skoot.decomposition.SelectiveIncrementalPCA

class skoot.decomposition.SelectiveIncrementalPCA(cols=None, as_df=True, trans_col_name=None, **kwargs)

Incremental principal components analysis (IPCA). (applied to selected columns).

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.

This algorithm has constant memory complexity, on the order of batch_size, enabling use of np.memmap files without loading the entire file into memory.

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 User Guide.

This class wraps scikit-learn’s IncrementalPCA. When a pd.DataFrame is passed to the fit method, the transformation is applied to the selected columns, which are subsequently dropped from the frame. All remaining columns are left alone.

Parameters:

cols : array-like, shape=(n_features,), optional (default=None)

The names of the columns on which to apply the transformation. If no column names are provided, the transformer will be fit on the entire frame. Note that the transformation will also only apply to the specified columns, and any other non-specified columns will still be present after the transformation.

as_df : bool, optional (default=True)

Whether to return a Pandas DataFrame in the transform method. If False, will return a Numpy ndarray instead. Since most skoot transformers depend on explicitly-named DataFrame features, the as_df parameter is True by default.

trans_col_name : str, unicode or iterable, optional

The name or list of names to apply to the transformed column(s). If a string is provided, it is used as a prefix for new columns. If an iterable is provided, its dimensions must match the number of produced columns. If None (default), will use the estimator class name as the prefix.

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.

See also

SelectiveKernelPCA, SelectiveNMF, SelectivePCA, SelectiveTruncatedSVD

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.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.decomposition import IncrementalPCA
>>> 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, copy=True, n_components=7, whiten=False)
>>> # or let the fit function itself divide the data into batches
>>> X_transformed = transformer.fit_transform(X)
>>> X_transformed.shape
(1797, 7)

Methods

fit(X[, y])	Fit the wrapped transformer.
fit_transform(X[, y])	Fit to data, then transform it.
get_params([deep])	Get parameters for this estimator.
set_params(**params)	Set the parameters of this estimator.
transform(X)	Transform a test dataframe.

__init__(cols=None, as_df=True, trans_col_name=None, **kwargs)

Initialize self. See help(type(self)) for accurate signature.

fit(X, y=None, **fit_kwargs)

Fit the wrapped transformer.

This method will fit the wrapped sklearn transformer on the selected columns, leaving other columns alone.

Parameters:

X : pd.DataFrame, shape=(n_samples, n_features)

The Pandas frame to fit. The frame will only be fit on the prescribed cols (see __init__) or all of them if cols is None. Furthermore, X will not be altered in the process of the fit.

y : array-like or None, shape=(n_samples,), optional (default=None)

Pass-through for sklearn.pipeline.Pipeline. Even if explicitly set, will not change behavior of fit.

fit_transform(X, y=None, **fit_params)

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 : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.

Returns:

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep : boolean, optional

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.

set_params(**params)

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.

Returns:self

transform(X)

Transform a test dataframe.

Parameters:

X : pd.DataFrame, shape=(n_samples, n_features)

The Pandas frame to transform. The operation will be applied to a copy of the input data, and the result will be returned.

Returns:

X : pd.DataFrame, shape=(n_samples, n_features)

The operation is applied to a copy of X, and the result set is returned.