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 ben_samples / batch_size
SVD computations to get the principal components, versus 1 large SVD of complexityO(n_samples * n_features ** 2)
for PCA.Read more in the User Guide.
New in version 0.16.
 Parameters
 n_componentsint or None, (default=None)
Number of components to keep. If
n_components
isNone
, thenn_components
is set tomin(n_samples, n_features)
. whitenbool, optional
When True (False by default) the
components_
vectors are divided byn_samples
timescomponents_
to ensure uncorrelated outputs with unit componentwise variances.Whitening will remove some information from the transformed signal (the relative variance scales of the components) but can sometimes improve the predictive accuracy of the downstream estimators by making data respect some hardwired assumptions.
 copybool, (default=True)
If False, X will be overwritten.
copy=False
can be used to save memory but is unsafe for general use. batch_sizeint or None, (default=None)
The number of samples to use for each batch. Only used when calling
fit
. Ifbatch_size
isNone
, thenbatch_size
is inferred from the data and set to5 * n_features
, to provide a balance between approximation accuracy and memory consumption.
 Attributes
 components_array, shape (n_components, n_features)
Components with maximum variance.
 explained_variance_array, shape (n_components,)
Variance explained by each of the selected components.
 explained_variance_ratio_array, shape (n_components,)
Percentage of variance explained by each of the selected components. If all components are stored, the sum of explained variances 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 2norms of the
n_components
variables in the lowerdimensional space. mean_array, shape (n_features,)
Perfeature empirical mean, aggregate over calls to
partial_fit
. var_array, shape (n_features,)
Perfeature empirical variance, aggregate over calls to
partial_fit
. 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/metmppca.pdf.
 n_components_int
The estimated number of components. Relevant when
n_components=None
. n_samples_seen_int
The number of samples processed by the estimator. Will be reset on new calls to fit, but increments across
partial_fit
calls. batch_size_int
Inferred batch size from
batch_size
.
See also
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 13, pp. 125141, May 2008. See https://www.cs.toronto.edu/~dross/ivt/RossLimLinYang_ijcv.pdf
This model is an extension of the Sequential KarhunenLoeve Transform from: A. Levy and M. Lindenbaum, Sequential KarhunenLoeve Basis Extraction and its Application to Images, IEEE Transactions on Image Processing, Volume 9, Number 8, pp. 13711374, August 2000. See https://www.cs.technion.ac.il/~mic/doc/sklip.pdf
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 252253.. 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 13, pp. 125141, May 2008.
G. Golub and C. Van Loan. Matrix Computations, Third Edition, Chapter 5, Section 5.4.4, pp. 252253.
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.
Compute data covariance with the generative model.
get_params
([deep])Get parameters for this estimator.
Compute data precision matrix with the generative model.
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
 Xarraylike or sparse matrix, shape (n_samples, n_features)
Training data, where n_samples is the number of samples and n_features is the number of features.
 yIgnored
 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
 X{arraylike, sparse matrix, dataframe} of shape (n_samples, n_features)
Input samples.
 yndarray of shape (n_samples,), 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, shape=(n_features, n_features)
Estimated covariance of data.

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
 paramsmapping of string to any
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
 Xarraylike, 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 arraylike, shape (n_samples, n_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
 Xarraylike, shape (n_samples, n_features)
Training data, where n_samples is the number of samples and n_features is the number of features.
 check_inputbool
Run check_array on X.
 yIgnored
 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 pipelines). 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
 selfobject
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
 Xarraylike, 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_newarraylike, 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)