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# Mathieu Blondel <mathieu@mblondel.org>
# Olivier Grisel <olivier.grisel@ensta.org>
# License: BSD
import numpy as np
import scipy.sparse as sp
from .utils import check_arrays
from .utils import warn_if_not_float
from .base import BaseEstimator, TransformerMixin
from .utils.sparsefuncs import inplace_csr_row_normalize_l1
from .utils.sparsefuncs import inplace_csr_row_normalize_l2
from .utils.sparsefuncs import inplace_csr_column_scale
from .utils.sparsefuncs import mean_variance_axis0
def _mean_and_std(X, axis=0, with_mean=True, with_std=True):
"""Compute mean and std dev for centering, scaling
Zero valued std components are reset to 1.0 to avoid NaNs when scaling.
"""
X = np.asarray(X)
Xr = np.rollaxis(X, axis)
if with_mean:
mean_ = Xr.mean(axis=0)
else:
mean_ = None
if with_std:
std_ = Xr.std(axis=0)
if isinstance(std_, np.ndarray):
std_[std_ == 0.0] = 1.0
elif std_ == 0.:
std_ = 1.
else:
std_ = None
return mean_, std_
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.
Parameters
----------
X : array-like or CSR 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 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_mean=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.
See also
--------
:class:`sklearn.preprocessing.Scaler` to perform centering and
scaling using the ``Transformer`` API (e.g. as part of a preprocessing
:class:`sklearn.pipeline.Pipeline`)
"""
if sp.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)
warn_if_not_float(X, estimator='The scale function')
if not sp.isspmatrix_csr(X):
X = X.tocsr()
copy = False
if copy:
X = X.copy()
_, var = mean_variance_axis0(X)
var[var == 0.0] = 1.0
inplace_csr_column_scale(X, 1 / np.sqrt(var))
else:
X = np.asarray(X)
warn_if_not_float(X, estimator='The scale function')
mean_, std_ = _mean_and_std(
X, axis, with_mean=with_mean, with_std=with_std)
if copy:
X = X.copy()
# 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_
if with_std:
Xr /= std_
return X
class Scaler(BaseEstimator, TransformerMixin):
"""Standardize features by removing the mean and scaling to unit variance
Centering and scaling happen indepently 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.
Parameters
----------
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 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).
Attributes
----------
`mean_` : array of floats with shape [n_features]
The mean value for each feature in the training set.
`std_` : array of floats with shape [n_features]
The standard deviation for each feature in the training set.
See also
--------
:func:`sklearn.preprocessing.scale` to perform centering and
scaling without using the ``Transformer`` object oriented API
:class:`sklearn.decomposition.RandomizedPCA` with `whiten=True`
to further remove the linear correlation across features.
"""
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 fit(self, X, y=None):
"""Compute the mean and std to be used for later scaling
Parameters
----------
X : array-like or CSR matrix with shape [n_samples, n_features]
The data used to compute the mean and standard deviation
used for later scaling along the features axis.
"""
if sp.issparse(X):
if self.with_mean:
raise ValueError(
"Cannot center sparse matrices: pass `with_mean=False` "
"instead See docstring for motivation and alternatives.")
warn_if_not_float(X, estimator=self)
copy = self.copy
if not sp.isspmatrix_csr(X):
X = X.tocsr()
copy = False
if copy:
X = X.copy()
self.mean_ = None
_, var = mean_variance_axis0(X)
self.std_ = np.sqrt(var)
self.std_[var == 0.0] = 1.0
inplace_csr_column_scale(X, 1 / self.std_)
return self
else:
X = np.asarray(X)
warn_if_not_float(X, estimator=self)
self.mean_, self.std_ = _mean_and_std(
X, axis=0, with_mean=self.with_mean, with_std=self.with_std)
return self
def transform(self, X, y=None, copy=None):
"""Perform standardization by centering and scaling
Parameters
----------
X : array-like with shape [n_samples, n_features]
The data used to scale along the features axis.
"""
copy = copy if copy is not None else self.copy
if sp.issparse(X):
if self.with_mean:
raise ValueError(
"Cannot center sparse matrices: pass `with_mean=False` "
"instead See docstring for motivation and alternatives.")
warn_if_not_float(X, estimator=self)
if not sp.isspmatrix_csr(X):
X = X.tocsr()
copy = False
if copy:
X = X.copy()
inplace_csr_column_scale(X, 1 / self.std_)
else:
X = np.asarray(X)
warn_if_not_float(X, estimator=self)
if copy:
X = X.copy()
if self.with_mean:
X -= self.mean_
if self.with_std:
X /= self.std_
return X
def inverse_transform(self, X, copy=None):
"""Scale back the data to the original representation
Parameters
----------
X : array-like with shape [n_samples, n_features]
The data used to scale along the features axis.
"""
copy = copy if copy is not None else self.copy
if sp.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 sp.isspmatrix_csr(X):
X = X.tocsr()
copy = False
if copy:
X = X.copy()
inplace_csr_column_scale(X, self.std_)
else:
X = np.asarray(X)
if copy:
X = X.copy()
if self.with_std:
X *= self.std_
if self.with_mean:
X += self.mean_
return X
def normalize(X, norm='l2', axis=1, copy=True):
"""Normalize a dataset along any axis
Parameters
----------
X : array or scipy.sparse matrix with 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' or 'l2', 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 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).
See also
--------
:class:`sklearn.preprocessing.Normalizer` to perform normalization
using the ``Transformer`` API (e.g. as part of a preprocessing
:class:`sklearn.pipeline.Pipeline`)
"""
if norm not in ('l1', 'l2'):
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_arrays(X, sparse_format=sparse_format, copy=copy)[0]
warn_if_not_float(X, 'The normalize function')
if axis == 0:
X = X.T
if sp.issparse(X):
if norm == 'l1':
inplace_csr_row_normalize_l1(X)
elif norm == 'l2':
inplace_csr_row_normalize_l2(X)
else:
if norm == 'l1':
norms = np.abs(X).sum(axis=1)[:, np.newaxis]
norms[norms == 0.0] = 1.0
elif norm == 'l2':
norms = np.sqrt(np.sum(X ** 2, axis=1))[:, np.newaxis]
norms[norms == 0.0] = 1.0
X /= norms
if axis == 0:
X = X.T
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.
Parameters
----------
norm : 'l1' or 'l2', optional ('l2' by default)
The norm to use to normalize each non zero sample.
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).
Notes
-----
This estimator is stateless (besides constructor parameters), the
fit method does nothing but is useful when used in a pipeline.
See also
--------
:func:`sklearn.preprocessing.normalize` equivalent function
without the object oriented 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.
"""
return self
def transform(self, X, y=None, copy=None):
"""Scale each non zero row of X to unit norm
Parameters
----------
X : array or scipy.sparse matrix with 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 = copy if copy is not None else self.copy
return normalize(X, norm=self.norm, axis=1, copy=copy)
def binarize(X, threshold=0.0, copy=True):
"""Boolean thresholding of array-like or scipy.sparse matrix
Parameters
----------
X : array or scipy.sparse matrix with 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.
threshold : float, optional (0.0 by default)
The lower bound that triggers feature values to be replaced by 1.0.
copy : boolean, optional, default is 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 and if axis is 1).
See also
--------
:class:`sklearn.preprocessing.Binarizer` to perform binarization
using the ``Transformer`` API (e.g. as part of a preprocessing
:class:`sklearn.pipeline.Pipeline`)
"""
X = check_arrays(X, sparse_format='csr', copy=copy)[0]
if sp.issparse(X):
cond = X.data > threshold
not_cond = np.logical_not(cond)
X.data[cond] = 1
# FIXME: if enough values became 0, it may be worth changing
# the sparsity structure
X.data[not_cond] = 0
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
The default threshold is 0.0 so that any non-zero values are set to 1.0
and zeros are left untouched.
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 occurences for instance.
It can also be used as a pre-processing step for estimators that
consider boolean random variables (e.g. modeled using the Bernoulli
distribution in a Bayesian setting).
Parameters
----------
threshold : float, optional (0.0 by default)
The lower bound that triggers feature values to be replaced by 1.0.
copy : boolean, optional, default is 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.
"""
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.
"""
return self
def transform(self, X, y=None, copy=None):
"""Binarize each element of X
Parameters
----------
X : array or scipy.sparse matrix with 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 = copy if copy is not None else self.copy
return binarize(X, threshold=self.threshold, copy=copy)
def _is_label_indicator_matrix(y):
return hasattr(y, "shape") and len(y.shape) == 2
def _is_multilabel(y):
return isinstance(y[0], tuple) or \
isinstance(y[0], list) or \
_is_label_indicator_matrix(y)
class LabelBinarizer(BaseEstimator, TransformerMixin):
"""Binarize labels in a one-vs-all fashion
Several regression and binary classification algorithms are
available in the scikit. A simple way to extend these algorithms
to the multi-class classification case is to use the so-called
one-vs-all scheme.
At learning time, this simply consists in learning one regressor
or binary classifier per class. In doing so, one needs to convert
multi-class labels to binary labels (belong or does not belong
to the class). LabelBinarizer makes this process easy with the
transform method.
At prediction time, one assigns the class for which the corresponding
model gave the greatest confidence. LabelBinarizer makes this easy
with the inverse_transform method.
Parameters
----------
neg_label: int (default: 0)
Value with which negative labels must be encoded.
pos_label: int (default: 1)
Value with which positive labels must be encoded.
Attributes
----------
`classes_`: array of shape [n_class]
Holds the label for each class.
Examples
--------
>>> from sklearn import preprocessing
>>> clf = preprocessing.LabelBinarizer()
>>> clf.fit([1, 2, 6, 4, 2])
LabelBinarizer(neg_label=0, pos_label=1)
>>> clf.classes_
array([1, 2, 4, 6])
>>> clf.transform([1, 6])
array([[ 1., 0., 0., 0.],
[ 0., 0., 0., 1.]])
>>> clf.fit_transform([(1, 2), (3,)])
array([[ 1., 1., 0.],
[ 0., 0., 1.]])
>>> clf.classes_
array([1, 2, 3])
"""
def __init__(self, neg_label=0, pos_label=1):
if neg_label >= pos_label:
raise ValueError("neg_label must be strictly less than pos_label.")
self.neg_label = neg_label
self.pos_label = pos_label
def _check_fitted(self):
if not hasattr(self, "classes_"):
raise ValueError("LabelBinarizer was not fitted yet.")
def fit(self, y):
"""Fit label binarizer
Parameters
----------
y : numpy array of shape [n_samples] or sequence of sequences
Target values. In the multilabel case the nested sequences can
have variable lengths.
Returns
-------
self : returns an instance of self.
"""
self.multilabel = _is_multilabel(y)
if self.multilabel:
self.indicator_matrix_ = _is_label_indicator_matrix(y)
if self.indicator_matrix_:
self.classes_ = np.arange(y.shape[1])
else:
self.classes_ = np.array(sorted(set.union(*map(set, y))))
else:
self.classes_ = np.unique(y)
return self
def transform(self, y):
"""Transform multi-class labels to binary labels
The output of transform is sometimes referred to by some authors as the
1-of-K coding scheme.
Parameters
----------
y : numpy array of shape [n_samples] or sequence of sequences
Target values. In the multilabel case the nested sequences can
have variable lengths.
Returns
-------
Y : numpy array of shape [n_samples, n_classes]
"""
self._check_fitted()
if self.multilabel or len(self.classes_) > 2:
if _is_label_indicator_matrix(y):
# nothing to do as y is already a label indicator matrix
return y
Y = np.zeros((len(y), len(self.classes_)))
else:
Y = np.zeros((len(y), 1))
Y += self.neg_label
y_is_multilabel = _is_multilabel(y)
if y_is_multilabel and not self.multilabel:
raise ValueError("The object was not " +
"fitted with multilabel input!")
elif self.multilabel:
if not _is_multilabel(y):
raise ValueError("y should be a list of label lists/tuples,"
"got %r" % (y,))
# inverse map: label => column index
imap = dict((v, k) for k, v in enumerate(self.classes_))
for i, label_tuple in enumerate(y):
for label in label_tuple:
Y[i, imap[label]] = self.pos_label
return Y
elif len(self.classes_) == 2:
Y[y == self.classes_[1], 0] = self.pos_label
return Y
elif len(self.classes_) >= 2:
for i, k in enumerate(self.classes_):
Y[y == k, i] = self.pos_label
return Y
else:
# Only one class, returns a matrix with all negative labels.
return Y
def inverse_transform(self, Y, threshold=None):
"""Transform binary labels back to multi-class labels
Parameters
----------
Y : numpy array of shape [n_samples, n_classes]
Target values.
threshold : float or None
Threshold used in the binary and multi-label cases.
Use 0 when:
- Y contains the output of decision_function (classifier)
Use 0.5 when:
- Y contains the output of predict_proba
If None, the threshold is assumed to be half way between
neg_label and pos_label.
Returns
-------
y : numpy array of shape [n_samples] or sequence of sequences
Target values. In the multilabel case the nested sequences can
have variable lengths.
Notes
-----
In the case when the binary labels are fractional
(probabilistic), inverse_transform chooses the class with the
greatest value. Typically, this allows to use the output of a
linear model's decision_function method directly as the input
of inverse_transform.
"""
self._check_fitted()
if threshold is None:
half = (self.pos_label - self.neg_label) / 2.0
threshold = self.neg_label + half
if self.multilabel:
Y = np.array(Y > threshold, dtype=int)
# Return the predictions in the same format as in fit
if self.indicator_matrix_:
# Label indicator matrix format
return Y
else:
# Lists of tuples format
return [tuple(self.classes_[np.flatnonzero(Y[i])])
for i in range(Y.shape[0])]
if len(Y.shape) == 1 or Y.shape[1] == 1:
y = np.array(Y.ravel() > threshold, dtype=int)
else:
y = Y.argmax(axis=1)
return self.classes_[y]
class KernelCenterer(BaseEstimator, TransformerMixin):
"""Center a kernel matrix
This is equivalent to centering phi(X) with
sklearn.preprocessing.Scaler(with_std=False).
"""
def fit(self, K):
"""Fit KernelCenterer
Parameters
----------
K : numpy array of shape [n_samples, n_samples]
Kernel matrix.
Returns
-------
self : returns an instance of self.
"""
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
Parameters
----------
K : numpy array of shape [n_samples1, n_samples2]
Kernel matrix.
Returns
-------
K_new : numpy array of shape [n_samples1, n_samples2]
"""
if copy:
K = K.copy()
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
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