:40] += 2 * np.array([-1, 1, -1, 1, -1])
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_
assert _infer_dimension_(spect, n, p) > 2
def test_infer_dim_2():
# TODO: explain what this is testing
# Or at least use explicit variable names...
n, p = 1000, 5
rng = np.random.RandomState(0)
X = rng.randn(n, p) * .1
X[:10] += np.array([3, 4, 5, 1, 2])
X[10:20] += np.array([6, 0, 7, 2, -1])
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_
assert _infer_dimension_(spect, n, p) > 1
def _fit_full(self, X, n_components):
"""Fit the model by computing full SVD on X"""
n_samples, n_features = X.shape
_validate_n_components(n_components, n_samples, n_features)
# Center data
self.mean_ = np.mean(X, axis=0)
X -= self.mean_
if X.shape[0] > X.shape[1] and (X.dtype == np.float64
or X.dtype == np.float32):
U, S, V = _daal4py_svd(X)
else:
U, S, V = np.linalg.svd(X, full_matrices=False)
# flip eigenvectors' sign to enforce deterministic output
U, V = svd_flip(U, V)
components_ = V
# Get variance explained by singular values
explained_variance_ = (S**2) / (n_samples - 1)
total_var = explained_variance_.sum()
explained_variance_ratio_ = explained_variance_ / total_var
# Postprocess the number of components required
if n_components == 'mle':
n_components = \
_infer_dimension_(explained_variance_, n_samples, n_features)
elif 0 < n_components < 1.0:
# number of components for which the cumulated explained
# variance percentage is superior to the desired threshold
ratio_cumsum = explained_variance_ratio_.cumsum()
n_components = np.searchsorted(ratio_cumsum, n_components) + 1
# Compute noise covariance using Probabilistic PCA model
# The sigma2 maximum likelihood (cf. eq. 12.46)
if n_components < min(n_features, n_samples):
self.noise_variance_ = explained_variance_[n_components:].mean()
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = explained_variance_[:n_components]
self.explained_variance_ratio_ = \
explained_variance_ratio_[:n_components]
self.singular_values_ = S[:n_components]
return U, S, V
def _fit_full_vanilla(self, X, n_components):
"""Fit the model by computing full SVD on X"""
n_samples, n_features = X.shape
# Center data
self.mean_ = np.mean(X, axis=0)
X -= self.mean_
U, S, V = np.linalg.svd(X, full_matrices=False)
# flip eigenvectors' sign to enforce deterministic output
U, V = svd_flip(U, V)
components_ = V
# Get variance explained by singular values
explained_variance_ = (S**2) / (n_samples - 1)
total_var = explained_variance_.sum()
explained_variance_ratio_ = explained_variance_ / total_var
# Postprocess the number of components required
if n_components == 'mle':
n_components = \
_infer_dimension_(explained_variance_, n_samples, n_features)
elif 0 < n_components < 1.0:
n_components = _n_components_from_fraction(
explained_variance_ratio_, n_components)
# Compute noise covariance using Probabilistic PCA model
# The sigma2 maximum likelihood (cf. eq. 12.46)
if n_components < min(n_features, n_samples):
self.noise_variance_ = explained_variance_[n_components:].mean()
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = explained_variance_[:n_components]
self.explained_variance_ratio_ = \
explained_variance_ratio_[:n_components]
self.singular_values_ = S[:n_components]
return U, S, V
def _fit_full(self, X, n_components):
X = check_array(X, dtype=[np.float64, np.float32])
n_samples, n_features = X.shape
self._validate_n_components(n_components, n_samples, n_features)
self._fit_full_daal4py(X, min(X.shape))
U = self._transform_daal4py(X,
whiten=True,
check_X=False,
scale_eigenvalues=True)
V = self.components_
S = self.singular_values_
if n_components == 'mle':
if sklearn_check_version('0.23'):
n_components = _infer_dimension(self.explained_variance_,
n_samples)
else:
n_components = _infer_dimension_(self.explained_variance_,
n_samples, n_features)
elif 0 < n_components < 1.0:
ratio_cumsum = stable_cumsum(self.explained_variance_ratio_)
n_components = np.searchsorted(
ratio_cumsum, n_components, side='right') + 1
if n_components < min(n_features, n_samples):
self.noise_variance_ = self.explained_variance_[
n_components:].mean()
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = self.components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = self.explained_variance_[:n_components]
self.explained_variance_ratio_ = self.explained_variance_ratio_[:
n_components]
self.singular_values_ = self.singular_values_[:n_components]
return U, S, V
def _fit_full_daal4py(self, X, n_components):
n_samples, n_features = X.shape
# due to need to flip components, need to do full decomposition
self._fit_daal4py(X, min(n_samples, n_features))
U = self._transform_daal4py(X,
whiten=True,
check_X=False,
scale_eigenvalues=True)
V = self.components_
U, V = svd_flip(U, V)
U = U.copy()
V = V.copy()
S = self.singular_values_.copy()
if n_components == 'mle':
n_components = \
_infer_dimension_(self.explained_variance_, n_samples, n_features)
elif 0 < n_components < 1.0:
# number of components for which the cumulated explained
# variance percentage is superior to the desired threshold
ratio_cumsum = stable_cumsum(self.explained_variance_ratio_)
n_components = np.searchsorted(ratio_cumsum, n_components) + 1
# Compute noise covariance using Probabilistic PCA model
# The sigma2 maximum likelihood (cf. eq. 12.46)
if n_components < min(n_features, n_samples):
self.noise_variance_ = self.explained_variance_[
n_components:].mean()
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = self.components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = self.explained_variance_[:n_components]
self.explained_variance_ratio_ = \
self.explained_variance_ratio_[:n_components]
self.singular_values_ = self.singular_values_[:n_components]
return U, S, V
def _fit_full(self, X, n_components):
n_samples, n_features = X.shape
self._validate_n_components(n_components, n_samples, n_features)
self._fit_full_daal4py(X, min(X.shape))
U = None
V = self.components_
S = self.singular_values_
if n_components == 'mle':
if sklearn_check_version('0.23'):
n_components = _infer_dimension(self.explained_variance_,
n_samples)
else:
n_components = \
_infer_dimension_(self.explained_variance_, n_samples, n_features)
elif 0 < n_components < 1.0:
ratio_cumsum = stable_cumsum(self.explained_variance_ratio_)
n_components = np.searchsorted(
ratio_cumsum, n_components, side='right') + 1
if n_components < min(n_features, n_samples):
self.noise_variance_ = self.explained_variance_[
n_components:].mean()
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = self.components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = self.explained_variance_[:n_components]
self.explained_variance_ratio_ = self.explained_variance_ratio_[:
n_components]
self.singular_values_ = self.singular_values_[:n_components]
return U, S, V
def _fit_full_daal4py(self, X, n_components):
n_samples, n_features = X.shape
n_sf_min = min(n_samples, n_features)
if n_components == 'mle':
daal_n_components = n_features
elif n_components < 1:
daal_n_components = n_sf_min
else:
daal_n_components = n_components
fpType = getFPType(X)
covariance_algo = daal4py.covariance(
fptype=fpType, outputMatrixType='covarianceMatrix')
covariance_res = covariance_algo.compute(X)
self.mean_ = covariance_res.mean.ravel()
covariance = covariance_res.covariance
variances_ = np.array([covariance[i, i] for i in range(n_features)])
pca_alg = daal4py.pca(fptype=fpType,
method='correlationDense',
resultsToCompute='eigenvalue',
isDeterministic=True,
nComponents=daal_n_components)
pca_res = pca_alg.compute(X, covariance)
components_ = pca_res.eigenvectors
explained_variance_ = np.maximum(pca_res.eigenvalues.ravel(), 0)
tot_var = explained_variance_.sum()
explained_variance_ratio_ = explained_variance_ / tot_var
if n_components == 'mle':
if sklearn_check_version('0.23'):
n_components = _infer_dimension(explained_variance_, n_samples)
else:
n_components = \
_infer_dimension_(explained_variance_, n_samples, n_features)
elif 0 < n_components < 1.0:
ratio_cumsum = stable_cumsum(explained_variance_ratio_)
n_components = np.searchsorted(
ratio_cumsum, n_components, side='right') + 1
if n_components < n_sf_min:
if explained_variance_.shape[0] == n_sf_min:
self.noise_variance_ = explained_variance_[n_components:].mean(
)
else:
resid_var_ = variances_.sum()
resid_var_ -= explained_variance_[:n_components].sum()
self.noise_variance_ = resid_var_ / (n_sf_min - n_components)
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = explained_variance_[:n_components]
self.explained_variance_ratio_ = explained_variance_ratio_[:
n_components]
self.singular_values_ = np.sqrt(
(n_samples - 1) * self.explained_variance_)
def _fit_full(self, X, n_components):
self.accountant.check(self.epsilon, 0)
n_samples, n_features = X.shape
if self.centered:
self.mean_ = np.zeros_like(np.mean(X, axis=0))
else:
if self.bounds is None:
warnings.warn(
"Bounds parameter hasn't been specified, so falling back to determining range from the data.\n"
"This will result in additional privacy leakage. To ensure differential privacy with no "
"additional privacy loss, specify `range` for each valued returned by np.mean().",
PrivacyLeakWarning)
self.bounds = (np.min(X, axis=0), np.max(X, axis=0))
self.bounds = check_bounds(self.bounds, n_features)
self.mean_ = mean(X,
epsilon=self.epsilon / 2,
bounds=self.bounds,
axis=0,
accountant=BudgetAccountant())
X -= self.mean_
if self.data_norm is None:
warnings.warn(
"Data norm has not been specified and will be calculated on the data provided. This will "
"result in additional privacy leakage. To ensure differential privacy and no additional "
"privacy leakage, specify `data_norm` at initialisation.",
PrivacyLeakWarning)
self.data_norm = np.linalg.norm(X, axis=1).max()
X = clip_to_norm(X, self.data_norm)
XtX = np.dot(X.T, X)
mech = Wishart().set_epsilon(self.epsilon if self.centered else self.epsilon / 2).\
set_sensitivity(self.data_norm)
noisy_input = mech.randomise(XtX)
u, s, v = np.linalg.svd(noisy_input)
u, v = svd_flip(u, v)
s = np.sqrt(s)
components_ = v
# Get variance explained by singular values
explained_variance_ = (s**2) / (n_samples - 1)
total_var = explained_variance_.sum()
explained_variance_ratio_ = explained_variance_ / total_var
singular_values_ = s.copy() # Store the singular values.
# Post-process the number of components required
if n_components == 'mle':
try:
n_components = sk_pca._infer_dimension(explained_variance_,
n_samples)
except AttributeError:
n_components = sk_pca._infer_dimension_(
explained_variance_, n_samples, n_features)
elif 0 < n_components < 1.0:
# number of components for which the cumulated explained
# variance percentage is superior to the desired threshold
ratio_cumsum = stable_cumsum(explained_variance_ratio_)
n_components = np.searchsorted(ratio_cumsum, n_components) + 1
# Compute noise covariance using Probabilistic PCA model
# The sigma2 maximum likelihood (cf. eq. 12.46)
if n_components < min(n_features, n_samples):
self.noise_variance_ = explained_variance_[n_components:].mean()
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = explained_variance_[:n_components]
self.explained_variance_ratio_ = explained_variance_ratio_[:
n_components]
self.singular_values_ = singular_values_[:n_components]
self.accountant.spend(self.epsilon, 0)
return u, s, v
