Principal Component Analysis (PCA)
Linear dimensionality reduction using Singular Value Decomposition of the data to project it to a lower dimensional space.
Configuration: |
n_components
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
svd_solver
- auto :
the solver is selected by a default policy based on X.shape and
n_components: 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 enabled. 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
- 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.
tol
Tolerance for singular values computed by svd_solver == ‘arpack’.
iterated_power
Number of iterations for the power method computed by
svd_solver == ‘randomized’.
whiten
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.
|
Attributes: |
components_
Principal axes in feature space, representing the directions of
maximum variance in the data. The components are sorted by
explained_variance_ .
explained_variance_
The amount of variance explained by each of the selected components.
Equal to n_components largest eigenvalues
of the covariance matrix of X.
explained_variance_ratio_
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.
mean_
Per-feature empirical mean, estimated from the training set.
Equal to X.mean(axis=0).
n_components_
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.
noise_variance_
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.
|
Inputs: | |
Outputs: |
- model : model
Model
|
- Output ports:
-
- Configuration:
- n_components
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
- svd_solver
- auto :
- the solver is selected by a default policy based on X.shape and
n_components: 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 enabled. 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
- 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.
- tol
Tolerance for singular values computed by svd_solver == ‘arpack’.
- iterated_power
Number of iterations for the power method computed by
svd_solver == ‘randomized’.
- whiten
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.
Some of the docstrings for this module have been automatically
extracted from the scikit-learn library
and are covered by their respective licenses.
-
class
node_decomposition.
PrincipalComponentAnalysis
[source]