type t = [ `BaseEstimator | `Object | `PCA | `TransformerMixin ] Obj.tval of_pyobject : Py.Object.t -> tval to_pyobject : [> tag ] Obj.t -> Py.Object.tval create :
?n_components:[ `S of string | `I of int | `F of float ] ->
?copy:bool ->
?whiten:bool ->
?svd_solver:[ `Auto | `Full | `Arpack | `Randomized ] ->
?tol:float ->
?iterated_power:[ `Auto | `I of int ] ->
?random_state:int ->
unit ->
tPrincipal 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.
It can also use the scipy.sparse.linalg ARPACK implementation of the truncated SVD.
Notice that this class does not support sparse input. See :class:`TruncatedSVD` for an alternative with sparse data.
Read more in the :ref:`User Guide <PCA>`.
Parameters ---------- n_components : int, float, None or str 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, optional (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 : str 'auto', 'full', 'arpack', 'randomized' If 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. If full : run exact full SVD calling the standard LAPACK solver via `scipy.linalg.svd` and select the components by postprocessing If arpack : run SVD truncated to n_components calling ARPACK solver via `scipy.sparse.linalg.svds`. It requires strictly 0 < n_components < min(X.shape) If randomized : run randomized SVD by the method of Halko et al.
.. versionadded:: 0.18.0
tol : float >= 0, optional (default .0) Tolerance for singular values computed by svd_solver == 'arpack'.
.. versionadded:: 0.18.0
iterated_power : int >= 0, or 'auto', (default 'auto') Number of iterations for the power method computed by svd_solver == 'randomized'.
.. versionadded:: 0.18.0
random_state : int, RandomState instance, default=None Used when ``svd_solver`` == 'arpack' or 'randomized'. Pass an int for reproducible results across multiple function calls. See :term:`Glossary <random_state>`.
.. versionadded:: 0.18.0
Attributes ---------- components_ : array, shape (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, shape (n_components,) The amount of variance explained by each of the selected components.
Equal to n_components largest eigenvalues of the covariance matrix of X.
.. versionadded:: 0.18
explained_variance_ratio_ : array, 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_ : array, 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_ : array, 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_features_ : int Number of features in the training data.
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.
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 of *Minka, T. P. 'Automatic choice of dimensionality for PCA'. In NIPS, pp. 598-604*
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. 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: *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.* and also *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.*
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...
val fit : ?y:Py.Object.t -> x:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> tFit the model with X.
Parameters ---------- X : array-like, shape (n_samples, n_features) Training data, where n_samples is the number of samples and n_features is the number of features.
y : None Ignored variable.
Returns ------- self : object Returns the instance itself.
val fit_transform :
?y:Py.Object.t ->
x:[> `ArrayLike ] Np.Obj.t ->
[> tag ] Obj.t ->
[> `ArrayLike ] Np.Obj.tFit the model with X and apply the dimensionality reduction on X.
Parameters ---------- X : array-like, shape (n_samples, n_features) Training data, where n_samples is the number of samples and n_features is the number of features.
y : None Ignored variable.
Returns ------- X_new : array-like, shape (n_samples, n_components) Transformed values.
Notes ----- This method returns a Fortran-ordered array. To convert it to a C-ordered array, use 'np.ascontiguousarray'.
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 : array, shape=(n_features, n_features) Estimated covariance of data.
Get parameters for this estimator.
Parameters ---------- deep : bool, default=True If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns ------- params : mapping of string to any Parameter names mapped to their values.
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 : array, shape=(n_features, n_features) Estimated precision of data.
val inverse_transform :
x:[> `ArrayLike ] Np.Obj.t ->
[> tag ] Obj.t ->
Py.Object.tTransform 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.
Returns ------- 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.
val score :
?y:Py.Object.t ->
x:[> `ArrayLike ] Np.Obj.t ->
[> tag ] Obj.t ->
floatReturn 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.
y : None Ignored variable.
Returns ------- ll : float Average log-likelihood of the samples under the current model.
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.
Returns ------- ll : array, shape (n_samples,) Log-likelihood of each sample under the current model.
val set_params : ?params:(string * Py.Object.t) list -> [> tag ] Obj.t -> tSet 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.
Parameters ---------- **params : dict Estimator parameters.
Returns ------- self : object Estimator instance.
Apply dimensionality reduction to X.
X is projected on the first principal components previously extracted from a training set.
Parameters ---------- X : array-like, shape (n_samples, n_features) New data, where n_samples is the number of samples and n_features is the number of features.
Returns ------- X_new : array-like, shape (n_samples, n_components)
Examples --------
>>> import numpy as np >>> from sklearn.decomposition import IncrementalPCA >>> X = np.array([-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]) >>> ipca = IncrementalPCA(n_components=2, batch_size=3) >>> ipca.fit(X) IncrementalPCA(batch_size=3, n_components=2) >>> ipca.transform(X) # doctest: +SKIP
Attribute components_: get value or raise Not_found if None.
Attribute components_: get value as an option.
Attribute explained_variance_: get value or raise Not_found if None.
Attribute explained_variance_: get value as an option.
Attribute explained_variance_ratio_: get value or raise Not_found if None.
Attribute explained_variance_ratio_: get value as an option.
Attribute singular_values_: get value or raise Not_found if None.
Attribute singular_values_: get value as an option.
val n_components_ : t -> intAttribute n_components_: get value or raise Not_found if None.
val n_components_opt : t -> int optionAttribute n_components_: get value as an option.
val n_features_ : t -> intAttribute n_features_: get value or raise Not_found if None.
val n_features_opt : t -> int optionAttribute n_features_: get value as an option.
val n_samples_ : t -> intAttribute n_samples_: get value or raise Not_found if None.
val n_samples_opt : t -> int optionAttribute n_samples_: get value as an option.
val noise_variance_ : t -> floatAttribute noise_variance_: get value or raise Not_found if None.
val noise_variance_opt : t -> float optionAttribute noise_variance_: get value as an option.
val to_string : t -> stringPrint the object to a human-readable representation.
val show : t -> stringPrint the object to a human-readable representation.
val pp : Format.formatter -> t -> unitPretty-print the object to a formatter.