`skoot.decomposition`.SelectivePCA¶

class skoot.decomposition.SelectivePCA(cols=None, as_df=True, trans_col_name=None, **kwargs)[source][source]¶

Principal component analysis (PCA) (applied to selected columns).

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 TruncatedSVD for an alternative with sparse data.

Read more in the User Guide.

This class wraps scikit-learn’s PCA. When a pd.DataFrame is passed to the fit method, the transformation is applied to the selected columns, which are subsequently dropped from the frame. All remaining columns are left alone.

Parameters:

cols : array-like, shape=(n_features,), optional (default=None)

The names of the columns on which to apply the transformation. If no column names are provided, the transformer will be fit on the entire frame. Note that the transformation will also only apply to the specified columns, and any other non-specified columns will still be present after the transformation.

as_df : bool, optional (default=True)

Whether to return a Pandas DataFrame in the transform method. If False, will return a Numpy ndarray instead. Since most skoot transformers depend on explicitly-named DataFrame features, the as_df parameter is True by default.

trans_col_name : str, unicode or iterable, optional

The name or list of names to apply to the transformed column(s). If a string is provided, it is used as a prefix for new columns. If an iterable is provided, its dimensions must match the number of produced columns. If None (default), will use the estimator class name as the prefix.

n_components : int, float, None or string

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 : string {‘auto’, ‘full’, ‘arpack’, ‘randomized’}

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.

New in version 0.18.0.

tol : float >= 0, optional (default .0)

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

New in version 0.18.0.

iterated_power : int >= 0, or ‘auto’, (default ‘auto’)

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

New in version 0.18.0.

random_state : int, RandomState instance or None, optional (default None)

If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when svd_solver == ‘arpack’ or ‘randomized’.

New in version 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.
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.

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(copy=True, iterated_power='auto', n_components=2, random_state=None,
  svd_solver='auto', tol=0.0, whiten=False)
>>> print(pca.explained_variance_ratio_)  
[0.9924... 0.0075...]
>>> print(pca.singular_values_)  
[6.30061... 0.54980...]

>>> 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_)  
[0.9924... 0.00755...]
>>> print(pca.singular_values_)  
[6.30061... 0.54980...]

>>> 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...]
>>> print(pca.singular_values_)  
[6.30061...]

Methods

`fit`(X[, y])	Fit the wrapped transformer.
`fit_transform`(X[, y])	Fit to data, then transform it.
`get_params`([deep])	Get parameters for this estimator.
`set_params`(**params)	Set the parameters of this estimator.
`transform`(X)	Transform a test dataframe.

__init__(cols=None, as_df=True, trans_col_name=None, **kwargs)[source]¶: Initialize self. See help(type(self)) for accurate signature.

fit(X, y=None, **fit_kwargs)[source]¶

Fit the wrapped transformer.

This method will fit the wrapped sklearn transformer on the selected columns, leaving other columns alone.

Parameters:

X : pd.DataFrame, shape=(n_samples, n_features)

The Pandas frame to fit. The frame will only be fit on the prescribed cols (see __init__) or all of them if cols is None. Furthermore, X will not be altered in the process of the fit.

y : array-like or None, shape=(n_samples,), optional (default=None)

Pass-through for sklearn.pipeline.Pipeline. Even if explicitly set, will not change behavior of fit.

fit_transform(X, y=None, **fit_params)[source]¶

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters:

X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.

Returns:

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters:

deep : boolean, optional

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.

set_params(**params)[source]¶

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:	self

transform(X)[source]¶

Transform a test dataframe.

Parameters:

X : pd.DataFrame, shape=(n_samples, n_features)

The Pandas frame to transform. The operation will be applied to a copy of the input data, and the result will be returned.

Returns:

X : pd.DataFrame, shape=(n_samples, n_features)

The operation is applied to a copy of X, and the result set is returned.

Examples using `skoot.decomposition.SelectivePCA`¶

Profiling estimators

skoot.decomposition.SelectivePCA¶

Examples using skoot.decomposition.SelectivePCA¶

`skoot.decomposition`.SelectivePCA¶

Examples using `skoot.decomposition.SelectivePCA`¶