`sklearn.decomposition`.IncrementalPCA¶

class sklearn.decomposition.IncrementalPCA(n_components=None, *, whiten=False, copy=True, batch_size=None)[source]¶

Incremental principal components analysis (IPCA).

Linear dimensionality reduction using Singular Value Decomposition of the data, keeping only the most significant singular vectors to project the data to a lower dimensional space. The input data is centered but not scaled for each feature before applying the SVD.

Depending on the size of the input data, this algorithm can be much more memory efficient than a PCA, and allows sparse input.

This algorithm has constant memory complexity, on the order of batch_size * n_features, enabling use of np.memmap files without loading the entire file into memory. For sparse matrices, the input is converted to dense in batches (in order to be able to subtract the mean) which avoids storing the entire dense matrix at any one time.

The computational overhead of each SVD is O(batch_size * n_features ** 2), but only 2 * batch_size samples remain in memory at a time. There will be n_samples / batch_size SVD computations to get the principal components, versus 1 large SVD of complexity O(n_samples * n_features ** 2) for PCA.

See also

PCA: Principal component analysis (PCA).
KernelPCA: Kernel Principal component analysis (KPCA).
SparsePCA: Sparse Principal Components Analysis (SparsePCA).
TruncatedSVD: Dimensionality reduction using truncated SVD.

Notes

Implements the incremental PCA model from: D. Ross, J. Lim, R. Lin, M. Yang, Incremental Learning for Robust Visual Tracking, International Journal of Computer Vision, Volume 77, Issue 1-3, pp. 125-141, May 2008. See https://www.cs.toronto.edu/~dross/ivt/RossLimLinYang_ijcv.pdf

This model is an extension of the Sequential Karhunen-Loeve Transform from: A. Levy and M. Lindenbaum, Sequential Karhunen-Loeve Basis Extraction and its Application to Images, IEEE Transactions on Image Processing, Volume 9, Number 8, pp. 1371-1374, August 2000.

We have specifically abstained from an optimization used by authors of both papers, a QR decomposition used in specific situations to reduce the algorithmic complexity of the SVD. The source for this technique is Matrix Computations, Third Edition, G. Holub and C. Van Loan, Chapter 5, section 5.4.4, pp 252-253.. This technique has been omitted because it is advantageous only when decomposing a matrix with n_samples (rows) >= 5/3 * n_features (columns), and hurts the readability of the implemented algorithm. This would be a good opportunity for future optimization, if it is deemed necessary.

References

D. Ross, J. Lim, R. Lin, M. Yang. Incremental Learning for Robust Visual Tracking, International Journal of Computer Vision, Volume 77, Issue 1-3, pp. 125-141, May 2008.

G. Golub and C. Van Loan. Matrix Computations, Third Edition, Chapter 5, Section 5.4.4, pp. 252-253.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.decomposition import IncrementalPCA
>>> from scipy import sparse
>>> X, _ = load_digits(return_X_y=True)
>>> transformer = IncrementalPCA(n_components=7, batch_size=200)
>>> # either partially fit on smaller batches of data
>>> transformer.partial_fit(X[:100, :])
IncrementalPCA(batch_size=200, n_components=7)
>>> # or let the fit function itself divide the data into batches
>>> X_sparse = sparse.csr_matrix(X)
>>> X_transformed = transformer.fit_transform(X_sparse)
>>> X_transformed.shape
(1797, 7)

Methods

`fit`(X[, y])	Fit the model with X, using minibatches of size batch_size.
`fit_transform`(X[, y])	Fit to data, then transform it.
`get_covariance`()	Compute data covariance with the generative model.
`get_feature_names_out`([input_features])	Get output feature names for transformation.
`get_params`([deep])	Get parameters for this estimator.
`get_precision`()	Compute data precision matrix with the generative model.
`inverse_transform`(X)	Transform data back to its original space.
`partial_fit`(X[, y, check_input])	Incremental fit with X.
`set_params`(**params)	Set the parameters of this estimator.
`transform`(X)	Apply dimensionality reduction to X.

fit(X, y=None)[source]¶

Fit the model with X, using minibatches of size batch_size.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features): Training data, where n_samples is the number of samples and n_features is the number of features.
yIgnored: Not used, present for API consistency by convention.

Returns:

selfobject: Returns the instance itself.

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:

Xarray-like of shape (n_samples, n_features): Input samples.
yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None: Target values (None for unsupervised transformations).
**fit_paramsdict: Additional fit parameters.

Returns:

X_newndarray array of shape (n_samples, n_features_new): Transformed array.

get_covariance()[source]¶

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:

covarray of shape=(n_features, n_features): Estimated covariance of data.

get_feature_names_out(input_features=None)[source]¶

Get output feature names for transformation.

Parameters:

input_featuresarray-like of str or None, default=None: Only used to validate feature names with the names seen in fit.

Returns:

feature_names_outndarray of str objects: Transformed feature names.

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

get_precision()[source]¶

Compute data precision matrix with the generative model.

Equals the inverse of the covariance but computed with the matrix inversion lemma for efficiency.

Returns:

precisionarray, shape=(n_features, n_features): Estimated precision of data.

inverse_transform(X)[source]¶

Transform data back to its original space.

In other words, return an input X_original whose transform would be X.

Parameters:

Xarray-like of 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 of shape (n_samples, n_features): Original data, where n_samples is the number of samples and n_features is the number of features.

Notes

If whitening is enabled, inverse_transform will compute the exact inverse operation, which includes reversing whitening.

partial_fit(X, y=None, check_input=True)[source]¶

Incremental fit with X. All of X is processed as a single batch.

Parameters:

Xarray-like of shape (n_samples, n_features): Training data, where n_samples is the number of samples and n_features is the number of features.
yIgnored: Not used, present for API consistency by convention.
check_inputbool, default=True: Run check_array on X.

Returns:

selfobject: Returns the instance itself.

set_params(**params)[source]¶

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

transform(X)[source]¶

Apply dimensionality reduction to X.

X is projected on the first principal components previously extracted from a training set, using minibatches of size batch_size if X is sparse.

Parameters:

X{array-like, sparse matrix} of 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_newndarray of shape (n_samples, n_components): Projection of X in the first principal 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) 

Examples using `sklearn.decomposition.IncrementalPCA`¶

Incremental PCA

sklearn.decomposition.IncrementalPCA¶

Examples using sklearn.decomposition.IncrementalPCA¶

`sklearn.decomposition`.IncrementalPCA¶

Examples using `sklearn.decomposition.IncrementalPCA`¶