# 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>
# License: BSD 3 clause
from __future__ import division
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 ..base import BaseEstimator, TransformerMixin
from ..externals import six
from ..externals.six import string_types
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)
BOUNDS_THRESHOLD = 1e-7
zip = six.moves.zip
map = six.moves.map
range = six.moves.range
__all__ = [
'Binarizer',
'KernelCenterer',
'MinMaxScaler',
'MaxAbsScaler',
'Normalizer',
'OneHotEncoder',
'RobustScaler',
'StandardScaler',
'QuantileTransformer',
'add_dummy_feature',
'binarize',
'normalize',
'scale',
'robust_scale',
'maxabs_scale',
'minmax_scale',
'quantile_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.
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,
warn_on_dtype=True, estimator='the scale function',
dtype=FLOAT_DTYPES)
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.mean(X, axis)
if with_std:
scale_ = np.std(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 = Xr.mean(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 = Xr.mean(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(BaseEstimator, TransformerMixin):
"""Transforms 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::
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.
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 : boolean, optional, 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, shape (n_features,)
Per feature adjustment for minimum.
scale_ : ndarray, shape (n_features,)
Per feature relative scaling of the data.
.. versionadded:: 0.17
*scale_* attribute.
data_min_ : ndarray, shape (n_features,)
Per feature minimum seen in the data
.. versionadded:: 0.17
*data_min_*
data_max_ : ndarray, shape (n_features,)
Per feature maximum seen in the data
.. versionadded:: 0.17
*data_max_*
data_range_ : ndarray, shape (n_features,)
Per feature range ``(data_max_ - data_min_)`` seen in the data
.. versionadded:: 0.17
*data_range_*
Examples
--------
>>> from sklearn.preprocessing import MinMaxScaler
>>>
>>> data = [[-1, 2], [-0.5, 6], [0, 10], [1, 18]]
>>> scaler = MinMaxScaler()
>>> print(scaler.fit(data))
MinMaxScaler(copy=True, feature_range=(0, 1))
>>> 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
-----
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_
[docs] def fit(self, X, y=None):
"""Compute the minimum and maximum to be used for later scaling.
Parameters
----------
X : array-like, 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)
[docs] 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 `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, shape [n_samples, n_features]
The data used to compute the mean and standard deviation
used for later scaling along the features axis.
y : Passthrough for ``Pipeline`` compatibility.
"""
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 no support sparse input. "
"You may consider to use MaxAbsScaler instead.")
X = check_array(X, copy=self.copy, warn_on_dtype=True,
estimator=self, dtype=FLOAT_DTYPES)
data_min = np.min(X, axis=0)
data_max = np.max(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 minmax_scale(X, feature_range=(0, 1), axis=0, copy=True):
"""Transforms 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::
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.
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, shape (n_samples, n_features)
The data.
feature_range : tuple (min, max), default=(0, 1)
Desired range of transformed 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
--------
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, warn_on_dtype=True,
dtype=FLOAT_DTYPES)
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(BaseEstimator, TransformerMixin):
"""Standardize features by removing the mean and scaling to unit variance
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 the
`transform` method.
Standardization of a dataset is a common requirement for many
machine learning estimators: they might behave badly if the
individual feature 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, shape (n_features,)
Per feature relative scaling of the data.
.. versionadded:: 0.17
*scale_*
mean_ : array of floats with shape [n_features]
The mean value for each feature in the training set.
var_ : array of floats with shape [n_features]
The variance for each feature in the training set. Used to compute
`scale_`
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 StandardScaler
>>>
>>> data = [[0, 0], [0, 0], [1, 1], [1, 1]]
>>> scaler = StandardScaler()
>>> print(scaler.fit(data))
StandardScaler(copy=True, with_mean=True, with_std=True)
>>> 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
-----
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_
[docs] 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 : Passthrough for ``Pipeline`` compatibility.
"""
# Reset internal state before fitting
self._reset()
return self.partial_fit(X, y)
[docs] 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 `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 : Passthrough for ``Pipeline`` compatibility.
"""
X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy,
warn_on_dtype=True, estimator=self, dtype=FLOAT_DTYPES)
# 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 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.with_std:
# First pass
if not hasattr(self, 'n_samples_seen_'):
self.mean_, self.var_ = mean_variance_axis(X, axis=0)
self.n_samples_seen_ = X.shape[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
else:
# First pass
if not hasattr(self, 'n_samples_seen_'):
self.mean_ = .0
self.n_samples_seen_ = 0
if self.with_std:
self.var_ = .0
else:
self.var_ = None
self.mean_, self.var_, self.n_samples_seen_ = \
_incremental_mean_and_var(X, self.mean_, self.var_,
self.n_samples_seen_)
if self.with_std:
self.scale_ = _handle_zeros_in_scale(np.sqrt(self.var_))
else:
self.scale_ = None
return self
class MaxAbsScaler(BaseEstimator, TransformerMixin):
"""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.
See also
--------
maxabs_scale: Equivalent function without the estimator API.
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>`.
"""
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_
[docs] 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)
[docs] 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 `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 : Passthrough for ``Pipeline`` compatibility.
"""
X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy,
estimator=self, dtype=FLOAT_DTYPES)
if sparse.issparse(X):
mins, maxs = min_max_axis(X, axis=0)
max_abs = np.maximum(np.abs(mins), np.abs(maxs))
else:
max_abs = np.abs(X).max(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 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
-----
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)
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(BaseEstimator, TransformerMixin):
"""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 (or each
sample, depending on the ``axis`` argument) 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.
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_(statistics)
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 _check_array(self, X, copy):
"""Makes sure centering is not enabled for sparse matrices."""
X = check_array(X, accept_sparse=('csr', 'csc'), copy=self.copy,
estimator=self, dtype=FLOAT_DTYPES)
if sparse.issparse(X):
if self.with_centering:
raise ValueError(
"Cannot center sparse matrices: use `with_centering=False`"
" instead. See docstring for motivation and alternatives.")
return X
[docs] 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.
"""
if sparse.issparse(X):
raise TypeError("RobustScaler cannot be fitted on sparse inputs")
X = self._check_array(X, self.copy)
if self.with_centering:
self.center_ = np.median(X, axis=0)
if self.with_scaling:
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))
q = np.percentile(X, self.quantile_range, axis=0)
self.scale_ = (q[1] - q[0])
self.scale_ = _handle_zeros_in_scale(self.scale_, copy=False)
return self
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`).
"""
s = RobustScaler(with_centering=with_centering, with_scaling=with_scaling,
quantile_range=quantile_range, copy=copy)
if axis == 0:
return s.fit_transform(X)
else:
return s.fit_transform(X.T).T
class PolynomialFeatures(BaseEstimator, TransformerMixin):
"""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).
Examples
--------
>>> 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):
self.degree = degree
self.interaction_only = interaction_only
self.include_bias = include_bias
@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, 'n_input_features_')
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
[docs] 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).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 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(BaseEstimator, TransformerMixin):
"""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).
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
[docs] 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
"""
X = check_array(X, accept_sparse='csr')
return self
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(BaseEstimator, TransformerMixin):
"""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).
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
[docs] 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
class KernelCenterer(BaseEstimator, TransformerMixin):
"""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>`.
"""
[docs] 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)
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
@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.ones(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.ones(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.ones((n_samples, 1)) * value, X))
def _transform_selected(X, transform, selected="all", copy=True):
"""Apply a transform function to portion of selected features
Parameters
----------
X : {array-like, sparse matrix}, shape [n_samples, n_features]
Dense array or sparse matrix.
transform : callable
A callable transform(X) -> X_transformed
copy : boolean, optional
Copy X even if it could be avoided.
selected: "all" or array of indices or mask
Specify which features to apply the transform to.
Returns
-------
X : array or sparse matrix, shape=(n_samples, n_features_new)
"""
X = check_array(X, accept_sparse='csc', copy=copy, dtype=FLOAT_DTYPES)
if isinstance(selected, six.string_types) and selected == "all":
return transform(X)
if len(selected) == 0:
return X
n_features = X.shape[1]
ind = np.arange(n_features)
sel = np.zeros(n_features, dtype=bool)
sel[np.asarray(selected)] = True
not_sel = np.logical_not(sel)
n_selected = np.sum(sel)
if n_selected == 0:
# No features selected.
return X
elif n_selected == n_features:
# All features selected.
return transform(X)
else:
X_sel = transform(X[:, ind[sel]])
X_not_sel = X[:, ind[not_sel]]
if sparse.issparse(X_sel) or sparse.issparse(X_not_sel):
return sparse.hstack((X_sel, X_not_sel))
else:
return np.hstack((X_sel, X_not_sel))
class OneHotEncoder(BaseEstimator, TransformerMixin):
"""Encode categorical integer features using a one-hot aka one-of-K scheme.
The input to this transformer should be a matrix of integers, denoting
the values taken on by categorical (discrete) features. The output will be
a sparse matrix where each column corresponds to one possible value of one
feature. It is assumed that input features take on values in the range
[0, n_values).
This encoding is needed for feeding categorical data to many scikit-learn
estimators, notably linear models and SVMs with the standard kernels.
Note: a one-hot encoding of y labels should use a LabelBinarizer
instead.
Read more in the :ref:`User Guide <preprocessing_categorical_features>`.
Parameters
----------
n_values : 'auto', int or array of ints
Number of values per feature.
- 'auto' : determine value range from training data.
- int : number of categorical values per feature.
Each feature value should be in ``range(n_values)``
- array : ``n_values[i]`` is the number of categorical values in
``X[:, i]``. Each feature value should be
in ``range(n_values[i])``
categorical_features : "all" or array of indices or mask
Specify what features are treated as categorical.
- 'all' (default): All features are treated as categorical.
- array of indices: Array of categorical feature indices.
- mask: Array of length n_features and with dtype=bool.
Non-categorical features are always stacked to the right of the matrix.
dtype : number type, default=np.float
Desired dtype of output.
sparse : boolean, default=True
Will return sparse matrix if set True else will return an array.
handle_unknown : str, 'error' or 'ignore'
Whether to raise an error or ignore if a unknown categorical feature is
present during transform.
Attributes
----------
active_features_ : array
Indices for active features, meaning values that actually occur
in the training set. Only available when n_values is ``'auto'``.
feature_indices_ : array of shape (n_features,)
Indices to feature ranges.
Feature ``i`` in the original data is mapped to features
from ``feature_indices_[i]`` to ``feature_indices_[i+1]``
(and then potentially masked by `active_features_` afterwards)
n_values_ : array of shape (n_features,)
Maximum number of values per feature.
Examples
--------
Given a dataset with three features and four samples, we let the encoder
find the maximum value per feature and transform the data to a binary
one-hot encoding.
>>> from sklearn.preprocessing import OneHotEncoder
>>> enc = OneHotEncoder()
>>> enc.fit([[0, 0, 3], [1, 1, 0], [0, 2, 1], \
[1, 0, 2]]) # doctest: +ELLIPSIS
OneHotEncoder(categorical_features='all', dtype=<... 'numpy.float64'>,
handle_unknown='error', n_values='auto', sparse=True)
>>> enc.n_values_
array([2, 3, 4])
>>> enc.feature_indices_
array([0, 2, 5, 9])
>>> enc.transform([[0, 1, 1]]).toarray()
array([[ 1., 0., 0., 1., 0., 0., 1., 0., 0.]])
See also
--------
sklearn.feature_extraction.DictVectorizer : performs a one-hot encoding of
dictionary items (also handles string-valued features).
sklearn.feature_extraction.FeatureHasher : performs an approximate one-hot
encoding of dictionary items or strings.
sklearn.preprocessing.LabelBinarizer : binarizes labels in a one-vs-all
fashion.
sklearn.preprocessing.MultiLabelBinarizer : transforms between iterable of
iterables and a multilabel format, e.g. a (samples x classes) binary
matrix indicating the presence of a class label.
sklearn.preprocessing.LabelEncoder : encodes labels with values between 0
and n_classes-1.
"""
def __init__(self, n_values="auto", categorical_features="all",
dtype=np.float64, sparse=True, handle_unknown='error'):
self.n_values = n_values
self.categorical_features = categorical_features
self.dtype = dtype
self.sparse = sparse
self.handle_unknown = handle_unknown
[docs] def fit(self, X, y=None):
"""Fit OneHotEncoder to X.
Parameters
----------
X : array-like, shape [n_samples, n_feature]
Input array of type int.
Returns
-------
self
"""
self.fit_transform(X)
return self
def _fit_transform(self, X):
"""Assumes X contains only categorical features."""
X = check_array(X, dtype=np.int)
if np.any(X < 0):
raise ValueError("X needs to contain only non-negative integers.")
n_samples, n_features = X.shape
if (isinstance(self.n_values, six.string_types) and
self.n_values == 'auto'):
n_values = np.max(X, axis=0) + 1
elif isinstance(self.n_values, numbers.Integral):
if (np.max(X, axis=0) >= self.n_values).any():
raise ValueError("Feature out of bounds for n_values=%d"
% self.n_values)
n_values = np.empty(n_features, dtype=np.int)
n_values.fill(self.n_values)
else:
try:
n_values = np.asarray(self.n_values, dtype=int)
except (ValueError, TypeError):
raise TypeError("Wrong type for parameter `n_values`. Expected"
" 'auto', int or array of ints, got %r"
% type(X))
if n_values.ndim < 1 or n_values.shape[0] != X.shape[1]:
raise ValueError("Shape mismatch: if n_values is an array,"
" it has to be of shape (n_features,).")
self.n_values_ = n_values
n_values = np.hstack([[0], n_values])
indices = np.cumsum(n_values)
self.feature_indices_ = indices
column_indices = (X + indices[:-1]).ravel()
row_indices = np.repeat(np.arange(n_samples, dtype=np.int32),
n_features)
data = np.ones(n_samples * n_features)
out = sparse.coo_matrix((data, (row_indices, column_indices)),
shape=(n_samples, indices[-1]),
dtype=self.dtype).tocsr()
if (isinstance(self.n_values, six.string_types) and
self.n_values == 'auto'):
mask = np.array(out.sum(axis=0)).ravel() != 0
active_features = np.where(mask)[0]
out = out[:, active_features]
self.active_features_ = active_features
return out if self.sparse else out.toarray()
def _transform(self, X):
"""Assumes X contains only categorical features."""
X = check_array(X, dtype=np.int)
if np.any(X < 0):
raise ValueError("X needs to contain only non-negative integers.")
n_samples, n_features = X.shape
indices = self.feature_indices_
if n_features != indices.shape[0] - 1:
raise ValueError("X has different shape than during fitting."
" Expected %d, got %d."
% (indices.shape[0] - 1, n_features))
# We use only those categorical features of X that are known using fit.
# i.e lesser than n_values_ using mask.
# This means, if self.handle_unknown is "ignore", the row_indices and
# col_indices corresponding to the unknown categorical feature are
# ignored.
mask = (X < self.n_values_).ravel()
if np.any(~mask):
if self.handle_unknown not in ['error', 'ignore']:
raise ValueError("handle_unknown should be either error or "
"unknown got %s" % self.handle_unknown)
if self.handle_unknown == 'error':
raise ValueError("unknown categorical feature present %s "
"during transform." % X.ravel()[~mask])
column_indices = (X + indices[:-1]).ravel()[mask]
row_indices = np.repeat(np.arange(n_samples, dtype=np.int32),
n_features)[mask]
data = np.ones(np.sum(mask))
out = sparse.coo_matrix((data, (row_indices, column_indices)),
shape=(n_samples, indices[-1]),
dtype=self.dtype).tocsr()
if (isinstance(self.n_values, six.string_types) and
self.n_values == 'auto'):
out = out[:, self.active_features_]
return out if self.sparse else out.toarray()
class QuantileTransformer(BaseEstimator, TransformerMixin):
"""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.
The cumulative density function of a feature is used to project the
original values. 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
----------
n_quantiles : int, optional (default=1000)
Number of quantiles to be computed. It corresponds to the number
of landmarks used to discretize the cumulative density function.
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
----------
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) # doctest: +ELLIPSIS
array([...])
See also
--------
quantile_transform : Equivalent function without the estimator API.
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
-----
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
# for compatibility issue with numpy<=1.8.X, references
# need to be a list scaled between 0 and 100
references = (self.references_ * 100).tolist()
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.percentile(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
# for compatibility issue with numpy<=1.8.X, references
# need to be a list scaled between 0 and 100
references = list(map(lambda x: x * 100, self.references_))
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.percentile(column_data, references))
self.quantiles_ = np.transpose(self.quantiles_)
def _transform_col(self, X_col, quantiles, inverse):
"""Private function to transform a single feature"""
if self.output_distribution == 'normal':
output_distribution = 'norm'
else:
output_distribution = self.output_distribution
output_distribution = getattr(stats, output_distribution)
# older version of scipy do not handle tuple as fill_value
# clipping the value before transform solve the issue
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 PDF
X_col = output_distribution.cdf(X_col)
# find index for lower and higher bounds
lower_bounds_idx = (X_col - BOUNDS_THRESHOLD <
lower_bound_x)
upper_bounds_idx = (X_col + BOUNDS_THRESHOLD >
upper_bound_x)
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 assending, and the
# lower for descending). We take the mean of these two
X_col = .5 * (np.interp(X_col, quantiles, self.references_)
- np.interp(-X_col, -quantiles[::-1],
-self.references_[::-1]))
else:
X_col = np.interp(X_col, 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 PDF
if not inverse:
X_col = output_distribution.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 = output_distribution.ppf(BOUNDS_THRESHOLD -
np.spacing(1))
clip_max = output_distribution.ppf(1 - (BOUNDS_THRESHOLD -
np.spacing(1)))
X_col = np.clip(X_col, clip_min, clip_max)
return X_col
def _check_inputs(self, X, accept_sparse_negative=False):
"""Check inputs before fit and transform"""
X = check_array(X, accept_sparse='csc', copy=self.copy,
dtype=[np.float64, np.float32])
# we only accept positive sparse matrix when ignore_implicit_zeros is
# false and that we call fit or transform.
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 PDF
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, 'quantiles_')
# 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 quantile_transform(X, axis=0, n_quantiles=1000,
output_distribution='uniform',
ignore_implicit_zeros=False,
subsample=int(1e5),
random_state=None,
copy=False):
"""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.
The cumulative density function of a feature is used to project the
original values. 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)
Number of quantiles to be computed. It corresponds to the number
of landmarks used to discretize the cumulative density function.
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
----------
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 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)
... # doctest: +ELLIPSIS
array([...])
See also
--------
QuantileTransformer : Performs quantile-based scaling using the
``Transformer`` API (e.g. as part of a preprocessing
:class:`sklearn.pipeline.Pipeline`).
scale : perform standardization that is faster, but less robust
to outliers.
robust_scale : perform robust standardization that removes the influence
of outliers but does not put outliers and inliers on the same scale.
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>`.
"""
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))
