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IncrementalPCA#

class cuml.decomposition.IncrementalPCA( *, n_components=None, whiten=False, copy=True, batch_size=None, verbose=False, output_type=None, )[source]#

Based on sklearn.decomposition.IncrementalPCA from scikit-learn 0.23.1

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.

Parameters:

n_componentsint or None, (default=None): Number of components to keep. If n_components is None, then n_components is set to min(n_samples, n_features).
whitenbool, optional: If True, de-correlates the components. This is done by dividing them by the corresponding singular values then multiplying by sqrt(n_samples). Whitening allows each component to have unit variance and removes multi-collinearity. It might be beneficial for downstream tasks like LinearRegression where correlated features cause problems.
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. If batch_size is None, then batch_size is inferred from the data and set to 5 * n_features, to provide a balance between approximation accuracy and memory consumption.
verboseint or boolean, default=False: Sets logging level. It must be one of cuml.common.logger.level_*. See Verbosity Levels for more info.
output_type{None, ‘input’, ‘cupy’, ‘numpy’, ‘cudf’, ‘pandas’}, default=None: Return results and set estimator attributes to the indicated output type. If None, the output type set at the module level (cuml.global_settings.output_type) will be used. See Output Data Type Configuration for more info.

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 2-norms of the n_components variables in the lower-dimensional space.
mean_array, shape (n_features,): Per-feature empirical mean, aggregate over calls to partial_fit.
var_array, shape (n_features,): Per-feature empirical variance, aggregate over calls to partial_fit.
noise_variance_float: The estimated noise covariance following the Probabilistic PCA model from [4].
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.

Methods

`fit`(X[, y])	Fit the model with X, using minibatches of size batch_size.
`partial_fit`(X[, y, check_input])	Incremental fit with X.
`transform`(X)	Apply dimensionality reduction to X.

Notes

Implements the incremental PCA model from [1]. This model is an extension of the Sequential Karhunen-Loeve Transform from [2]. 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 [3]. This technique has been omitted because it is advantageous only when decomposing a matrix with n_samples >= 5/3 * n_features where n_samples and n_features are the matrix rows and columns, respectively. In addition, it hurts the readability of the implemented algorithm. This would be a good opportunity for future optimization, if it is deemed necessary.

References

[1]

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.

[2]

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.

[3]

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

[4]

C. Bishop, 1999. “Pattern Recognition and Machine Learning”, Section 12.2.1, pp. 574

Examples

>>> from cuml.decomposition import IncrementalPCA
>>> import cupy as cp
>>> import cupyx
>>>
>>> X = cupyx.scipy.sparse.random(1000, 4, format='csr',
...                               density=0.07, random_state=5)
>>> ipca = IncrementalPCA(n_components=2, batch_size=200)
>>> ipca.fit(X)
IncrementalPCA(batch_size=200, n_components=2)
>>>
>>> # Components:
>>> ipca.components_
array([[ 0.23698335, -0.06073393,  0.04310868,  0.9686547 ],
       [ 0.27040346, -0.57185116,  0.76248786, -0.13594291]])
>>>
>>> # Singular Values:
>>> ipca.singular_values_
array([5.06637586, 4.59406975])
>>>
>>> # Explained Variance:
>>> ipca.explained_variance_
array([0.02569386, 0.0211266 ])
>>>
>>> # Explained Variance Ratio:
>>> ipca.explained_variance_ratio_
array([0.30424536, 0.25016372])
>>>
>>> # Mean:
>>> ipca.mean_
array([0.02693948, 0.0326928 , 0.03818463, 0.03861492])
>>>
>>> # Noise Variance:
>>> ipca.noise_variance_.item()
0.0037122774558343763

as_sklearn()[source]#

Convert this estimator into an equivalent scikit-learn (or scikit-learn extension) estimator.

Returns:

sklearn.base.BaseEstimator: A scikit-learn compatible estimator instance that mirrors the trained state of the current estimator.

fit( X, y=None, ) → IncrementalPCA[source]#

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

Parameters:

Xarray-like 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(self, X, y=None)[source]#

Fit the model with X and apply the dimensionality reduction on X.

Parameters:

Xarray-like (device or host) shape = (n_samples, n_features): Dense or sparse matrix with dtype float32 or float64. Acceptable dense formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series.
yarray-like (device or host) shape = (n_samples, 1): Dense matrix with dtype float32 or float64. Acceptable formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series.

Returns:

transcuDF, CuPy or NumPy object depending on cuML’s output type configuration, cupyx.scipy.sparse for sparse output, shape = (n_samples, n_components)

Transformed values

For more information on how to configure cuML’s dense output type, refer to: Output Data Type Configuration.

classmethod from_sklearn(model)[source]#

Create a cuml estimator from a scikit-learn estimator.

Parameters:

modelsklearn.base.BaseEstimator: A compatible scikit-learn (or scikit-learn extension) estimator.

Returns:

cls: A new instance of this cuml estimator class that mirrors the state of the input estimator.

Notes

output_type of the estimator is set to “numpy” by default, as these cannot be inferred from training arguments. If something different is required, then please use cuml’s output_type configuration utilities.

get_feature_names_out(input_features=None)[source]#

Get output feature names for transformation.

The feature names out will prefixed by the lowercased class name. For example, if the transformer outputs 3 features, then the feature names out are: ["class_name0", "class_name1", "class_name2"].

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]#: Returns a dict of all params owned by this class. If the child class has appropriately overridden the _get_param_names method and does not need anything other than what is there in this method, then it doesn’t have to override this method

inverse_transform( self, X, *, return_sparse=False, sparse_tol=1e-10, )[source]#

Transform data back to its original space.

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

Parameters:

Xarray-like (device or host) shape = (n_samples, n_features): Dense or sparse matrix with dtype float32 or float64. Acceptable dense formats: CUDA array interface compliant objects like CuPy, cuDF DataFrame/Series, NumPy ndarray and Pandas DataFrame/Series.
return_sparsebool, optional (default = False): Ignored when the model is not fit on a sparse matrix If True, the method will convert the result to a cupyx.scipy.sparse.csr_matrix object. NOTE: Currently, there is a loss of information when converting to csr matrix (cusolver bug). Default will be switched to True once this is solved.
sparse_tolfloat, optional (default = 1e-10): Ignored when return_sparse=False. If True, values in the inverse transform below this parameter are clipped to 0.

Returns:

X_invcuDF, CuPy or NumPy object depending on cuML’s output type configuration, cupyx.scipy.sparse for sparse output, shape = (n_samples, n_features)

Transformed values

For more information on how to configure cuML’s dense output type, refer to: Output Data Type Configuration.

partial_fit( X, y=None, *, check_input=True, ) → IncrementalPCA[source]#

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

Parameters:

Xarray-like 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.
check_inputbool: Run check_array on X.
yIgnored

Returns:

selfobject: Returns the instance itself.

set_params(**params)[source]#: Accepts a dict of params and updates the corresponding ones owned by this class. If the child class has appropriately overridden the _get_param_names method and does not need anything other than what is, there in this method, then it doesn’t have to override this method

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:

Xarray-like or sparse matrix, 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_newarray-like, shape (n_samples, n_components)