#!/usr/bin/env python3
""" Principal Component Analysis algorithm module. """
from dask_ml.decomposition import PCA as PCA_MCPU
from sklearn.decomposition import PCA as PCA_CPU
from dasf.transforms.base import Fit, FitTransform, TargeteredTransform
from dasf.utils.funcs import is_dask_gpu_supported, is_dask_supported, is_gpu_supported
try:
from cuml.dask.decomposition import PCA as PCA_MGPU
from cuml.decomposition import PCA as PCA_GPU
except ImportError:
pass
[docs]
class PCA(Fit, FitTransform, TargeteredTransform):
"""
Principal component analysis (PCA).
Linear dimensionality reduction using Singular Value Decomposition of the
data to project it to a lower dimensional space. The input data is centered
but not scaled for each feature before applying the SVD.
It uses the LAPACK implementation of the full SVD or a randomized truncated
SVD by the method of Halko et al. 2009, depending on the shape of the input
data and the number of components to extract.
With sparse inputs, the ARPACK implementation of the truncated SVD can be
used (i.e. through :func:`scipy.sparse.linalg.svds`). Alternatively, one
may consider :class:`TruncatedSVD` where the data are not centered.
Notice that this class only supports sparse inputs for some solvers such as
"arpack" and "covariance_eigh". See :class:`TruncatedSVD` for an
alternative with sparse data.
For a usage example, see
:ref:`sphx_glr_auto_examples_decomposition_plot_pca_iris.py`
Read more in the :ref:`User Guide <PCA>`.
Parameters
----------
n_components : int, float or 'mle', default=None
Number of components to keep.
if n_components is not set all components are kept::
n_components == min(n_samples, n_features)
If ``n_components == 'mle'`` and ``svd_solver == 'full'``, Minka's
MLE is used to guess the dimension. Use of ``n_components == 'mle'``
will interpret ``svd_solver == 'auto'`` as ``svd_solver == 'full'``.
If ``0 < n_components < 1`` and ``svd_solver == 'full'``, select the
number of components such that the amount of variance that needs to be
explained is greater than the percentage specified by n_components.
If ``svd_solver == 'arpack'``, the number of components must be
strictly less than the minimum of n_features and n_samples.
Hence, the None case results in::
n_components == min(n_samples, n_features) - 1
copy : bool, default=True
If False, data passed to fit are overwritten and running
fit(X).transform(X) will not yield the expected results,
use fit_transform(X) instead.
whiten : bool, default=False
When True (False by default) the `components_` vectors are multiplied
by the square root of n_samples and then divided by the singular values
to ensure uncorrelated outputs with unit component-wise variances.
Whitening will remove some information from the transformed signal
(the relative variance scales of the components) but can sometime
improve the predictive accuracy of the downstream estimators by
making their data respect some hard-wired assumptions.
svd_solver : {'auto', 'full', 'covariance_eigh', 'arpack', 'randomized'},\
default='auto'
"auto" :
The solver is selected by a default 'auto' policy is based on `X.shape` and
`n_components`: if the input data has fewer than 1000 features and
more than 10 times as many samples, then the "covariance_eigh"
solver is used. Otherwise, if the input data is larger than 500x500
and the number of components to extract is lower than 80% of the
smallest dimension of the data, then the more efficient
"randomized" method is selected. Otherwise the exact "full" SVD is
computed and optionally truncated afterwards.
"full" :
Run exact full SVD calling the standard LAPACK solver via
`scipy.linalg.svd` and select the components by postprocessing
"covariance_eigh" :
Precompute the covariance matrix (on centered data), run a
classical eigenvalue decomposition on the covariance matrix
typically using LAPACK and select the components by postprocessing.
This solver is very efficient for n_samples >> n_features and small
n_features. It is, however, not tractable otherwise for large
n_features (large memory footprint required to materialize the
covariance matrix). Also note that compared to the "full" solver,
this solver effectively doubles the condition number and is
therefore less numerical stable (e.g. on input data with a large
range of singular values).
"arpack" :
Run SVD truncated to `n_components` calling ARPACK solver via
`scipy.sparse.linalg.svds`. It requires strictly
`0 < n_components < min(X.shape)`
"randomized" :
Run randomized SVD by the method of Halko et al.
.. versionadded:: 0.18.0
.. versionchanged:: 1.5
Added the 'covariance_eigh' solver.
tol : float, default=0.0
Tolerance for singular values computed by svd_solver == 'arpack'.
Must be of range [0.0, infinity).
.. versionadded:: 0.18.0
iterated_power : int or 'auto', default='auto'
Number of iterations for the power method computed by
svd_solver == 'randomized'.
Must be of range [0, infinity).
.. versionadded:: 0.18.0
n_oversamples : int, default=10
This parameter is only relevant when `svd_solver="randomized"`.
It corresponds to the additional number of random vectors to sample the
range of `X` so as to ensure proper conditioning. See
:func:`~sklearn.utils.extmath.randomized_svd` for more details.
.. versionadded:: 1.1
power_iteration_normalizer : {'auto', 'QR', 'LU', 'none'}, default='auto'
Power iteration normalizer for randomized SVD solver.
Not used by ARPACK. See :func:`~sklearn.utils.extmath.randomized_svd`
for more details.
.. versionadded:: 1.1
random_state : int, RandomState instance or None, default=None
Used when the 'arpack' or 'randomized' solvers are used. Pass an int
for reproducible results across multiple function calls.
See :term:`Glossary <random_state>`.
.. versionadded:: 0.18.0
Attributes
----------
components_ : ndarray of shape (n_components, n_features)
Principal axes in feature space, representing the directions of
maximum variance in the data. Equivalently, the right singular
vectors of the centered input data, parallel to its eigenvectors.
The components are sorted by decreasing ``explained_variance_``.
explained_variance_ : ndarray of shape (n_components,)
The amount of variance explained by each of the selected components.
The variance estimation uses `n_samples - 1` degrees of freedom.
Equal to n_components largest eigenvalues
of the covariance matrix of X.
.. versionadded:: 0.18
explained_variance_ratio_ : ndarray of shape (n_components,)
Percentage of variance explained by each of the selected components.
If ``n_components`` is not set then all components are stored and the
sum of the ratios is equal to 1.0.
singular_values_ : ndarray of shape (n_components,)
The singular values corresponding to each of the selected components.
The singular values are equal to the 2-norms of the ``n_components``
variables in the lower-dimensional space.
.. versionadded:: 0.19
mean_ : ndarray of shape (n_features,)
Per-feature empirical mean, estimated from the training set.
Equal to `X.mean(axis=0)`.
n_components_ : int
The estimated number of components. When n_components is set
to 'mle' or a number between 0 and 1 (with svd_solver == 'full') this
number is estimated from input data. Otherwise it equals the parameter
n_components, or the lesser value of n_features and n_samples
if n_components is None.
n_samples_ : int
Number of samples in the training data.
noise_variance_ : float
The estimated noise covariance following the Probabilistic PCA model
from Tipping and Bishop 1999. See "Pattern Recognition and
Machine Learning" by C. Bishop, 12.2.1 p. 574 or
http://www.miketipping.com/papers/met-mppca.pdf. It is required to
compute the estimated data covariance and score samples.
Equal to the average of (min(n_features, n_samples) - n_components)
smallest eigenvalues of the covariance matrix of X.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
See Also
--------
KernelPCA : Kernel Principal Component Analysis.
SparsePCA : Sparse Principal Component Analysis.
TruncatedSVD : Dimensionality reduction using truncated SVD.
IncrementalPCA : Incremental Principal Component Analysis.
References
----------
For n_components == 'mle', this class uses the method from:
`Minka, T. P.. "Automatic choice of dimensionality for PCA".
In NIPS, pp. 598-604 <https://tminka.github.io/papers/pca/minka-pca.pdf>`_
Implements the probabilistic PCA model from:
`Tipping, M. E., and Bishop, C. M. (1999). "Probabilistic principal
component analysis". Journal of the Royal Statistical Society:
Series B (Statistical Methodology), 61(3), 611-622.
<http://www.miketipping.com/papers/met-mppca.pdf>`_
via the score and score_samples methods.
For svd_solver == 'arpack', refer to `scipy.sparse.linalg.svds`.
For svd_solver == 'randomized', see:
:doi:`Halko, N., Martinsson, P. G., and Tropp, J. A. (2011).
"Finding structure with randomness: Probabilistic algorithms for
constructing approximate matrix decompositions".
SIAM review, 53(2), 217-288.
<10.1137/090771806>`
and also
:doi:`Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011).
"A randomized algorithm for the decomposition of matrices".
Applied and Computational Harmonic Analysis, 30(1), 47-68.
<10.1016/j.acha.2010.02.003>`
Examples
--------
>>> import numpy as np
>>> from sklearn.decomposition import PCA
>>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
>>> pca = PCA(n_components=2)
>>> pca.fit(X)
PCA(n_components=2)
>>> print(pca.explained_variance_ratio_)
[0.9924... 0.0075...]
>>> print(pca.singular_values_)
[6.30061... 0.54980...]
>>> pca = PCA(n_components=2, svd_solver='full')
>>> pca.fit(X)
PCA(n_components=2, svd_solver='full')
>>> print(pca.explained_variance_ratio_)
[0.9924... 0.00755...]
>>> print(pca.singular_values_)
[6.30061... 0.54980...]
>>> pca = PCA(n_components=1, svd_solver='arpack')
>>> pca.fit(X)
PCA(n_components=1, svd_solver='arpack')
>>> print(pca.explained_variance_ratio_)
[0.99244...]
>>> print(pca.singular_values_)
[6.30061...]
"""
def __init__(
self,
n_components=None,
copy=True,
whiten=False,
svd_solver="auto",
tol=0.0,
iterated_power="auto",
random_state=None,
*args,
**kwargs,
):
TargeteredTransform.__init__(self, *args, **kwargs)
self.__pca_cpu = PCA_CPU(
n_components=n_components,
copy=copy,
whiten=whiten,
svd_solver=svd_solver,
tol=tol,
iterated_power=iterated_power,
random_state=random_state,
)
self.__pca_mcpu = PCA_MCPU(
n_components=n_components,
copy=copy,
whiten=whiten,
svd_solver=svd_solver,
tol=tol,
iterated_power=iterated_power,
random_state=random_state,
)
if is_gpu_supported():
try:
if not isinstance(iterated_power, int):
iterated_power = 15 # Default
self.__pca_gpu = PCA_GPU(
n_components=n_components,
copy=copy,
whiten=whiten,
svd_solver=svd_solver,
tol=tol,
iterated_power=iterated_power,
random_state=random_state,
)
except TypeError:
self.__pca_gpu = None
except NameError:
self.__pca_gpu = None
else:
self.__pca_gpu = None
# XXX: PCA in Multi GPU requires a Client instance,
# skip if not present.
if is_dask_gpu_supported():
self.__pca_mgpu = PCA_MGPU(
n_components=n_components,
copy=copy,
whiten=whiten,
svd_solver=svd_solver,
tol=tol,
iterated_power=iterated_power,
random_state=random_state,
)
else:
self.__pca_mgpu = None
[docs]
def _lazy_fit_cpu(self, X, y=None, sample_weights=None):
"""
Fit the model with X using Dask with CPUs only.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
Training data, where `n_samples` is the number of samples
and `n_features` is the number of features.
y : Ignored
Ignored.
Returns
-------
self : object
Returns the instance itself.
"""
return self.__pca_mcpu.fit(X=X)
[docs]
def _lazy_fit_gpu(self, X, y=None, sample_weights=None):
"""
Fit the model with X using Dask with GPUs only.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
Training data, where `n_samples` is the number of samples
and `n_features` is the number of features.
y : Ignored
Ignored.
Returns
-------
self : object
Returns the instance itself.
"""
if self.__pca_mgpu is None:
raise NotImplementedError("GPU is not supported")
return self.__pca_mgpu.fit(X=X)
[docs]
def _fit_cpu(self, X, y=None, sample_weights=None):
"""
Fit the model with X using CPU only
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
Training data, where `n_samples` is the number of samples
and `n_features` is the number of features.
y : Ignored
Ignored.
Returns
-------
self : object
Returns the instance itself.
"""
return self.__pca_cpu.fit(X=X)
[docs]
def _fit_gpu(self, X, y=None, sample_weights=None):
"""
Fit the model with X with GPU only.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
Training data, where `n_samples` is the number of samples
and `n_features` is the number of features.
y : Ignored
Ignored.
Returns
-------
self : object
Returns the instance itself.
"""
if self.__pca_gpu is None:
raise NotImplementedError("GPU is not supported")
return self.__pca_gpu.fit(X=X)
[docs]
def _get_covariance_cpu(self):
"""
Compute data covariance with the generative model for CPU only.
``cov = components_.T * S**2 * components_ + sigma2 * eye(n_features)``
where S**2 contains the explained variances, and sigma2 contains the
noise variances.
Returns
-------
cov : array of shape=(n_features, n_features)
Estimated covariance of data.
"""
return self.__pca_cpu.get_covariance()
[docs]
def get_covariance(self):
"""
Generic function to get the covariance.
Returns
-------
cov : array of shape=(n_features, n_features)
Estimated covariance of data.
"""
if not is_dask_supported() and not is_gpu_supported():
return self._get_covariance_cpu()
else:
raise NotImplementedError("GPU is not supported")
[docs]
def _get_precision_cpu(self):
"""
Compute data precision matrix with the generative model for CPU only.
Equals the inverse of the covariance but computed with
the matrix inversion lemma for efficiency.
Returns
-------
precision : array, shape=(n_features, n_features)
Estimated precision of data.
"""
return self.__pca_cpu.get_precision()
[docs]
def get_precision(self):
"""
Generic function to get the precision.
Returns
-------
precision : array, shape=(n_features, n_features)
Estimated precision of data.
"""
if not is_dask_supported() and not is_gpu_supported():
return self._get_precision_cpu()
else:
raise NotImplementedError("GPU is not supported")