msmbuilder.decomposition.
PCA
(n_components=None, copy=True, whiten=False, svd_solver='auto', tol=0.0, iterated_power='auto', random_state=None)¶Principal component analysis (PCA)
Linear dimensionality reduction using Singular Value Decomposition of the data to project it to a lower dimensional space.
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.
It can also use the scipy.sparse.linalg ARPACK implementation of the truncated SVD.
Notice that this class does not support sparse input. See
TruncatedSVD
for an alternative with sparse data.
Read more in the User Guide.
Parameters: |
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components_
¶array, [n_components, n_features] – Principal axes in feature space, representing the directions of
maximum variance in the data. The components are sorted by
explained_variance_
.
explained_variance_
¶array, [n_components] – The amount of variance explained by each of the selected components.
New in version 0.18.
explained_variance_ratio_
¶array, [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 explained variances is equal to 1.0.
mean_
¶array, [n_features] – Per-feature empirical mean, estimated from the training set.
Equal to X.mean(axis=1).
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 n_features if n_components is None.
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 computed the estimated data covariance and score samples.
References
For n_components == ‘mle’, this class uses the method of Thomas P. Minka: Automatic Choice of Dimensionality for PCA. NIPS 2000: 598-604
Implements the probabilistic PCA model from: M. Tipping and C. Bishop, Probabilistic Principal Component Analysis, Journal of the Royal Statistical Society, Series B, 61, Part 3, pp. 611-622 via the score and score_samples methods. See http://www.miketipping.com/papers/met-mppca.pdf
For svd_solver == ‘arpack’, refer to scipy.sparse.linalg.svds.
For svd_solver == ‘randomized’, see: Finding structure with randomness: Stochastic algorithms for constructing approximate matrix decompositions Halko, et al., 2009 (arXiv:909) A randomized algorithm for the decomposition of matrices Per-Gunnar Martinsson, Vladimir Rokhlin and Mark Tygert
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(copy=True, iterated_power='auto', n_components=2, random_state=None,
svd_solver='auto', tol=0.0, whiten=False)
>>> print(pca.explained_variance_ratio_)
[ 0.99244... 0.00755...]
>>> pca = PCA(n_components=2, svd_solver='full')
>>> pca.fit(X)
PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,
svd_solver='full', tol=0.0, whiten=False)
>>> print(pca.explained_variance_ratio_)
[ 0.99244... 0.00755...]
>>> pca = PCA(n_components=1, svd_solver='arpack')
>>> pca.fit(X)
PCA(copy=True, iterated_power='auto', n_components=1, random_state=None,
svd_solver='arpack', tol=0.0, whiten=False)
>>> print(pca.explained_variance_ratio_)
[ 0.99244...]
See also
KernelPCA
, SparsePCA
, TruncatedSVD
, IncrementalPCA
__init__
(n_components=None, copy=True, whiten=False, svd_solver='auto', tol=0.0, iterated_power='auto', random_state=None)¶Methods
__init__ ([n_components, copy, whiten, ...]) |
|
fit (sequences[, y]) |
Fit the model |
fit_transform (sequences[, y]) |
Fit the model and apply dimensionality reduction |
get_covariance () |
Compute data covariance with the generative model. |
get_params ([deep]) |
Get parameters for this estimator. |
get_precision () |
Compute data precision matrix with the generative model. |
inverse_transform (X[, y]) |
Transform data back to its original space. |
partial_transform (sequence) |
Apply dimensionality reduction to single sequence |
score (X[, y]) |
Return the average log-likelihood of all samples. |
score_samples (X) |
Return the log-likelihood of each sample. |
set_params (\*\*params) |
Set the parameters of this estimator. |
summarize () |
|
transform (sequences) |
Apply dimensionality reduction to sequences |
fit
(sequences, y=None)¶Fit the model
Parameters: |
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Returns: | |
Return type: | self |
fit_transform
(sequences, y=None)¶Fit the model and apply dimensionality reduction
Parameters: |
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Returns: | sequence_new |
Return type: | list of array-like, each of shape (n_samples_i, n_components) |
get_covariance
()¶Compute data covariance with the generative model.
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 – Estimated covariance of data. |
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Return type: | array, shape=(n_features, n_features) |
get_params
(deep=True)¶Get parameters for this estimator.
Parameters: | deep (boolean, optional) – If True, will return the parameters for this estimator and contained subobjects that are estimators. |
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Returns: | params – Parameter names mapped to their values. |
Return type: | mapping of string to any |
get_precision
()¶Compute data precision matrix with the generative model.
Equals the inverse of the covariance but computed with the matrix inversion lemma for efficiency.
Returns: | precision – Estimated precision of data. |
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Return type: | array, shape=(n_features, n_features) |
inverse_transform
(X, y=None)¶Transform data back to its original space.
In other words, return an input X_original whose transform would be X.
Parameters: | X (array-like, shape (n_samples, n_components)) – New data, where n_samples is the number of samples and n_components is the number of components. |
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Returns: | |
Return type: | X_original array-like, shape (n_samples, n_features) |
Notes
If whitening is enabled, inverse_transform will compute the exact inverse operation, which includes reversing whitening.
partial_transform
(sequence)¶Apply dimensionality reduction to single sequence
Parameters: | sequence (array like, shape (n_samples, n_features)) – A single sequence to transform |
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Returns: | out |
Return type: | array like, shape (n_samples, n_features) |
score
(X, y=None)¶Return the average log-likelihood of all samples.
See. “Pattern Recognition and Machine Learning” by C. Bishop, 12.2.1 p. 574 or http://www.miketipping.com/papers/met-mppca.pdf
Parameters: | X (array, shape(n_samples, n_features)) – The data. |
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Returns: | ll – Average log-likelihood of the samples under the current model |
Return type: | float |
score_samples
(X)¶Return the log-likelihood of each sample.
See. “Pattern Recognition and Machine Learning” by C. Bishop, 12.2.1 p. 574 or http://www.miketipping.com/papers/met-mppca.pdf
Parameters: | X (array, shape(n_samples, n_features)) – The data. |
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Returns: | ll – Log-likelihood of each sample under the current model |
Return type: | array, shape (n_samples,) |
set_params
(**params)¶Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects
(such as pipelines). The latter have parameters of the form
<component>__<parameter>
so that it’s possible to update each
component of a nested object.
Returns: | |
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Return type: | self |
transform
(sequences)¶Apply dimensionality reduction to sequences
Parameters: | sequences (list of array-like, each of shape (n_samples_i, n_features)) – Sequence data to transform, where n_samples_i in the number of samples in sequence i and n_features is the number of features. |
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Returns: | sequence_new |
Return type: | list of array-like, each of shape (n_samples_i, n_components) |