Learn more »
Push, build, and install
RubyGems
npm packages
Python packages
Maven artifacts
PHP packages
Go Modules
Bower components
Debian packages
RPM packages
NuGet packages
/ preprocessing / _data.py
# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Mathieu Blondel <mathieu@mblondel.org>
# Olivier Grisel <olivier.grisel@ensta.org>
# Andreas Mueller <amueller@ais.uni-bonn.de>
# Eric Martin <eric@ericmart.in>
# Giorgio Patrini <giorgio.patrini@anu.edu.au>
# Eric Chang <ericchang2017@u.northwestern.edu>
# License: BSD 3 clause
from itertools import chain, combinations
import numbers
import warnings
from itertools import combinations_with_replacement as combinations_w_r
import numpy as np
from scipy import sparse
from scipy import stats
from scipy import optimize
from scipy.special import boxcox
from ..base import BaseEstimator, TransformerMixin
from ..utils import check_array
from ..utils.extmath import row_norms
from ..utils.extmath import _incremental_mean_and_var
from ..utils.sparsefuncs_fast import (inplace_csr_row_normalize_l1,
inplace_csr_row_normalize_l2)
from ..utils.sparsefuncs import (inplace_column_scale,
mean_variance_axis, incr_mean_variance_axis,
min_max_axis)
from ..utils.validation import (check_is_fitted, check_random_state,
FLOAT_DTYPES)
from ._csr_polynomial_expansion import _csr_polynomial_expansion
from ._encoders import OneHotEncoder
BOUNDS_THRESHOLD = 1e-7
__all__ = [
'Binarizer',
'KernelCenterer',
'MinMaxScaler',
'MaxAbsScaler',
'Normalizer',
'OneHotEncoder',
'RobustScaler',
'StandardScaler',
'QuantileTransformer',
'PowerTransformer',
'add_dummy_feature',
'binarize',
'normalize',
'scale',
'robust_scale',
'maxabs_scale',
'minmax_scale',
'quantile_transform',
'power_transform',
]
def _handle_zeros_in_scale(scale, copy=True):
''' Makes sure that whenever scale is zero, we handle it correctly.
This happens in most scalers when we have constant features.'''
# if we are fitting on 1D arrays, scale might be a scalar
if np.isscalar(scale):
if scale == .0:
scale = 1.
return scale
elif isinstance(scale, np.ndarray):
if copy:
# New array to avoid side-effects
scale = scale.copy()
scale[scale == 0.0] = 1.0
return scale
def scale(X, axis=0, with_mean=True, with_std=True, copy=True):
"""Standardize a dataset along any axis
Center to the mean and component wise scale to unit variance.
Read more in the :ref:`User Guide <preprocessing_scaler>`.
Parameters
----------
X : {array-like, sparse matrix}
The data to center and scale.
axis : int (0 by default)
axis used to compute the means and standard deviations along. If 0,
independently standardize each feature, otherwise (if 1) standardize
each sample.
with_mean : boolean, True by default
If True, center the data before scaling.
with_std : boolean, True by default
If True, scale the data to unit variance (or equivalently,
unit standard deviation).
copy : boolean, optional, default True
set to False to perform inplace row normalization and avoid a
copy (if the input is already a numpy array or a scipy.sparse
CSC matrix and if axis is 1).
Notes
-----
This implementation will refuse to center scipy.sparse matrices
since it would make them non-sparse and would potentially crash the
program with memory exhaustion problems.
Instead the caller is expected to either set explicitly
`with_mean=False` (in that case, only variance scaling will be
performed on the features of the CSC matrix) or to call `X.toarray()`
if he/she expects the materialized dense array to fit in memory.
To avoid memory copy the caller should pass a CSC matrix.
NaNs are treated as missing values: disregarded to compute the statistics,
and maintained during the data transformation.
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 :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
See also
--------
StandardScaler: Performs scaling to unit variance using the``Transformer`` API
(e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`).
""" # noqa
X = check_array(X, accept_sparse='csc', copy=copy, ensure_2d=False,
estimator='the scale function', dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
if sparse.issparse(X):
if with_mean:
raise ValueError(
"Cannot center sparse matrices: pass `with_mean=False` instead"
" See docstring for motivation and alternatives.")
if axis != 0:
raise ValueError("Can only scale sparse matrix on axis=0, "
" got axis=%d" % axis)
if with_std:
_, var = mean_variance_axis(X, axis=0)
var = _handle_zeros_in_scale(var, copy=False)
inplace_column_scale(X, 1 / np.sqrt(var))
else:
X = np.asarray(X)
if with_mean:
mean_ = np.nanmean(X, axis)
if with_std:
scale_ = np.nanstd(X, axis)
# Xr is a view on the original array that enables easy use of
# broadcasting on the axis in which we are interested in
Xr = np.rollaxis(X, axis)
if with_mean:
Xr -= mean_
mean_1 = np.nanmean(Xr, axis=0)
# Verify that mean_1 is 'close to zero'. If X contains very
# large values, mean_1 can also be very large, due to a lack of
# precision of mean_. In this case, a pre-scaling of the
# concerned feature is efficient, for instance by its mean or
# maximum.
if not np.allclose(mean_1, 0):
warnings.warn("Numerical issues were encountered "
"when centering the data "
"and might not be solved. Dataset may "
"contain too large values. You may need "
"to prescale your features.")
Xr -= mean_1
if with_std:
scale_ = _handle_zeros_in_scale(scale_, copy=False)
Xr /= scale_
if with_mean:
mean_2 = np.nanmean(Xr, axis=0)
# If mean_2 is not 'close to zero', it comes from the fact that
# scale_ is very small so that mean_2 = mean_1/scale_ > 0, even
# if mean_1 was close to zero. The problem is thus essentially
# due to the lack of precision of mean_. A solution is then to
# subtract the mean again:
if not np.allclose(mean_2, 0):
warnings.warn("Numerical issues were encountered "
"when scaling the data "
"and might not be solved. The standard "
"deviation of the data is probably "
"very close to 0. ")
Xr -= mean_2
return X
class MinMaxScaler(TransformerMixin, BaseEstimator):
"""Transform features by scaling each feature to a given range.
This estimator scales and translates each feature individually such
that it is in the given range on the training set, e.g. between
zero and one.
The transformation is given by::
X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))
X_scaled = X_std * (max - min) + min
where min, max = feature_range.
The transformation is calculated as::
X_scaled = scale * X + min - X.min(axis=0) * scale
where scale = (max - min) / (X.max(axis=0) - X.min(axis=0))
This transformation is often used as an alternative to zero mean,
unit variance scaling.
Read more in the :ref:`User Guide <preprocessing_scaler>`.
Parameters
----------
feature_range : tuple (min, max), default=(0, 1)
Desired range of transformed data.
copy : bool, default=True
Set to False to perform inplace row normalization and avoid a
copy (if the input is already a numpy array).
Attributes
----------
min_ : ndarray of shape (n_features,)
Per feature adjustment for minimum. Equivalent to
``min - X.min(axis=0) * self.scale_``
scale_ : ndarray of shape (n_features,)
Per feature relative scaling of the data. Equivalent to
``(max - min) / (X.max(axis=0) - X.min(axis=0))``
.. versionadded:: 0.17
*scale_* attribute.
data_min_ : ndarray of shape (n_features,)
Per feature minimum seen in the data
.. versionadded:: 0.17
*data_min_*
data_max_ : ndarray of shape (n_features,)
Per feature maximum seen in the data
.. versionadded:: 0.17
*data_max_*
data_range_ : ndarray of shape (n_features,)
Per feature range ``(data_max_ - data_min_)`` seen in the data
.. versionadded:: 0.17
*data_range_*
n_samples_seen_ : int
The number of samples processed by the estimator.
It will be reset on new calls to fit, but increments across
``partial_fit`` calls.
Examples
--------
>>> from sklearn.preprocessing import MinMaxScaler
>>> data = [[-1, 2], [-0.5, 6], [0, 10], [1, 18]]
>>> scaler = MinMaxScaler()
>>> print(scaler.fit(data))
MinMaxScaler()
>>> print(scaler.data_max_)
[ 1. 18.]
>>> print(scaler.transform(data))
[[0. 0. ]
[0.25 0.25]
[0.5 0.5 ]
[1. 1. ]]
>>> print(scaler.transform([[2, 2]]))
[[1.5 0. ]]
See also
--------
minmax_scale: Equivalent function without the estimator API.
Notes
-----
NaNs are treated as missing values: disregarded in fit, and maintained in
transform.
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
"""
def __init__(self, feature_range=(0, 1), copy=True):
self.feature_range = feature_range
self.copy = copy
def _reset(self):
"""Reset internal data-dependent state of the scaler, if necessary.
__init__ parameters are not touched.
"""
# Checking one attribute is enough, becase they are all set together
# in partial_fit
if hasattr(self, 'scale_'):
del self.scale_
del self.min_
del self.n_samples_seen_
del self.data_min_
del self.data_max_
del self.data_range_
def fit(self, X, y=None):
"""Compute the minimum and maximum to be used for later scaling.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data used to compute the per-feature minimum and maximum
used for later scaling along the features axis.
y : None
Ignored.
Returns
-------
self : object
Fitted scaler.
"""
# Reset internal state before fitting
self._reset()
return self.partial_fit(X, y)
def partial_fit(self, X, y=None):
"""Online computation of min and max on X for later scaling.
All of X is processed as a single batch. This is intended for cases
when :meth:`fit` is not feasible due to very large number of
`n_samples` or because X is read from a continuous stream.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data used to compute the mean and standard deviation
used for later scaling along the features axis.
y : None
Ignored.
Returns
-------
self : object
Transformer instance.
"""
feature_range = self.feature_range
if feature_range[0] >= feature_range[1]:
raise ValueError("Minimum of desired feature range must be smaller"
" than maximum. Got %s." % str(feature_range))
if sparse.issparse(X):
raise TypeError("MinMaxScaler does not support sparse input. "
"Consider using MaxAbsScaler instead.")
X = check_array(X,
estimator=self, dtype=FLOAT_DTYPES,
force_all_finite="allow-nan")
data_min = np.nanmin(X, axis=0)
data_max = np.nanmax(X, axis=0)
# First pass
if not hasattr(self, 'n_samples_seen_'):
self.n_samples_seen_ = X.shape[0]
# Next steps
else:
data_min = np.minimum(self.data_min_, data_min)
data_max = np.maximum(self.data_max_, data_max)
self.n_samples_seen_ += X.shape[0]
data_range = data_max - data_min
self.scale_ = ((feature_range[1] - feature_range[0]) /
_handle_zeros_in_scale(data_range))
self.min_ = feature_range[0] - data_min * self.scale_
self.data_min_ = data_min
self.data_max_ = data_max
self.data_range_ = data_range
return self
def transform(self, X):
"""Scale features of X according to feature_range.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Input data that will be transformed.
Returns
-------
Xt : array-like of shape (n_samples, n_features)
Transformed data.
"""
check_is_fitted(self)
X = check_array(X, copy=self.copy, dtype=FLOAT_DTYPES,
force_all_finite="allow-nan")
X *= self.scale_
X += self.min_
return X
def inverse_transform(self, X):
"""Undo the scaling of X according to feature_range.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Input data that will be transformed. It cannot be sparse.
Returns
-------
Xt : array-like of shape (n_samples, n_features)
Transformed data.
"""
check_is_fitted(self)
X = check_array(X, copy=self.copy, dtype=FLOAT_DTYPES,
force_all_finite="allow-nan")
X -= self.min_
X /= self.scale_
return X
def _more_tags(self):
return {'allow_nan': True}
def minmax_scale(X, feature_range=(0, 1), axis=0, copy=True):
"""Transform features by scaling each feature to a given range.
This estimator scales and translates each feature individually such
that it is in the given range on the training set, i.e. between
zero and one.
The transformation is given by (when ``axis=0``)::
X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))
X_scaled = X_std * (max - min) + min
where min, max = feature_range.
The transformation is calculated as (when ``axis=0``)::
X_scaled = scale * X + min - X.min(axis=0) * scale
where scale = (max - min) / (X.max(axis=0) - X.min(axis=0))
This transformation is often used as an alternative to zero mean,
unit variance scaling.
Read more in the :ref:`User Guide <preprocessing_scaler>`.
.. versionadded:: 0.17
*minmax_scale* function interface
to :class:`sklearn.preprocessing.MinMaxScaler`.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data.
feature_range : tuple (min, max), default=(0, 1)
Desired range of transformed data.
axis : int, default=0
Axis used to scale along. If 0, independently scale each feature,
otherwise (if 1) scale each sample.
copy : bool, default=True
Set to False to perform inplace scaling and avoid a copy (if the input
is already a numpy array).
See also
--------
MinMaxScaler: Performs scaling to a given range using the``Transformer`` API
(e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`).
Notes
-----
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
""" # noqa
# Unlike the scaler object, this function allows 1d input.
# If copy is required, it will be done inside the scaler object.
X = check_array(X, copy=False, ensure_2d=False,
dtype=FLOAT_DTYPES, force_all_finite='allow-nan')
original_ndim = X.ndim
if original_ndim == 1:
X = X.reshape(X.shape[0], 1)
s = MinMaxScaler(feature_range=feature_range, copy=copy)
if axis == 0:
X = s.fit_transform(X)
else:
X = s.fit_transform(X.T).T
if original_ndim == 1:
X = X.ravel()
return X
class StandardScaler(TransformerMixin, BaseEstimator):
"""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
:meth:`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 :ref:`User Guide <preprocessing_scaler>`.
Parameters
----------
copy : boolean, optional, 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_mean : boolean, True by default
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_std : boolean, True by default
If True, scale the data to unit variance (or equivalently,
unit standard deviation).
Attributes
----------
scale_ : ndarray or None, shape (n_features,)
Per feature relative scaling of the data. This is calculated using
`np.sqrt(var_)`. Equal to ``None`` when ``with_std=False``.
.. versionadded:: 0.17
*scale_*
mean_ : ndarray or None, shape (n_features,)
The mean value for each feature in the training set.
Equal to ``None`` when ``with_mean=False``.
var_ : ndarray or None, shape (n_features,)
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 array, shape (n_features,)
The number of samples processed by the estimator for each feature.
If there are not missing samples, the ``n_samples_seen`` will be an
integer, otherwise it will be an array.
Will be reset on new calls to fit, but increments across
``partial_fit`` calls.
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.]]
See also
--------
scale: Equivalent function without the estimator API.
:class:`sklearn.decomposition.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 :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
""" # noqa
def __init__(self, copy=True, with_mean=True, with_std=True):
self.with_mean = with_mean
self.with_std = with_std
self.copy = copy
def _reset(self):
"""Reset internal data-dependent state of the scaler, if necessary.
__init__ parameters are not touched.
"""
# Checking one attribute is enough, becase they are all set together
# in partial_fit
if hasattr(self, 'scale_'):
del self.scale_
del self.n_samples_seen_
del self.mean_
del self.var_
def fit(self, X, y=None):
"""Compute the mean and std to be used for later scaling.
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
The data used to compute the mean and standard deviation
used for later scaling along the features axis.
y
Ignored
"""
# Reset internal state before fitting
self._reset()
return self.partial_fit(X, y)
def partial_fit(self, X, y=None):
"""
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 :meth:`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}, shape [n_samples, n_features]
The data used to compute the mean and standard deviation
used for later scaling along the features axis.
y : None
Ignored.
Returns
-------
self : object
Transformer instance.
"""
X = check_array(X, accept_sparse=('csr', 'csc'),
estimator=self, dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
# Even in the case of `with_mean=False`, we update the mean anyway
# This is needed for the incremental computation of the var
# See incr_mean_variance_axis and _incremental_mean_variance_axis
# if n_samples_seen_ is an integer (i.e. no missing values), we need to
# transform it to a NumPy array of shape (n_features,) required by
# incr_mean_variance_axis and _incremental_variance_axis
if (hasattr(self, 'n_samples_seen_') and
isinstance(self.n_samples_seen_, numbers.Integral)):
self.n_samples_seen_ = np.repeat(
self.n_samples_seen_, X.shape[1]).astype(np.int64, copy=False)
if sparse.issparse(X):
if self.with_mean:
raise ValueError(
"Cannot center sparse matrices: pass `with_mean=False` "
"instead. See docstring for motivation and alternatives.")
sparse_constructor = (sparse.csr_matrix
if X.format == 'csr' else sparse.csc_matrix)
counts_nan = sparse_constructor(
(np.isnan(X.data), X.indices, X.indptr),
shape=X.shape).sum(axis=0).A.ravel()
if not hasattr(self, 'n_samples_seen_'):
self.n_samples_seen_ = (
X.shape[0] - counts_nan).astype(np.int64, copy=False)
if self.with_std:
# First pass
if not hasattr(self, 'scale_'):
self.mean_, self.var_ = mean_variance_axis(X, axis=0)
# Next passes
else:
self.mean_, self.var_, self.n_samples_seen_ = \
incr_mean_variance_axis(X, axis=0,
last_mean=self.mean_,
last_var=self.var_,
last_n=self.n_samples_seen_)
else:
self.mean_ = None
self.var_ = None
if hasattr(self, 'scale_'):
self.n_samples_seen_ += X.shape[0] - counts_nan
else:
if not hasattr(self, 'n_samples_seen_'):
self.n_samples_seen_ = np.zeros(X.shape[1], dtype=np.int64)
# First pass
if not hasattr(self, 'scale_'):
self.mean_ = .0
if self.with_std:
self.var_ = .0
else:
self.var_ = None
if not self.with_mean and not self.with_std:
self.mean_ = None
self.var_ = None
self.n_samples_seen_ += X.shape[0] - np.isnan(X).sum(axis=0)
else:
self.mean_, self.var_, self.n_samples_seen_ = \
_incremental_mean_and_var(X, self.mean_, self.var_,
self.n_samples_seen_)
# for backward-compatibility, reduce n_samples_seen_ to an integer
# if the number of samples is the same for each feature (i.e. no
# missing values)
if np.ptp(self.n_samples_seen_) == 0:
self.n_samples_seen_ = self.n_samples_seen_[0]
if self.with_std:
self.scale_ = _handle_zeros_in_scale(np.sqrt(self.var_))
else:
self.scale_ = None
return self
def transform(self, X, copy=None):
"""Perform standardization by centering and scaling
Parameters
----------
X : array-like, shape [n_samples, n_features]
The data used to scale along the features axis.
copy : bool, optional (default: None)
Copy the input X or not.
"""
check_is_fitted(self)
copy = copy if copy is not None else self.copy
X = check_array(X, accept_sparse='csr', copy=copy,
estimator=self, dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
if sparse.issparse(X):
if self.with_mean:
raise ValueError(
"Cannot center sparse matrices: pass `with_mean=False` "
"instead. See docstring for motivation and alternatives.")
if self.scale_ is not None:
inplace_column_scale(X, 1 / self.scale_)
else:
if self.with_mean:
X -= self.mean_
if self.with_std:
X /= self.scale_
return X
def inverse_transform(self, X, copy=None):
"""Scale back the data to the original representation
Parameters
----------
X : array-like, shape [n_samples, n_features]
The data used to scale along the features axis.
copy : bool, optional (default: None)
Copy the input X or not.
Returns
-------
X_tr : array-like, shape [n_samples, n_features]
Transformed array.
"""
check_is_fitted(self)
copy = copy if copy is not None else self.copy
if sparse.issparse(X):
if self.with_mean:
raise ValueError(
"Cannot uncenter sparse matrices: pass `with_mean=False` "
"instead See docstring for motivation and alternatives.")
if not sparse.isspmatrix_csr(X):
X = X.tocsr()
copy = False
if copy:
X = X.copy()
if self.scale_ is not None:
inplace_column_scale(X, self.scale_)
else:
X = np.asarray(X)
if copy:
X = X.copy()
if self.with_std:
X *= self.scale_
if self.with_mean:
X += self.mean_
return X
def _more_tags(self):
return {'allow_nan': True}
class MaxAbsScaler(TransformerMixin, BaseEstimator):
"""Scale each feature by its maximum absolute value.
This estimator scales and translates each feature individually such
that the maximal absolute value of each feature in the
training set will be 1.0. It does not shift/center the data, and
thus does not destroy any sparsity.
This scaler can also be applied to sparse CSR or CSC matrices.
.. versionadded:: 0.17
Parameters
----------
copy : boolean, optional, default is True
Set to False to perform inplace scaling and avoid a copy (if the input
is already a numpy array).
Attributes
----------
scale_ : ndarray, shape (n_features,)
Per feature relative scaling of the data.
.. versionadded:: 0.17
*scale_* attribute.
max_abs_ : ndarray, shape (n_features,)
Per feature maximum absolute value.
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.
Examples
--------
>>> from sklearn.preprocessing import MaxAbsScaler
>>> X = [[ 1., -1., 2.],
... [ 2., 0., 0.],
... [ 0., 1., -1.]]
>>> transformer = MaxAbsScaler().fit(X)
>>> transformer
MaxAbsScaler()
>>> transformer.transform(X)
array([[ 0.5, -1. , 1. ],
[ 1. , 0. , 0. ],
[ 0. , 1. , -0.5]])
See also
--------
maxabs_scale: Equivalent function without the estimator API.
Notes
-----
NaNs are treated as missing values: disregarded in fit, and maintained in
transform.
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
"""
def __init__(self, copy=True):
self.copy = copy
def _reset(self):
"""Reset internal data-dependent state of the scaler, if necessary.
__init__ parameters are not touched.
"""
# Checking one attribute is enough, becase they are all set together
# in partial_fit
if hasattr(self, 'scale_'):
del self.scale_
del self.n_samples_seen_
del self.max_abs_
def fit(self, X, y=None):
"""Compute the maximum absolute value to be used for later scaling.
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
The data used to compute the per-feature minimum and maximum
used for later scaling along the features axis.
"""
# Reset internal state before fitting
self._reset()
return self.partial_fit(X, y)
def partial_fit(self, X, y=None):
"""
Online computation of max absolute value of X for later scaling.
All of X is processed as a single batch. This is intended for cases
when :meth:`fit` is not feasible due to very large number of
`n_samples` or because X is read from a continuous stream.
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
The data used to compute the mean and standard deviation
used for later scaling along the features axis.
y : None
Ignored.
Returns
-------
self : object
Transformer instance.
"""
X = check_array(X, accept_sparse=('csr', 'csc'),
estimator=self, dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
if sparse.issparse(X):
mins, maxs = min_max_axis(X, axis=0, ignore_nan=True)
max_abs = np.maximum(np.abs(mins), np.abs(maxs))
else:
max_abs = np.nanmax(np.abs(X), axis=0)
# First pass
if not hasattr(self, 'n_samples_seen_'):
self.n_samples_seen_ = X.shape[0]
# Next passes
else:
max_abs = np.maximum(self.max_abs_, max_abs)
self.n_samples_seen_ += X.shape[0]
self.max_abs_ = max_abs
self.scale_ = _handle_zeros_in_scale(max_abs)
return self
def transform(self, X):
"""Scale the data
Parameters
----------
X : {array-like, sparse matrix}
The data that should be scaled.
"""
check_is_fitted(self)
X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy,
estimator=self, dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
if sparse.issparse(X):
inplace_column_scale(X, 1.0 / self.scale_)
else:
X /= self.scale_
return X
def inverse_transform(self, X):
"""Scale back the data to the original representation
Parameters
----------
X : {array-like, sparse matrix}
The data that should be transformed back.
"""
check_is_fitted(self)
X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy,
estimator=self, dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
if sparse.issparse(X):
inplace_column_scale(X, self.scale_)
else:
X *= self.scale_
return X
def _more_tags(self):
return {'allow_nan': True}
def maxabs_scale(X, axis=0, copy=True):
"""Scale each feature to the [-1, 1] range without breaking the sparsity.
This estimator scales each feature individually such
that the maximal absolute value of each feature in the
training set will be 1.0.
This scaler can also be applied to sparse CSR or CSC matrices.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The data.
axis : int (0 by default)
axis used to scale along. If 0, independently scale each feature,
otherwise (if 1) scale each sample.
copy : boolean, optional, default is True
Set to False to perform inplace scaling and avoid a copy (if the input
is already a numpy array).
See also
--------
MaxAbsScaler: Performs scaling to the [-1, 1] range using the``Transformer`` API
(e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`).
Notes
-----
NaNs are treated as missing values: disregarded to compute the statistics,
and maintained during the data transformation.
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
""" # noqa
# Unlike the scaler object, this function allows 1d input.
# If copy is required, it will be done inside the scaler object.
X = check_array(X, accept_sparse=('csr', 'csc'), copy=False,
ensure_2d=False, dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
original_ndim = X.ndim
if original_ndim == 1:
X = X.reshape(X.shape[0], 1)
s = MaxAbsScaler(copy=copy)
if axis == 0:
X = s.fit_transform(X)
else:
X = s.fit_transform(X.T).T
if original_ndim == 1:
X = X.ravel()
return X
class RobustScaler(TransformerMixin, BaseEstimator):
"""Scale features using statistics that are robust to outliers.
This Scaler removes the median and scales the data according to
the quantile range (defaults to IQR: Interquartile Range).
The IQR is the range between the 1st quartile (25th quantile)
and the 3rd quartile (75th quantile).
Centering and scaling happen independently on each feature by
computing the relevant statistics on the samples in the training
set. Median and interquartile range are then stored to be used on
later data using the ``transform`` method.
Standardization of a dataset is a common requirement for many
machine learning estimators. Typically this is done by removing the mean
and scaling to unit variance. However, outliers can often influence the
sample mean / variance in a negative way. In such cases, the median and
the interquartile range often give better results.
.. versionadded:: 0.17
Read more in the :ref:`User Guide <preprocessing_scaler>`.
Parameters
----------
with_centering : boolean, True by default
If True, center the data before scaling.
This will cause ``transform`` to 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_scaling : boolean, True by default
If True, scale the data to interquartile range.
quantile_range : tuple (q_min, q_max), 0.0 < q_min < q_max < 100.0
Default: (25.0, 75.0) = (1st quantile, 3rd quantile) = IQR
Quantile range used to calculate ``scale_``.
.. versionadded:: 0.18
copy : boolean, optional, default is 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.
Attributes
----------
center_ : array of floats
The median value for each feature in the training set.
scale_ : array of floats
The (scaled) interquartile range for each feature in the training set.
.. versionadded:: 0.17
*scale_* attribute.
Examples
--------
>>> from sklearn.preprocessing import RobustScaler
>>> X = [[ 1., -2., 2.],
... [ -2., 1., 3.],
... [ 4., 1., -2.]]
>>> transformer = RobustScaler().fit(X)
>>> transformer
RobustScaler()
>>> transformer.transform(X)
array([[ 0. , -2. , 0. ],
[-1. , 0. , 0.4],
[ 1. , 0. , -1.6]])
See also
--------
robust_scale: Equivalent function without the estimator API.
:class:`sklearn.decomposition.PCA`
Further removes the linear correlation across features with
'whiten=True'.
Notes
-----
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
https://en.wikipedia.org/wiki/Median
https://en.wikipedia.org/wiki/Interquartile_range
"""
def __init__(self, with_centering=True, with_scaling=True,
quantile_range=(25.0, 75.0), copy=True):
self.with_centering = with_centering
self.with_scaling = with_scaling
self.quantile_range = quantile_range
self.copy = copy
def fit(self, X, y=None):
"""Compute the median and quantiles to be used for scaling.
Parameters
----------
X : array-like, shape [n_samples, n_features]
The data used to compute the median and quantiles
used for later scaling along the features axis.
"""
# at fit, convert sparse matrices to csc for optimized computation of
# the quantiles
X = check_array(X, accept_sparse='csc', estimator=self,
dtype=FLOAT_DTYPES, force_all_finite='allow-nan')
q_min, q_max = self.quantile_range
if not 0 <= q_min <= q_max <= 100:
raise ValueError("Invalid quantile range: %s" %
str(self.quantile_range))
if self.with_centering:
if sparse.issparse(X):
raise ValueError(
"Cannot center sparse matrices: use `with_centering=False`"
" instead. See docstring for motivation and alternatives.")
self.center_ = np.nanmedian(X, axis=0)
else:
self.center_ = None
if self.with_scaling:
quantiles = []
for feature_idx in range(X.shape[1]):
if sparse.issparse(X):
column_nnz_data = X.data[X.indptr[feature_idx]:
X.indptr[feature_idx + 1]]
column_data = np.zeros(shape=X.shape[0], dtype=X.dtype)
column_data[:len(column_nnz_data)] = column_nnz_data
else:
column_data = X[:, feature_idx]
quantiles.append(np.nanpercentile(column_data,
self.quantile_range))
quantiles = np.transpose(quantiles)
self.scale_ = quantiles[1] - quantiles[0]
self.scale_ = _handle_zeros_in_scale(self.scale_, copy=False)
else:
self.scale_ = None
return self
def transform(self, X):
"""Center and scale the data.
Parameters
----------
X : {array-like, sparse matrix}
The data used to scale along the specified axis.
"""
check_is_fitted(self)
X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy,
estimator=self, dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
if sparse.issparse(X):
if self.with_scaling:
inplace_column_scale(X, 1.0 / self.scale_)
else:
if self.with_centering:
X -= self.center_
if self.with_scaling:
X /= self.scale_
return X
def inverse_transform(self, X):
"""Scale back the data to the original representation
Parameters
----------
X : array-like
The data used to scale along the specified axis.
"""
check_is_fitted(self)
X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy,
estimator=self, dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
if sparse.issparse(X):
if self.with_scaling:
inplace_column_scale(X, self.scale_)
else:
if self.with_scaling:
X *= self.scale_
if self.with_centering:
X += self.center_
return X
def _more_tags(self):
return {'allow_nan': True}
def robust_scale(X, axis=0, with_centering=True, with_scaling=True,
quantile_range=(25.0, 75.0), copy=True):
"""Standardize a dataset along any axis
Center to the median and component wise scale
according to the interquartile range.
Read more in the :ref:`User Guide <preprocessing_scaler>`.
Parameters
----------
X : array-like
The data to center and scale.
axis : int (0 by default)
axis used to compute the medians and IQR along. If 0,
independently scale each feature, otherwise (if 1) scale
each sample.
with_centering : boolean, True by default
If True, center the data before scaling.
with_scaling : boolean, True by default
If True, scale the data to unit variance (or equivalently,
unit standard deviation).
quantile_range : tuple (q_min, q_max), 0.0 < q_min < q_max < 100.0
Default: (25.0, 75.0) = (1st quantile, 3rd quantile) = IQR
Quantile range used to calculate ``scale_``.
.. versionadded:: 0.18
copy : boolean, optional, default is True
set to False to perform inplace row normalization and avoid a
copy (if the input is already a numpy array or a scipy.sparse
CSR matrix and if axis is 1).
Notes
-----
This implementation will refuse to center scipy.sparse matrices
since it would make them non-sparse and would potentially crash the
program with memory exhaustion problems.
Instead the caller is expected to either set explicitly
`with_centering=False` (in that case, only variance scaling will be
performed on the features of the CSR matrix) or to call `X.toarray()`
if he/she expects the materialized dense array to fit in memory.
To avoid memory copy the caller should pass a CSR matrix.
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
See also
--------
RobustScaler: Performs centering and scaling using the ``Transformer`` API
(e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`).
"""
X = check_array(X, accept_sparse=('csr', 'csc'), copy=False,
ensure_2d=False, dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
original_ndim = X.ndim
if original_ndim == 1:
X = X.reshape(X.shape[0], 1)
s = RobustScaler(with_centering=with_centering, with_scaling=with_scaling,
quantile_range=quantile_range, copy=copy)
if axis == 0:
X = s.fit_transform(X)
else:
X = s.fit_transform(X.T).T
if original_ndim == 1:
X = X.ravel()
return X
class PolynomialFeatures(TransformerMixin, BaseEstimator):
"""Generate polynomial and interaction features.
Generate a new feature matrix consisting of all polynomial combinations
of the features with degree less than or equal to the specified degree.
For example, if an input sample is two dimensional and of the form
[a, b], the degree-2 polynomial features are [1, a, b, a^2, ab, b^2].
Parameters
----------
degree : integer
The degree of the polynomial features. Default = 2.
interaction_only : boolean, default = False
If true, only interaction features are produced: features that are
products of at most ``degree`` *distinct* input features (so not
``x[1] ** 2``, ``x[0] * x[2] ** 3``, etc.).
include_bias : boolean
If True (default), then include a bias column, the feature in which
all polynomial powers are zero (i.e. a column of ones - acts as an
intercept term in a linear model).
order : str in {'C', 'F'}, default 'C'
Order of output array in the dense case. 'F' order is faster to
compute, but may slow down subsequent estimators.
.. versionadded:: 0.21
Examples
--------
>>> import numpy as np
>>> from sklearn.preprocessing import PolynomialFeatures
>>> X = np.arange(6).reshape(3, 2)
>>> X
array([[0, 1],
[2, 3],
[4, 5]])
>>> poly = PolynomialFeatures(2)
>>> poly.fit_transform(X)
array([[ 1., 0., 1., 0., 0., 1.],
[ 1., 2., 3., 4., 6., 9.],
[ 1., 4., 5., 16., 20., 25.]])
>>> poly = PolynomialFeatures(interaction_only=True)
>>> poly.fit_transform(X)
array([[ 1., 0., 1., 0.],
[ 1., 2., 3., 6.],
[ 1., 4., 5., 20.]])
Attributes
----------
powers_ : array, shape (n_output_features, n_input_features)
powers_[i, j] is the exponent of the jth input in the ith output.
n_input_features_ : int
The total number of input features.
n_output_features_ : int
The total number of polynomial output features. The number of output
features is computed by iterating over all suitably sized combinations
of input features.
Notes
-----
Be aware that the number of features in the output array scales
polynomially in the number of features of the input array, and
exponentially in the degree. High degrees can cause overfitting.
See :ref:`examples/linear_model/plot_polynomial_interpolation.py
<sphx_glr_auto_examples_linear_model_plot_polynomial_interpolation.py>`
"""
def __init__(self, degree=2, interaction_only=False, include_bias=True,
order='C'):
self.degree = degree
self.interaction_only = interaction_only
self.include_bias = include_bias
self.order = order
@staticmethod
def _combinations(n_features, degree, interaction_only, include_bias):
comb = (combinations if interaction_only else combinations_w_r)
start = int(not include_bias)
return chain.from_iterable(comb(range(n_features), i)
for i in range(start, degree + 1))
@property
def powers_(self):
check_is_fitted(self)
combinations = self._combinations(self.n_input_features_, self.degree,
self.interaction_only,
self.include_bias)
return np.vstack([np.bincount(c, minlength=self.n_input_features_)
for c in combinations])
def get_feature_names(self, input_features=None):
"""
Return feature names for output features
Parameters
----------
input_features : list of string, length n_features, optional
String names for input features if available. By default,
"x0", "x1", ... "xn_features" is used.
Returns
-------
output_feature_names : list of string, length n_output_features
"""
powers = self.powers_
if input_features is None:
input_features = ['x%d' % i for i in range(powers.shape[1])]
feature_names = []
for row in powers:
inds = np.where(row)[0]
if len(inds):
name = " ".join("%s^%d" % (input_features[ind], exp)
if exp != 1 else input_features[ind]
for ind, exp in zip(inds, row[inds]))
else:
name = "1"
feature_names.append(name)
return feature_names
def fit(self, X, y=None):
"""
Compute number of output features.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The data.
Returns
-------
self : instance
"""
n_samples, n_features = check_array(X, accept_sparse=True).shape
combinations = self._combinations(n_features, self.degree,
self.interaction_only,
self.include_bias)
self.n_input_features_ = n_features
self.n_output_features_ = sum(1 for _ in combinations)
return self
def transform(self, X):
"""Transform data to polynomial features
Parameters
----------
X : array-like or CSR/CSC sparse matrix, shape [n_samples, n_features]
The data to transform, row by row.
Prefer CSR over CSC for sparse input (for speed), but CSC is
required if the degree is 4 or higher. If the degree is less than
4 and the input format is CSC, it will be converted to CSR, have
its polynomial features generated, then converted back to CSC.
If the degree is 2 or 3, the method described in "Leveraging
Sparsity to Speed Up Polynomial Feature Expansions of CSR Matrices
Using K-Simplex Numbers" by Andrew Nystrom and John Hughes is
used, which is much faster than the method used on CSC input. For
this reason, a CSC input will be converted to CSR, and the output
will be converted back to CSC prior to being returned, hence the
preference of CSR.
Returns
-------
XP : np.ndarray or CSR/CSC sparse matrix, shape [n_samples, NP]
The matrix of features, where NP is the number of polynomial
features generated from the combination of inputs.
"""
check_is_fitted(self)
X = check_array(X, order='F', dtype=FLOAT_DTYPES,
accept_sparse=('csr', 'csc'))
n_samples, n_features = X.shape
if n_features != self.n_input_features_:
raise ValueError("X shape does not match training shape")
if sparse.isspmatrix_csr(X):
if self.degree > 3:
return self.transform(X.tocsc()).tocsr()
to_stack = []
if self.include_bias:
to_stack.append(np.ones(shape=(n_samples, 1), dtype=X.dtype))
to_stack.append(X)
for deg in range(2, self.degree+1):
Xp_next = _csr_polynomial_expansion(X.data, X.indices,
X.indptr, X.shape[1],
self.interaction_only,
deg)
if Xp_next is None:
break
to_stack.append(Xp_next)
XP = sparse.hstack(to_stack, format='csr')
elif sparse.isspmatrix_csc(X) and self.degree < 4:
return self.transform(X.tocsr()).tocsc()
else:
if sparse.isspmatrix(X):
combinations = self._combinations(n_features, self.degree,
self.interaction_only,
self.include_bias)
columns = []
for comb in combinations:
if comb:
out_col = 1
for col_idx in comb:
out_col = X[:, col_idx].multiply(out_col)
columns.append(out_col)
else:
bias = sparse.csc_matrix(np.ones((X.shape[0], 1)))
columns.append(bias)
XP = sparse.hstack(columns, dtype=X.dtype).tocsc()
else:
XP = np.empty((n_samples, self.n_output_features_),
dtype=X.dtype, order=self.order)
# What follows is a faster implementation of:
# for i, comb in enumerate(combinations):
# XP[:, i] = X[:, comb].prod(1)
# This implementation uses two optimisations.
# First one is broadcasting,
# multiply ([X1, ..., Xn], X1) -> [X1 X1, ..., Xn X1]
# multiply ([X2, ..., Xn], X2) -> [X2 X2, ..., Xn X2]
# ...
# multiply ([X[:, start:end], X[:, start]) -> ...
# Second optimisation happens for degrees >= 3.
# Xi^3 is computed reusing previous computation:
# Xi^3 = Xi^2 * Xi.
if self.include_bias:
XP[:, 0] = 1
current_col = 1
else:
current_col = 0
# d = 0
XP[:, current_col:current_col + n_features] = X
index = list(range(current_col,
current_col + n_features))
current_col += n_features
index.append(current_col)
# d >= 1
for _ in range(1, self.degree):
new_index = []
end = index[-1]
for feature_idx in range(n_features):
start = index[feature_idx]
new_index.append(current_col)
if self.interaction_only:
start += (index[feature_idx + 1] -
index[feature_idx])
next_col = current_col + end - start
if next_col <= current_col:
break
# XP[:, start:end] are terms of degree d - 1
# that exclude feature #feature_idx.
np.multiply(XP[:, start:end],
X[:, feature_idx:feature_idx + 1],
out=XP[:, current_col:next_col],
casting='no')
current_col = next_col
new_index.append(current_col)
index = new_index
return XP
def normalize(X, norm='l2', axis=1, copy=True, return_norm=False):
"""Scale input vectors individually to unit norm (vector length).
Read more in the :ref:`User Guide <preprocessing_normalization>`.
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
The data to normalize, element by element.
scipy.sparse matrices should be in CSR format to avoid an
un-necessary copy.
norm : 'l1', 'l2', or 'max', optional ('l2' by default)
The norm to use to normalize each non zero sample (or each non-zero
feature if axis is 0).
axis : 0 or 1, optional (1 by default)
axis used to normalize the data along. If 1, independently normalize
each sample, otherwise (if 0) normalize each feature.
copy : boolean, optional, default True
set to False to perform inplace row normalization and avoid a
copy (if the input is already a numpy array or a scipy.sparse
CSR matrix and if axis is 1).
return_norm : boolean, default False
whether to return the computed norms
Returns
-------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
Normalized input X.
norms : array, shape [n_samples] if axis=1 else [n_features]
An array of norms along given axis for X.
When X is sparse, a NotImplementedError will be raised
for norm 'l1' or 'l2'.
See also
--------
Normalizer: Performs normalization using the ``Transformer`` API
(e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`).
Notes
-----
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
"""
if norm not in ('l1', 'l2', 'max'):
raise ValueError("'%s' is not a supported norm" % norm)
if axis == 0:
sparse_format = 'csc'
elif axis == 1:
sparse_format = 'csr'
else:
raise ValueError("'%d' is not a supported axis" % axis)
X = check_array(X, sparse_format, copy=copy,
estimator='the normalize function', dtype=FLOAT_DTYPES)
if axis == 0:
X = X.T
if sparse.issparse(X):
if return_norm and norm in ('l1', 'l2'):
raise NotImplementedError("return_norm=True is not implemented "
"for sparse matrices with norm 'l1' "
"or norm 'l2'")
if norm == 'l1':
inplace_csr_row_normalize_l1(X)
elif norm == 'l2':
inplace_csr_row_normalize_l2(X)
elif norm == 'max':
_, norms = min_max_axis(X, 1)
norms_elementwise = norms.repeat(np.diff(X.indptr))
mask = norms_elementwise != 0
X.data[mask] /= norms_elementwise[mask]
else:
if norm == 'l1':
norms = np.abs(X).sum(axis=1)
elif norm == 'l2':
norms = row_norms(X)
elif norm == 'max':
norms = np.max(X, axis=1)
norms = _handle_zeros_in_scale(norms, copy=False)
X /= norms[:, np.newaxis]
if axis == 0:
X = X.T
if return_norm:
return X, norms
else:
return X
class Normalizer(TransformerMixin, BaseEstimator):
"""Normalize samples individually to unit norm.
Each sample (i.e. each row of the data matrix) with at least one
non zero component is rescaled independently of other samples so
that its norm (l1 or l2) equals one.
This transformer is able to work both with dense numpy arrays and
scipy.sparse matrix (use CSR format if you want to avoid the burden of
a copy / conversion).
Scaling inputs to unit norms is a common operation for text
classification or clustering for instance. For instance the dot
product of two l2-normalized TF-IDF vectors is the cosine similarity
of the vectors and is the base similarity metric for the Vector
Space Model commonly used by the Information Retrieval community.
Read more in the :ref:`User Guide <preprocessing_normalization>`.
Parameters
----------
norm : 'l1', 'l2', or 'max', optional ('l2' by default)
The norm to use to normalize each non zero sample.
copy : boolean, optional, default True
set to False to perform inplace row normalization and avoid a
copy (if the input is already a numpy array or a scipy.sparse
CSR matrix).
Examples
--------
>>> from sklearn.preprocessing import Normalizer
>>> X = [[4, 1, 2, 2],
... [1, 3, 9, 3],
... [5, 7, 5, 1]]
>>> transformer = Normalizer().fit(X) # fit does nothing.
>>> transformer
Normalizer()
>>> transformer.transform(X)
array([[0.8, 0.2, 0.4, 0.4],
[0.1, 0.3, 0.9, 0.3],
[0.5, 0.7, 0.5, 0.1]])
Notes
-----
This estimator is stateless (besides constructor parameters), the
fit method does nothing but is useful when used in a pipeline.
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
See also
--------
normalize: Equivalent function without the estimator API.
"""
def __init__(self, norm='l2', copy=True):
self.norm = norm
self.copy = copy
def fit(self, X, y=None):
"""Do nothing and return the estimator unchanged
This method is just there to implement the usual API and hence
work in pipelines.
Parameters
----------
X : array-like
"""
check_array(X, accept_sparse='csr')
return self
def transform(self, X, copy=None):
"""Scale each non zero row of X to unit norm
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
The data to normalize, row by row. scipy.sparse matrices should be
in CSR format to avoid an un-necessary copy.
copy : bool, optional (default: None)
Copy the input X or not.
"""
copy = copy if copy is not None else self.copy
X = check_array(X, accept_sparse='csr')
return normalize(X, norm=self.norm, axis=1, copy=copy)
def _more_tags(self):
return {'stateless': True}
def binarize(X, threshold=0.0, copy=True):
"""Boolean thresholding of array-like or scipy.sparse matrix
Read more in the :ref:`User Guide <preprocessing_binarization>`.
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
The data to binarize, element by element.
scipy.sparse matrices should be in CSR or CSC format to avoid an
un-necessary copy.
threshold : float, optional (0.0 by default)
Feature values below or equal to this are replaced by 0, above it by 1.
Threshold may not be less than 0 for operations on sparse matrices.
copy : boolean, optional, default True
set to False to perform inplace binarization and avoid a copy
(if the input is already a numpy array or a scipy.sparse CSR / CSC
matrix and if axis is 1).
See also
--------
Binarizer: Performs binarization using the ``Transformer`` API
(e.g. as part of a preprocessing :class:`sklearn.pipeline.Pipeline`).
"""
X = check_array(X, accept_sparse=['csr', 'csc'], copy=copy)
if sparse.issparse(X):
if threshold < 0:
raise ValueError('Cannot binarize a sparse matrix with threshold '
'< 0')
cond = X.data > threshold
not_cond = np.logical_not(cond)
X.data[cond] = 1
X.data[not_cond] = 0
X.eliminate_zeros()
else:
cond = X > threshold
not_cond = np.logical_not(cond)
X[cond] = 1
X[not_cond] = 0
return X
class Binarizer(TransformerMixin, BaseEstimator):
"""Binarize data (set feature values to 0 or 1) according to a threshold
Values greater than the threshold map to 1, while values less than
or equal to the threshold map to 0. With the default threshold of 0,
only positive values map to 1.
Binarization is a common operation on text count data where the
analyst can decide to only consider the presence or absence of a
feature rather than a quantified number of occurrences for instance.
It can also be used as a pre-processing step for estimators that
consider boolean random variables (e.g. modelled using the Bernoulli
distribution in a Bayesian setting).
Read more in the :ref:`User Guide <preprocessing_binarization>`.
Parameters
----------
threshold : float, optional (0.0 by default)
Feature values below or equal to this are replaced by 0, above it by 1.
Threshold may not be less than 0 for operations on sparse matrices.
copy : boolean, optional, default True
set to False to perform inplace binarization and avoid a copy (if
the input is already a numpy array or a scipy.sparse CSR matrix).
Examples
--------
>>> from sklearn.preprocessing import Binarizer
>>> X = [[ 1., -1., 2.],
... [ 2., 0., 0.],
... [ 0., 1., -1.]]
>>> transformer = Binarizer().fit(X) # fit does nothing.
>>> transformer
Binarizer()
>>> transformer.transform(X)
array([[1., 0., 1.],
[1., 0., 0.],
[0., 1., 0.]])
Notes
-----
If the input is a sparse matrix, only the non-zero values are subject
to update by the Binarizer class.
This estimator is stateless (besides constructor parameters), the
fit method does nothing but is useful when used in a pipeline.
See also
--------
binarize: Equivalent function without the estimator API.
"""
def __init__(self, threshold=0.0, copy=True):
self.threshold = threshold
self.copy = copy
def fit(self, X, y=None):
"""Do nothing and return the estimator unchanged
This method is just there to implement the usual API and hence
work in pipelines.
Parameters
----------
X : array-like
"""
check_array(X, accept_sparse='csr')
return self
def transform(self, X, copy=None):
"""Binarize each element of X
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
The data to binarize, element by element.
scipy.sparse matrices should be in CSR format to avoid an
un-necessary copy.
copy : bool
Copy the input X or not.
"""
copy = copy if copy is not None else self.copy
return binarize(X, threshold=self.threshold, copy=copy)
def _more_tags(self):
return {'stateless': True}
class KernelCenterer(TransformerMixin, BaseEstimator):
"""Center a kernel matrix
Let K(x, z) be a kernel defined by phi(x)^T phi(z), where phi is a
function mapping x to a Hilbert space. KernelCenterer centers (i.e.,
normalize to have zero mean) the data without explicitly computing phi(x).
It is equivalent to centering phi(x) with
sklearn.preprocessing.StandardScaler(with_std=False).
Read more in the :ref:`User Guide <kernel_centering>`.
Attributes
----------
K_fit_rows_ : array, shape (n_samples,)
Average of each column of kernel matrix
K_fit_all_ : float
Average of kernel matrix
Examples
--------
>>> from sklearn.preprocessing import KernelCenterer
>>> from sklearn.metrics.pairwise import pairwise_kernels
>>> X = [[ 1., -2., 2.],
... [ -2., 1., 3.],
... [ 4., 1., -2.]]
>>> K = pairwise_kernels(X, metric='linear')
>>> K
array([[ 9., 2., -2.],
[ 2., 14., -13.],
[ -2., -13., 21.]])
>>> transformer = KernelCenterer().fit(K)
>>> transformer
KernelCenterer()
>>> transformer.transform(K)
array([[ 5., 0., -5.],
[ 0., 14., -14.],
[ -5., -14., 19.]])
"""
def __init__(self):
# Needed for backported inspect.signature compatibility with PyPy
pass
def fit(self, K, y=None):
"""Fit KernelCenterer
Parameters
----------
K : numpy array of shape [n_samples, n_samples]
Kernel matrix.
Returns
-------
self : returns an instance of self.
"""
K = check_array(K, dtype=FLOAT_DTYPES)
if K.shape[0] != K.shape[1]:
raise ValueError("Kernel matrix must be a square matrix."
" Input is a {}x{} matrix."
.format(K.shape[0], K.shape[1]))
n_samples = K.shape[0]
self.K_fit_rows_ = np.sum(K, axis=0) / n_samples
self.K_fit_all_ = self.K_fit_rows_.sum() / n_samples
return self
def transform(self, K, copy=True):
"""Center kernel matrix.
Parameters
----------
K : numpy array of shape [n_samples1, n_samples2]
Kernel matrix.
copy : boolean, optional, default True
Set to False to perform inplace computation.
Returns
-------
K_new : numpy array of shape [n_samples1, n_samples2]
"""
check_is_fitted(self)
K = check_array(K, copy=copy, dtype=FLOAT_DTYPES)
K_pred_cols = (np.sum(K, axis=1) /
self.K_fit_rows_.shape[0])[:, np.newaxis]
K -= self.K_fit_rows_
K -= K_pred_cols
K += self.K_fit_all_
return K
@property
def _pairwise(self):
return True
def add_dummy_feature(X, value=1.0):
"""Augment dataset with an additional dummy feature.
This is useful for fitting an intercept term with implementations which
cannot otherwise fit it directly.
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
Data.
value : float
Value to use for the dummy feature.
Returns
-------
X : {array, sparse matrix}, shape [n_samples, n_features + 1]
Same data with dummy feature added as first column.
Examples
--------
>>> from sklearn.preprocessing import add_dummy_feature
>>> add_dummy_feature([[0, 1], [1, 0]])
array([[1., 0., 1.],
[1., 1., 0.]])
"""
X = check_array(X, accept_sparse=['csc', 'csr', 'coo'], dtype=FLOAT_DTYPES)
n_samples, n_features = X.shape
shape = (n_samples, n_features + 1)
if sparse.issparse(X):
if sparse.isspmatrix_coo(X):
# Shift columns to the right.
col = X.col + 1
# Column indices of dummy feature are 0 everywhere.
col = np.concatenate((np.zeros(n_samples), col))
# Row indices of dummy feature are 0, ..., n_samples-1.
row = np.concatenate((np.arange(n_samples), X.row))
# Prepend the dummy feature n_samples times.
data = np.concatenate((np.full(n_samples, value), X.data))
return sparse.coo_matrix((data, (row, col)), shape)
elif sparse.isspmatrix_csc(X):
# Shift index pointers since we need to add n_samples elements.
indptr = X.indptr + n_samples
# indptr[0] must be 0.
indptr = np.concatenate((np.array([0]), indptr))
# Row indices of dummy feature are 0, ..., n_samples-1.
indices = np.concatenate((np.arange(n_samples), X.indices))
# Prepend the dummy feature n_samples times.
data = np.concatenate((np.full(n_samples, value), X.data))
return sparse.csc_matrix((data, indices, indptr), shape)
else:
klass = X.__class__
return klass(add_dummy_feature(X.tocoo(), value))
else:
return np.hstack((np.full((n_samples, 1), value), X))
class QuantileTransformer(TransformerMixin, BaseEstimator):
"""Transform features using quantiles information.
This method transforms the features to follow a uniform or a normal
distribution. Therefore, for a given feature, this transformation tends
to spread out the most frequent values. It also reduces the impact of
(marginal) outliers: this is therefore a robust preprocessing scheme.
The transformation is applied on each feature independently. First an
estimate of the cumulative distribution function of a feature is
used to map the original values to a uniform distribution. The obtained
values are then mapped to the desired output distribution using the
associated quantile function. Features values of new/unseen data that fall
below or above the fitted range will be mapped to the bounds of the output
distribution. Note that this transform is non-linear. It may distort linear
correlations between variables measured at the same scale but renders
variables measured at different scales more directly comparable.
Read more in the :ref:`User Guide <preprocessing_transformer>`.
.. versionadded:: 0.19
Parameters
----------
n_quantiles : int, optional (default=1000 or n_samples)
Number of quantiles to be computed. It corresponds to the number
of landmarks used to discretize the cumulative distribution function.
If n_quantiles is larger than the number of samples, n_quantiles is set
to the number of samples as a larger number of quantiles does not give
a better approximation of the cumulative distribution function
estimator.
output_distribution : str, optional (default='uniform')
Marginal distribution for the transformed data. The choices are
'uniform' (default) or 'normal'.
ignore_implicit_zeros : bool, optional (default=False)
Only applies to sparse matrices. If True, the sparse entries of the
matrix are discarded to compute the quantile statistics. If False,
these entries are treated as zeros.
subsample : int, optional (default=1e5)
Maximum number of samples used to estimate the quantiles for
computational efficiency. Note that the subsampling procedure may
differ for value-identical sparse and dense matrices.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by np.random. Note that this is used by subsampling and smoothing
noise.
copy : boolean, optional, (default=True)
Set to False to perform inplace transformation and avoid a copy (if the
input is already a numpy array).
Attributes
----------
n_quantiles_ : integer
The actual number of quantiles used to discretize the cumulative
distribution function.
quantiles_ : ndarray, shape (n_quantiles, n_features)
The values corresponding the quantiles of reference.
references_ : ndarray, shape(n_quantiles, )
Quantiles of references.
Examples
--------
>>> import numpy as np
>>> from sklearn.preprocessing import QuantileTransformer
>>> rng = np.random.RandomState(0)
>>> X = np.sort(rng.normal(loc=0.5, scale=0.25, size=(25, 1)), axis=0)
>>> qt = QuantileTransformer(n_quantiles=10, random_state=0)
>>> qt.fit_transform(X)
array([...])
See also
--------
quantile_transform : Equivalent function without the estimator API.
PowerTransformer : Perform mapping to a normal distribution using a power
transform.
StandardScaler : Perform standardization that is faster, but less robust
to outliers.
RobustScaler : Perform robust standardization that removes the influence
of outliers but does not put outliers and inliers on the same scale.
Notes
-----
NaNs are treated as missing values: disregarded in fit, and maintained in
transform.
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
"""
def __init__(self, n_quantiles=1000, output_distribution='uniform',
ignore_implicit_zeros=False, subsample=int(1e5),
random_state=None, copy=True):
self.n_quantiles = n_quantiles
self.output_distribution = output_distribution
self.ignore_implicit_zeros = ignore_implicit_zeros
self.subsample = subsample
self.random_state = random_state
self.copy = copy
def _dense_fit(self, X, random_state):
"""Compute percentiles for dense matrices.
Parameters
----------
X : ndarray, shape (n_samples, n_features)
The data used to scale along the features axis.
"""
if self.ignore_implicit_zeros:
warnings.warn("'ignore_implicit_zeros' takes effect only with"
" sparse matrix. This parameter has no effect.")
n_samples, n_features = X.shape
references = self.references_ * 100
self.quantiles_ = []
for col in X.T:
if self.subsample < n_samples:
subsample_idx = random_state.choice(n_samples,
size=self.subsample,
replace=False)
col = col.take(subsample_idx, mode='clip')
self.quantiles_.append(np.nanpercentile(col, references))
self.quantiles_ = np.transpose(self.quantiles_)
def _sparse_fit(self, X, random_state):
"""Compute percentiles for sparse matrices.
Parameters
----------
X : sparse matrix CSC, shape (n_samples, n_features)
The data used to scale along the features axis. The sparse matrix
needs to be nonnegative.
"""
n_samples, n_features = X.shape
references = self.references_ * 100
self.quantiles_ = []
for feature_idx in range(n_features):
column_nnz_data = X.data[X.indptr[feature_idx]:
X.indptr[feature_idx + 1]]
if len(column_nnz_data) > self.subsample:
column_subsample = (self.subsample * len(column_nnz_data) //
n_samples)
if self.ignore_implicit_zeros:
column_data = np.zeros(shape=column_subsample,
dtype=X.dtype)
else:
column_data = np.zeros(shape=self.subsample, dtype=X.dtype)
column_data[:column_subsample] = random_state.choice(
column_nnz_data, size=column_subsample, replace=False)
else:
if self.ignore_implicit_zeros:
column_data = np.zeros(shape=len(column_nnz_data),
dtype=X.dtype)
else:
column_data = np.zeros(shape=n_samples, dtype=X.dtype)
column_data[:len(column_nnz_data)] = column_nnz_data
if not column_data.size:
# if no nnz, an error will be raised for computing the
# quantiles. Force the quantiles to be zeros.
self.quantiles_.append([0] * len(references))
else:
self.quantiles_.append(
np.nanpercentile(column_data, references))
self.quantiles_ = np.transpose(self.quantiles_)
def fit(self, X, y=None):
"""Compute the quantiles used for transforming.
Parameters
----------
X : ndarray or sparse matrix, shape (n_samples, n_features)
The data used to scale along the features axis. If a sparse
matrix is provided, it will be converted into a sparse
``csc_matrix``. Additionally, the sparse matrix needs to be
nonnegative if `ignore_implicit_zeros` is False.
Returns
-------
self : object
"""
if self.n_quantiles <= 0:
raise ValueError("Invalid value for 'n_quantiles': %d. "
"The number of quantiles must be at least one."
% self.n_quantiles)
if self.subsample <= 0:
raise ValueError("Invalid value for 'subsample': %d. "
"The number of subsamples must be at least one."
% self.subsample)
if self.n_quantiles > self.subsample:
raise ValueError("The number of quantiles cannot be greater than"
" the number of samples used. Got {} quantiles"
" and {} samples.".format(self.n_quantiles,
self.subsample))
X = self._check_inputs(X, copy=False)
n_samples = X.shape[0]
if self.n_quantiles > n_samples:
warnings.warn("n_quantiles (%s) is greater than the total number "
"of samples (%s). n_quantiles is set to "
"n_samples."
% (self.n_quantiles, n_samples))
self.n_quantiles_ = max(1, min(self.n_quantiles, n_samples))
rng = check_random_state(self.random_state)
# Create the quantiles of reference
self.references_ = np.linspace(0, 1, self.n_quantiles_,
endpoint=True)
if sparse.issparse(X):
self._sparse_fit(X, rng)
else:
self._dense_fit(X, rng)
return self
def _transform_col(self, X_col, quantiles, inverse):
"""Private function to transform a single feature"""
output_distribution = self.output_distribution
if not inverse:
lower_bound_x = quantiles[0]
upper_bound_x = quantiles[-1]
lower_bound_y = 0
upper_bound_y = 1
else:
lower_bound_x = 0
upper_bound_x = 1
lower_bound_y = quantiles[0]
upper_bound_y = quantiles[-1]
# for inverse transform, match a uniform distribution
with np.errstate(invalid='ignore'): # hide NaN comparison warnings
if output_distribution == 'normal':
X_col = stats.norm.cdf(X_col)
# else output distribution is already a uniform distribution
# find index for lower and higher bounds
with np.errstate(invalid='ignore'): # hide NaN comparison warnings
if output_distribution == 'normal':
lower_bounds_idx = (X_col - BOUNDS_THRESHOLD <
lower_bound_x)
upper_bounds_idx = (X_col + BOUNDS_THRESHOLD >
upper_bound_x)
if output_distribution == 'uniform':
lower_bounds_idx = (X_col == lower_bound_x)
upper_bounds_idx = (X_col == upper_bound_x)
isfinite_mask = ~np.isnan(X_col)
X_col_finite = X_col[isfinite_mask]
if not inverse:
# Interpolate in one direction and in the other and take the
# mean. This is in case of repeated values in the features
# and hence repeated quantiles
#
# If we don't do this, only one extreme of the duplicated is
# used (the upper when we do ascending, and the
# lower for descending). We take the mean of these two
X_col[isfinite_mask] = .5 * (
np.interp(X_col_finite, quantiles, self.references_)
- np.interp(-X_col_finite, -quantiles[::-1],
-self.references_[::-1]))
else:
X_col[isfinite_mask] = np.interp(X_col_finite,
self.references_, quantiles)
X_col[upper_bounds_idx] = upper_bound_y
X_col[lower_bounds_idx] = lower_bound_y
# for forward transform, match the output distribution
if not inverse:
with np.errstate(invalid='ignore'): # hide NaN comparison warnings
if output_distribution == 'normal':
X_col = stats.norm.ppf(X_col)
# find the value to clip the data to avoid mapping to
# infinity. Clip such that the inverse transform will be
# consistent
clip_min = stats.norm.ppf(BOUNDS_THRESHOLD - np.spacing(1))
clip_max = stats.norm.ppf(1 - (BOUNDS_THRESHOLD -
np.spacing(1)))
X_col = np.clip(X_col, clip_min, clip_max)
# else output distribution is uniform and the ppf is the
# identity function so we let X_col unchanged
return X_col
def _check_inputs(self, X, accept_sparse_negative=False, copy=False):
"""Check inputs before fit and transform"""
X = check_array(X, accept_sparse='csc', copy=copy,
dtype=FLOAT_DTYPES,
force_all_finite='allow-nan')
# we only accept positive sparse matrix when ignore_implicit_zeros is
# false and that we call fit or transform.
with np.errstate(invalid='ignore'): # hide NaN comparison warnings
if (not accept_sparse_negative and not self.ignore_implicit_zeros
and (sparse.issparse(X) and np.any(X.data < 0))):
raise ValueError('QuantileTransformer only accepts'
' non-negative sparse matrices.')
# check the output distribution
if self.output_distribution not in ('normal', 'uniform'):
raise ValueError("'output_distribution' has to be either 'normal'"
" or 'uniform'. Got '{}' instead.".format(
self.output_distribution))
return X
def _check_is_fitted(self, X):
"""Check the inputs before transforming"""
check_is_fitted(self)
# check that the dimension of X are adequate with the fitted data
if X.shape[1] != self.quantiles_.shape[1]:
raise ValueError('X does not have the same number of features as'
' the previously fitted data. Got {} instead of'
' {}.'.format(X.shape[1],
self.quantiles_.shape[1]))
def _transform(self, X, inverse=False):
"""Forward and inverse transform.
Parameters
----------
X : ndarray, shape (n_samples, n_features)
The data used to scale along the features axis.
inverse : bool, optional (default=False)
If False, apply forward transform. If True, apply
inverse transform.
Returns
-------
X : ndarray, shape (n_samples, n_features)
Projected data
"""
if sparse.issparse(X):
for feature_idx in range(X.shape[1]):
column_slice = slice(X.indptr[feature_idx],
X.indptr[feature_idx + 1])
X.data[column_slice] = self._transform_col(
X.data[column_slice], self.quantiles_[:, feature_idx],
inverse)
else:
for feature_idx in range(X.shape[1]):
X[:, feature_idx] = self._transform_col(
X[:, feature_idx], self.quantiles_[:, feature_idx],
inverse)
return X
def transform(self, X):
"""Feature-wise transformation of the data.
Parameters
----------
X : ndarray or sparse matrix, shape (n_samples, n_features)
The data used to scale along the features axis. If a sparse
matrix is provided, it will be converted into a sparse
``csc_matrix``. Additionally, the sparse matrix needs to be
nonnegative if `ignore_implicit_zeros` is False.
Returns
-------
Xt : ndarray or sparse matrix, shape (n_samples, n_features)
The projected data.
"""
X = self._check_inputs(X, copy=self.copy)
self._check_is_fitted(X)
return self._transform(X, inverse=False)
def inverse_transform(self, X):
"""Back-projection to the original space.
Parameters
----------
X : ndarray or sparse matrix, shape (n_samples, n_features)
The data used to scale along the features axis. If a sparse
matrix is provided, it will be converted into a sparse
``csc_matrix``. Additionally, the sparse matrix needs to be
nonnegative if `ignore_implicit_zeros` is False.
Returns
-------
Xt : ndarray or sparse matrix, shape (n_samples, n_features)
The projected data.
"""
X = self._check_inputs(X, accept_sparse_negative=True, copy=self.copy)
self._check_is_fitted(X)
return self._transform(X, inverse=True)
def _more_tags(self):
return {'allow_nan': True}
def quantile_transform(X, axis=0, n_quantiles=1000,
output_distribution='uniform',
ignore_implicit_zeros=False,
subsample=int(1e5),
random_state=None,
copy="warn"):
"""Transform features using quantiles information.
This method transforms the features to follow a uniform or a normal
distribution. Therefore, for a given feature, this transformation tends
to spread out the most frequent values. It also reduces the impact of
(marginal) outliers: this is therefore a robust preprocessing scheme.
The transformation is applied on each feature independently. First an
estimate of the cumulative distribution function of a feature is
used to map the original values to a uniform distribution. The obtained
values are then mapped to the desired output distribution using the
associated quantile function. Features values of new/unseen data that fall
below or above the fitted range will be mapped to the bounds of the output
distribution. Note that this transform is non-linear. It may distort linear
correlations between variables measured at the same scale but renders
variables measured at different scales more directly comparable.
Read more in the :ref:`User Guide <preprocessing_transformer>`.
Parameters
----------
X : array-like, sparse matrix
The data to transform.
axis : int, (default=0)
Axis used to compute the means and standard deviations along. If 0,
transform each feature, otherwise (if 1) transform each sample.
n_quantiles : int, optional (default=1000 or n_samples)
Number of quantiles to be computed. It corresponds to the number
of landmarks used to discretize the cumulative distribution function.
If n_quantiles is larger than the number of samples, n_quantiles is set
to the number of samples as a larger number of quantiles does not give
a better approximation of the cumulative distribution function
estimator.
output_distribution : str, optional (default='uniform')
Marginal distribution for the transformed data. The choices are
'uniform' (default) or 'normal'.
ignore_implicit_zeros : bool, optional (default=False)
Only applies to sparse matrices. If True, the sparse entries of the
matrix are discarded to compute the quantile statistics. If False,
these entries are treated as zeros.
subsample : int, optional (default=1e5)
Maximum number of samples used to estimate the quantiles for
computational efficiency. Note that the subsampling procedure may
differ for value-identical sparse and dense matrices.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by np.random. Note that this is used by subsampling and smoothing
noise.
copy : boolean, optional, (default="warn")
Set to False to perform inplace transformation and avoid a copy (if the
input is already a numpy array). If True, a copy of `X` is transformed,
leaving the original `X` unchanged
.. deprecated:: 0.21
The default value of parameter `copy` will be changed from False
to True in 0.23. The current default of False is being changed to
make it more consistent with the default `copy` values of other
functions in :mod:`sklearn.preprocessing`. Furthermore, the
current default of False may have unexpected side effects by
modifying the value of `X` inplace
Returns
-------
Xt : ndarray or sparse matrix, shape (n_samples, n_features)
The transformed data.
Examples
--------
>>> import numpy as np
>>> from sklearn.preprocessing import quantile_transform
>>> rng = np.random.RandomState(0)
>>> X = np.sort(rng.normal(loc=0.5, scale=0.25, size=(25, 1)), axis=0)
>>> quantile_transform(X, n_quantiles=10, random_state=0, copy=True)
array([...])
See also
--------
QuantileTransformer : Performs quantile-based scaling using the
``Transformer`` API (e.g. as part of a preprocessing
:class:`sklearn.pipeline.Pipeline`).
power_transform : Maps data to a normal distribution using a
power transformation.
scale : Performs standardization that is faster, but less robust
to outliers.
robust_scale : Performs robust standardization that removes the influence
of outliers but does not put outliers and inliers on the same scale.
Notes
-----
NaNs are treated as missing values: disregarded in fit, and maintained in
transform.
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
"""
if copy == "warn":
warnings.warn("The default value of `copy` will change from False to "
"True in 0.23 in order to make it more consistent with "
"the default `copy` values of other functions in "
":mod:`sklearn.preprocessing` and prevent "
"unexpected side effects by modifying the value of `X` "
"inplace. To avoid inplace modifications of `X`, it is "
"recommended to explicitly set `copy=True`",
FutureWarning)
copy = False
n = QuantileTransformer(n_quantiles=n_quantiles,
output_distribution=output_distribution,
subsample=subsample,
ignore_implicit_zeros=ignore_implicit_zeros,
random_state=random_state,
copy=copy)
if axis == 0:
return n.fit_transform(X)
elif axis == 1:
return n.fit_transform(X.T).T
else:
raise ValueError("axis should be either equal to 0 or 1. Got"
" axis={}".format(axis))
class PowerTransformer(TransformerMixin, BaseEstimator):
"""Apply a power transform featurewise to make data more Gaussian-like.
Power transforms are a family of parametric, monotonic transformations
that are applied to make data more Gaussian-like. This is useful for
modeling issues related to heteroscedasticity (non-constant variance),
or other situations where normality is desired.
Currently, PowerTransformer supports the Box-Cox transform and the
Yeo-Johnson transform. The optimal parameter for stabilizing variance and
minimizing skewness is estimated through maximum likelihood.
Box-Cox requires input data to be strictly positive, while Yeo-Johnson
supports both positive or negative data.
By default, zero-mean, unit-variance normalization is applied to the
transformed data.
Read more in the :ref:`User Guide <preprocessing_transformer>`.
Parameters
----------
method : str, (default='yeo-johnson')
The power transform method. Available methods are:
- 'yeo-johnson' [1]_, works with positive and negative values
- 'box-cox' [2]_, only works with strictly positive values
standardize : boolean, default=True
Set to True to apply zero-mean, unit-variance normalization to the
transformed output.
copy : boolean, optional, default=True
Set to False to perform inplace computation during transformation.
Attributes
----------
lambdas_ : array of float, shape (n_features,)
The parameters of the power transformation for the selected features.
Examples
--------
>>> import numpy as np
>>> from sklearn.preprocessing import PowerTransformer
>>> pt = PowerTransformer()
>>> data = [[1, 2], [3, 2], [4, 5]]
>>> print(pt.fit(data))
PowerTransformer()
>>> print(pt.lambdas_)
[ 1.386... -3.100...]
>>> print(pt.transform(data))
[[-1.316... -0.707...]
[ 0.209... -0.707...]
[ 1.106... 1.414...]]
See also
--------
power_transform : Equivalent function without the estimator API.
QuantileTransformer : Maps data to a standard normal distribution with
the parameter `output_distribution='normal'`.
Notes
-----
NaNs are treated as missing values: disregarded in ``fit``, and maintained
in ``transform``.
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
References
----------
.. [1] I.K. Yeo and R.A. Johnson, "A new family of power transformations to
improve normality or symmetry." Biometrika, 87(4), pp.954-959,
(2000).
.. [2] G.E.P. Box and D.R. Cox, "An Analysis of Transformations", Journal
of the Royal Statistical Society B, 26, 211-252 (1964).
"""
def __init__(self, method='yeo-johnson', standardize=True, copy=True):
self.method = method
self.standardize = standardize
self.copy = copy
def fit(self, X, y=None):
"""Estimate the optimal parameter lambda for each feature.
The optimal lambda parameter for minimizing skewness is estimated on
each feature independently using maximum likelihood.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The data used to estimate the optimal transformation parameters.
y : Ignored
Returns
-------
self : object
"""
self._fit(X, y=y, force_transform=False)
return self
def fit_transform(self, X, y=None):
return self._fit(X, y, force_transform=True)
def _fit(self, X, y=None, force_transform=False):
X = self._check_input(X, check_positive=True, check_method=True)
if not self.copy and not force_transform: # if call from fit()
X = X.copy() # force copy so that fit does not change X inplace
optim_function = {'box-cox': self._box_cox_optimize,
'yeo-johnson': self._yeo_johnson_optimize
}[self.method]
with np.errstate(invalid='ignore'): # hide NaN warnings
self.lambdas_ = np.array([optim_function(col) for col in X.T])
if self.standardize or force_transform:
transform_function = {'box-cox': boxcox,
'yeo-johnson': self._yeo_johnson_transform
}[self.method]
for i, lmbda in enumerate(self.lambdas_):
with np.errstate(invalid='ignore'): # hide NaN warnings
X[:, i] = transform_function(X[:, i], lmbda)
if self.standardize:
self._scaler = StandardScaler(copy=False)
if force_transform:
X = self._scaler.fit_transform(X)
else:
self._scaler.fit(X)
return X
def transform(self, X):
"""Apply the power transform to each feature using the fitted lambdas.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The data to be transformed using a power transformation.
Returns
-------
X_trans : array-like, shape (n_samples, n_features)
The transformed data.
"""
check_is_fitted(self)
X = self._check_input(X, check_positive=True, check_shape=True)
transform_function = {'box-cox': boxcox,
'yeo-johnson': self._yeo_johnson_transform
}[self.method]
for i, lmbda in enumerate(self.lambdas_):
with np.errstate(invalid='ignore'): # hide NaN warnings
X[:, i] = transform_function(X[:, i], lmbda)
if self.standardize:
X = self._scaler.transform(X)
return X
def inverse_transform(self, X):
"""Apply the inverse power transformation using the fitted lambdas.
The inverse of the Box-Cox transformation is given by::
if lambda_ == 0:
X = exp(X_trans)
else:
X = (X_trans * lambda_ + 1) ** (1 / lambda_)
The inverse of the Yeo-Johnson transformation is given by::
if X >= 0 and lambda_ == 0:
X = exp(X_trans) - 1
elif X >= 0 and lambda_ != 0:
X = (X_trans * lambda_ + 1) ** (1 / lambda_) - 1
elif X < 0 and lambda_ != 2:
X = 1 - (-(2 - lambda_) * X_trans + 1) ** (1 / (2 - lambda_))
elif X < 0 and lambda_ == 2:
X = 1 - exp(-X_trans)
Parameters
----------
X : array-like, shape (n_samples, n_features)
The transformed data.
Returns
-------
X : array-like, shape (n_samples, n_features)
The original data
"""
check_is_fitted(self)
X = self._check_input(X, check_shape=True)
if self.standardize:
X = self._scaler.inverse_transform(X)
inv_fun = {'box-cox': self._box_cox_inverse_tranform,
'yeo-johnson': self._yeo_johnson_inverse_transform
}[self.method]
for i, lmbda in enumerate(self.lambdas_):
with np.errstate(invalid='ignore'): # hide NaN warnings
X[:, i] = inv_fun(X[:, i], lmbda)
return X
def _box_cox_inverse_tranform(self, x, lmbda):
"""Return inverse-transformed input x following Box-Cox inverse
transform with parameter lambda.
"""
if lmbda == 0:
x_inv = np.exp(x)
else:
x_inv = (x * lmbda + 1) ** (1 / lmbda)
return x_inv
def _yeo_johnson_inverse_transform(self, x, lmbda):
"""Return inverse-transformed input x following Yeo-Johnson inverse
transform with parameter lambda.
"""
x_inv = np.zeros_like(x)
pos = x >= 0
# when x >= 0
if abs(lmbda) < np.spacing(1.):
x_inv[pos] = np.exp(x[pos]) - 1
else: # lmbda != 0
x_inv[pos] = np.power(x[pos] * lmbda + 1, 1 / lmbda) - 1
# when x < 0
if abs(lmbda - 2) > np.spacing(1.):
x_inv[~pos] = 1 - np.power(-(2 - lmbda) * x[~pos] + 1,
1 / (2 - lmbda))
else: # lmbda == 2
x_inv[~pos] = 1 - np.exp(-x[~pos])
return x_inv
def _yeo_johnson_transform(self, x, lmbda):
"""Return transformed input x following Yeo-Johnson transform with
parameter lambda.
"""
out = np.zeros_like(x)
pos = x >= 0 # binary mask
# when x >= 0
if abs(lmbda) < np.spacing(1.):
out[pos] = np.log1p(x[pos])
else: # lmbda != 0
out[pos] = (np.power(x[pos] + 1, lmbda) - 1) / lmbda
# when x < 0
if abs(lmbda - 2) > np.spacing(1.):
out[~pos] = -(np.power(-x[~pos] + 1, 2 - lmbda) - 1) / (2 - lmbda)
else: # lmbda == 2
out[~pos] = -np.log1p(-x[~pos])
return out
def _box_cox_optimize(self, x):
"""Find and return optimal lambda parameter of the Box-Cox transform by
MLE, for observed data x.
We here use scipy builtins which uses the brent optimizer.
"""
# the computation of lambda is influenced by NaNs so we need to
# get rid of them
_, lmbda = stats.boxcox(x[~np.isnan(x)], lmbda=None)
return lmbda
def _yeo_johnson_optimize(self, x):
"""Find and return optimal lambda parameter of the Yeo-Johnson
transform by MLE, for observed data x.
Like for Box-Cox, MLE is done via the brent optimizer.
"""
def _neg_log_likelihood(lmbda):
"""Return the negative log likelihood of the observed data x as a
function of lambda."""
x_trans = self._yeo_johnson_transform(x, lmbda)
n_samples = x.shape[0]
loglike = -n_samples / 2 * np.log(x_trans.var())
loglike += (lmbda - 1) * (np.sign(x) * np.log1p(np.abs(x))).sum()
return -loglike
# the computation of lambda is influenced by NaNs so we need to
# get rid of them
x = x[~np.isnan(x)]
# choosing bracket -2, 2 like for boxcox
return optimize.brent(_neg_log_likelihood, brack=(-2, 2))
def _check_input(self, X, check_positive=False, check_shape=False,
check_method=False):
"""Validate the input before fit and transform.
Parameters
----------
X : array-like, shape (n_samples, n_features)
check_positive : bool
If True, check that all data is positive and non-zero (only if
``self.method=='box-cox'``).
check_shape : bool
If True, check that n_features matches the length of self.lambdas_
check_method : bool
If True, check that the transformation method is valid.
"""
X = check_array(X, ensure_2d=True, dtype=FLOAT_DTYPES, copy=self.copy,
force_all_finite='allow-nan')
with np.warnings.catch_warnings():
np.warnings.filterwarnings(
'ignore', r'All-NaN (slice|axis) encountered')
if (check_positive and self.method == 'box-cox' and
np.nanmin(X) <= 0):
raise ValueError("The Box-Cox transformation can only be "
"applied to strictly positive data")
if check_shape and not X.shape[1] == len(self.lambdas_):
raise ValueError("Input data has a different number of features "
"than fitting data. Should have {n}, data has {m}"
.format(n=len(self.lambdas_), m=X.shape[1]))
valid_methods = ('box-cox', 'yeo-johnson')
if check_method and self.method not in valid_methods:
raise ValueError("'method' must be one of {}, "
"got {} instead."
.format(valid_methods, self.method))
return X
def _more_tags(self):
return {'allow_nan': True}
def power_transform(X, method='warn', standardize=True, copy=True):
"""
Power transforms are a family of parametric, monotonic transformations
that are applied to make data more Gaussian-like. This is useful for
modeling issues related to heteroscedasticity (non-constant variance),
or other situations where normality is desired.
Currently, power_transform supports the Box-Cox transform and the
Yeo-Johnson transform. The optimal parameter for stabilizing variance and
minimizing skewness is estimated through maximum likelihood.
Box-Cox requires input data to be strictly positive, while Yeo-Johnson
supports both positive or negative data.
By default, zero-mean, unit-variance normalization is applied to the
transformed data.
Read more in the :ref:`User Guide <preprocessing_transformer>`.
Parameters
----------
X : array-like, shape (n_samples, n_features)
The data to be transformed using a power transformation.
method : str
The power transform method. Available methods are:
- 'yeo-johnson' [1]_, works with positive and negative values
- 'box-cox' [2]_, only works with strictly positive values
The default method will be changed from 'box-cox' to 'yeo-johnson'
in version 0.23. To suppress the FutureWarning, explicitly set the
parameter.
standardize : boolean, default=True
Set to True to apply zero-mean, unit-variance normalization to the
transformed output.
copy : boolean, optional, default=True
Set to False to perform inplace computation during transformation.
Returns
-------
X_trans : array-like, shape (n_samples, n_features)
The transformed data.
Examples
--------
>>> import numpy as np
>>> from sklearn.preprocessing import power_transform
>>> data = [[1, 2], [3, 2], [4, 5]]
>>> print(power_transform(data, method='box-cox'))
[[-1.332... -0.707...]
[ 0.256... -0.707...]
[ 1.076... 1.414...]]
See also
--------
PowerTransformer : Equivalent transformation with the
``Transformer`` API (e.g. as part of a preprocessing
:class:`sklearn.pipeline.Pipeline`).
quantile_transform : Maps data to a standard normal distribution with
the parameter `output_distribution='normal'`.
Notes
-----
NaNs are treated as missing values: disregarded in ``fit``, and maintained
in ``transform``.
For a comparison of the different scalers, transformers, and normalizers,
see :ref:`examples/preprocessing/plot_all_scaling.py
<sphx_glr_auto_examples_preprocessing_plot_all_scaling.py>`.
References
----------
.. [1] I.K. Yeo and R.A. Johnson, "A new family of power transformations to
improve normality or symmetry." Biometrika, 87(4), pp.954-959,
(2000).
.. [2] G.E.P. Box and D.R. Cox, "An Analysis of Transformations", Journal
of the Royal Statistical Society B, 26, 211-252 (1964).
"""
if method == 'warn':
warnings.warn("The default value of 'method' will change from "
"'box-cox' to 'yeo-johnson' in version 0.23. Set "
"the 'method' argument explicitly to silence this "
"warning in the meantime.",
FutureWarning)
method = 'box-cox'
pt = PowerTransformer(method=method, standardize=standardize, copy=copy)
return pt.fit_transform(X)