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{‘input’, ‘array’, ‘dataframe’, ‘series’, ‘df_obj’, ‘numba’, ‘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, convert_dtype])	Fit the model with X, using minibatches of size batch_size.
`partial_fit`(X[, y, check_input])	Incremental fit with X.
`transform`(X, *[, convert_dtype])	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()
>>>
>>> # 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

fit(X, y=None, *, convert_dtype=True) → 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.

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.

transform(X, *, convert_dtype=False) → CumlArray[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.
convert_dtypebool, optional (default = False): When set to True, the transform method will automatically convert the input to the data type which was used to train the model. This will increase memory used for the method.

Returns:

X_newarray-like, shape (n_samples, n_components)