type t =
[ `BaseEstimator | `IncrementalPCA | `Object | `TransformerMixin ] Obj.tval of_pyobject : Py.Object.t -> tval to_pyobject : [> tag ] Obj.t -> Py.Object.tval create :
?n_components:int ->
?whiten:bool ->
?copy:bool ->
?batch_size:int ->
unit ->
tIncremental 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.
Read more in the :ref:`User Guide <IncrementalPCA>`.
.. versionadded:: 0.16
Parameters ---------- n_components : int 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)``.
whiten : bool, optional When True (False by default) the ``components_`` vectors are divided by ``n_samples`` times ``components_`` 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 sometimes improve the predictive accuracy of the downstream estimators by making data respect some hard-wired assumptions.
copy : bool, (default=True) If False, X will be overwritten. ``copy=False`` can be used to save memory but is unsafe for general use.
batch_size : int 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.
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 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.
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``.
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)
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.* See https://www.cs.technion.ac.il/~mic/doc/skl-ip.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 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.
See also -------- PCA KernelPCA SparsePCA TruncatedSVD
val fit : ?y:Py.Object.t -> x:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> tFit the model with X, using minibatches of size batch_size.
Parameters ---------- X : array-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.
y : Ignored
Returns ------- self : object Returns the instance itself.
val fit_transform :
?y:[> `ArrayLike ] Np.Obj.t ->
?fit_params:(string * Py.Object.t) list ->
x:[> `ArrayLike ] Np.Obj.t ->
[> tag ] Obj.t ->
[> `ArrayLike ] Np.Obj.tFit 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 : array-like, sparse matrix, dataframe of shape (n_samples, n_features)
y : ndarray of shape (n_samples,), default=None Target values.
**fit_params : dict Additional fit parameters.
Returns ------- X_new : ndarray array of shape (n_samples, n_features_new) Transformed array.
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 ------- cov : array, shape=(n_features, n_features) Estimated covariance of data.
Get parameters for this estimator.
Parameters ---------- deep : bool, default=True 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.
Compute data precision matrix with the generative model.
Equals the inverse of the covariance but computed with the matrix inversion lemma for efficiency.
Returns ------- precision : array, shape=(n_features, n_features) Estimated precision of data.
val inverse_transform :
x:[> `ArrayLike ] Np.Obj.t ->
[> tag ] Obj.t ->
Py.Object.tTransform data back to its original space.
In other words, return an input X_original whose transform would be X.
Parameters ---------- X : array-like, 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, shape (n_samples, n_features)
Notes ----- If whitening is enabled, inverse_transform will compute the exact inverse operation, which includes reversing whitening.
val partial_fit :
?y:Py.Object.t ->
?check_input:bool ->
x:[> `ArrayLike ] Np.Obj.t ->
[> tag ] Obj.t ->
tIncremental fit with X. All of X is processed as a single batch.
Parameters ---------- X : array-like, shape (n_samples, n_features) Training data, where n_samples is the number of samples and n_features is the number of features. check_input : bool Run check_array on X.
y : Ignored
Returns ------- self : object Returns the instance itself.
val set_params : ?params:(string * Py.Object.t) list -> [> tag ] Obj.t -> tSet 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 ---------- **params : dict Estimator parameters.
Returns ------- self : object Estimator instance.
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, 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_new : array-like, 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) # doctest: +SKIP
Attribute components_: get value or raise Not_found if None.
Attribute components_: get value as an option.
Attribute explained_variance_: get value or raise Not_found if None.
Attribute explained_variance_: get value as an option.
Attribute explained_variance_ratio_: get value or raise Not_found if None.
Attribute explained_variance_ratio_: get value as an option.
Attribute singular_values_: get value or raise Not_found if None.
Attribute singular_values_: get value as an option.
val noise_variance_ : t -> floatAttribute noise_variance_: get value or raise Not_found if None.
val noise_variance_opt : t -> float optionAttribute noise_variance_: get value as an option.
val n_components_ : t -> intAttribute n_components_: get value or raise Not_found if None.
val n_components_opt : t -> int optionAttribute n_components_: get value as an option.
val n_samples_seen_ : t -> intAttribute n_samples_seen_: get value or raise Not_found if None.
val n_samples_seen_opt : t -> int optionAttribute n_samples_seen_: get value as an option.
val batch_size_ : t -> intAttribute batch_size_: get value or raise Not_found if None.
val batch_size_opt : t -> int optionAttribute batch_size_: get value as an option.
val to_string : t -> stringPrint the object to a human-readable representation.
val show : t -> stringPrint the object to a human-readable representation.
val pp : Format.formatter -> t -> unitPretty-print the object to a formatter.