Principal Component Analysis (PCA)

../../../../_images/PCA.svg

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]

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 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 n_components cannot be equal to n_features for svd_solver == ‘arpack’.

  • 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.

  • 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 < X.shape

    randomized :

    run randomized SVD by the method of Halko et al.

    New in version 0.18.0.

  • tol

    Tolerance for singular values computed by svd_solver == ‘arpack’.

    New in version 0.18.0.

  • iterated_power

    Number of iterations for the power method computed by svd_solver == ‘randomized’.

    New in version 0.18.0.

  • 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.

    New in version 0.18.

  • 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 explained variances 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 n_features 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 computed 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