sklearn.preprocessing.StandardScaler

class sklearn.preprocessing.StandardScaler(*, copy=True, with_mean=True, with_std=True) [source]

Standardize features by removing the mean and scaling to unit variance

The standard score of a sample x is calculated as:

z = (x - u) / s

where u is the mean of the training samples or zero if with_mean=False, and s is the standard deviation of the training samples or one if with_std=False.

Centering and scaling happen independently on each feature by computing the relevant statistics on the samples in the training set. Mean and standard deviation are then stored to be used on later data using transform.

Standardization of a dataset is a common requirement for many machine learning estimators: they might behave badly if the individual features do not more or less look like standard normally distributed data (e.g. Gaussian with 0 mean and unit variance).

For instance many elements used in the objective function of a learning algorithm (such as the RBF kernel of Support Vector Machines or the L1 and L2 regularizers of linear models) assume that all features are centered around 0 and have variance in the same order. If a feature has a variance that is orders of magnitude larger that others, it might dominate the objective function and make the estimator unable to learn from other features correctly as expected.

This scaler can also be applied to sparse CSR or CSC matrices by passing with_mean=False to avoid breaking the sparsity structure of the data.

Read more in the User Guide.

Parameters

copybool, default=True

If False, try to avoid a copy and do inplace scaling instead. This is not guaranteed to always work inplace; e.g. if the data is not a NumPy array or scipy.sparse CSR matrix, a copy may still be returned.

with_meanbool, default=True

If True, center the data before scaling. This does not work (and will raise an exception) when attempted on sparse matrices, because centering them entails building a dense matrix which in common use cases is likely to be too large to fit in memory.

with_stdbool, default=True

If True, scale the data to unit variance (or equivalently, unit standard deviation).

Attributes

scale_ndarray of shape (n_features,) or None

Per feature relative scaling of the data to achieve zero mean and unit variance. Generally this is calculated using np.sqrt(var_). If a variance is zero, we can’t achieve unit variance, and the data is left as-is, giving a scaling factor of 1. scale_ is equal to None when with_std=False.

New in version 0.17: scale_

mean_ndarray of shape (n_features,) or None

The mean value for each feature in the training set. Equal to None when with_mean=False.

var_ndarray of shape (n_features,) or None

The variance for each feature in the training set. Used to compute scale_. Equal to None when with_std=False.

n_samples_seen_int or ndarray of shape (n_features,)

The number of samples processed by the estimator for each feature. If there are no missing samples, the n_samples_seen will be an integer, otherwise it will be an array of dtype int. If sample_weights are used it will be a float (if no missing data) or an array of dtype float that sums the weights seen so far. Will be reset on new calls to fit, but increments across partial_fit calls.

See also

scale

Equivalent function without the estimator API.

PCA

Further removes the linear correlation across features with ‘whiten=True’.

Notes

NaNs are treated as missing values: disregarded in fit, and maintained in transform.

We use a biased estimator for the standard deviation, equivalent to numpy.std(x, ddof=0). Note that the choice of ddof is unlikely to affect model performance.

For a comparison of the different scalers, transformers, and normalizers, see examples/preprocessing/plot_all_scaling.py.

Examples

>>> from sklearn.preprocessing import StandardScaler
>>> data = [[0, 0], [0, 0], [1, 1], [1, 1]]
>>> scaler = StandardScaler()
>>> print(scaler.fit(data))
StandardScaler()
>>> print(scaler.mean_)
[0.5 0.5]
>>> print(scaler.transform(data))
[[-1. -1.]
 [-1. -1.]
 [ 1.  1.]
 [ 1.  1.]]
>>> print(scaler.transform([[2, 2]]))
[[3. 3.]]

Methods

fit(X[, y, sample_weight])	Compute the mean and std to be used for later scaling.
fit_transform(X[, y])	Fit to data, then transform it.
get_params([deep])	Get parameters for this estimator.
inverse_transform(X[, copy])	Scale back the data to the original representation
partial_fit(X[, y, sample_weight])	Online computation of mean and std on X for later scaling.
set_params(**params)	Set the parameters of this estimator.
transform(X[, copy])	Perform standardization by centering and scaling

fit(X, y=None, sample_weight=None) [source]

Compute the mean and std to be used for later scaling.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features)

The data used to compute the mean and standard deviation used for later scaling along the features axis.

yNone

Ignored.

sample_weightarray-like of shape (n_samples,), default=None

Individual weights for each sample.

New in version 0.24: parameter sample_weight support to StandardScaler.

Returns

selfobject

Fitted scaler.

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

Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), 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_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

paramsdict

Parameter names mapped to their values.

inverse_transform(X, copy=None) [source]

Scale back the data to the original representation

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features)

The data used to scale along the features axis.

copybool, default=None

Copy the input X or not.

Returns

X_tr{ndarray, sparse matrix} of shape (n_samples, n_features)

Transformed array.

partial_fit(X, y=None, sample_weight=None) [source]

Online computation of mean and std on X for later scaling.

All of X is processed as a single batch. This is intended for cases when fit is not feasible due to very large number of n_samples or because X is read from a continuous stream.

The algorithm for incremental mean and std is given in Equation 1.5a,b in Chan, Tony F., Gene H. Golub, and Randall J. LeVeque. “Algorithms for computing the sample variance: Analysis and recommendations.” The American Statistician 37.3 (1983): 242-247:

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features)

The data used to compute the mean and standard deviation used for later scaling along the features axis.

yNone

Ignored.

sample_weightarray-like of shape (n_samples,), default=None

Individual weights for each sample.

New in version 0.24: parameter sample_weight support to StandardScaler.

Returns

selfobject

Fitted scaler.

set_params(**params) [source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). 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

selfestimator instance

Estimator instance.

transform(X, copy=None) [source]

Perform standardization by centering and scaling

Parameters

X{array-like, sparse matrix of shape (n_samples, n_features)

The data used to scale along the features axis.

copybool, default=None

Copy the input X or not.

Returns

X_tr{ndarray, sparse matrix} of shape (n_samples, n_features)

Transformed array.

Examples using sklearn.preprocessing.StandardScaler