609 lines
19 KiB
Python
609 lines
19 KiB
Python
""" Transformers to perform common preprocessing steps.
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"""
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# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
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# Mathieu Blondel <mathieu@mblondel.org>
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# Olivier Grisel <olivier.grisel@ensta.org>
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# License: BSD
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import numpy as np
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import scipy.sparse as sp
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from ..utils import check_arrays
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from ..base import BaseEstimator, TransformerMixin
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from ._preprocessing import inplace_csr_row_normalize_l1
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from ._preprocessing import inplace_csr_row_normalize_l2
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def _mean_and_std(X, axis=0, with_mean=True, with_std=True):
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"""Compute mean and std dev for centering, scaling
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Zero valued std components are reseted to 1.0 to avoid NaNs when scaling.
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"""
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X = np.asanyarray(X)
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Xr = np.rollaxis(X, axis)
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if with_mean:
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mean_ = Xr.mean(axis=0)
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else:
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mean_ = None
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if with_std:
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std_ = Xr.std(axis=0)
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if isinstance(std_, np.ndarray):
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std_[std_ == 0.0] = 1.0
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elif std_ == 0.:
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std_ = 1.
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else:
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std_ = None
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return mean_, std_
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def scale(X, axis=0, with_mean=True, with_std=True, copy=True):
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"""Method to standardize a dataset along any axis
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Center to the mean and component wise scale to unit variance.
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Parameters
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----------
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X : array-like
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The data to center and scale.
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axis : int (0 by default)
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axis used to compute the means and standard deviations along
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with_mean : boolean, True by default
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If True, center the data before scaling.
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with_std : boolean, True by default
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If True, scale the data to unit variance (or equivalently,
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unit standard deviation).
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copy : boolean, optional, default is True
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set to False to perform inplace row normalization and avoid a
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copy (if the input is already a numpy array or a scipy.sparse
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CSR matrix and if axis is 1).
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See also
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--------
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:class:`scikits.learn.preprocessing.Scaler` to perform centering and
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scaling using the ``Transformer`` API (e.g. as part of a preprocessing
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:class:`scikits.learn.pipeline.Pipeline`)
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"""
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if sp.issparse(X):
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raise NotImplementedError(
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"Scaling is not yet implement for sparse matrices")
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X = np.asanyarray(X)
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mean_, std_ = _mean_and_std(
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X, axis, with_mean=with_mean, with_std=with_std)
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if copy:
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X = X.copy()
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Xr = np.rollaxis(X, axis)
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if with_mean:
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Xr -= mean_
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if with_std:
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Xr /= std_
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return X
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class Scaler(BaseEstimator):
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"""Standardize features by removing the mean and scaling to unit variance
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Centering and scaling happen indepently on each feature by computing
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the relevant statistics on the samples in the training set. Mean and
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standard deviation are then stored to be used on later data using the
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`transform` method.
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Standardization of a dataset is a common requirement for many
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machine learning estimators: they might behave badly if the
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individual feature do not more or less look like standard normally
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distributed data (e.g. Gaussian with 0 mean and unit variance).
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For instance many elements used in the objective function of
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a learning algorithm (such as the RBF kernel of Support Vector
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Machines or the L1 and L2 regularizers of linear models) assume that
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all features are centered around 0 and have variance in the same
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order. If a feature has a variance that is orders of magnitude larger
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that others, it might dominate the objective function and make the
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estimator unable to learn from other features correctly as expected.
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Parameters
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----------
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with_mean : boolean, True by default
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If True, center the data before scaling.
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with_std : boolean, True by default
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If True, scale the data to unit variance (or equivalently,
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unit standard deviation).
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copy : boolean, optional, default is True
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set to False to perform inplace row normalization and avoid a
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copy (if the input is already a numpy array or a scipy.sparse
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CSR matrix and if axis is 1).
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Attributes
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----------
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mean_ : array of floats with shape [n_features]
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The mean value for each feature in the training set.
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std_ : array of floats with shape [n_features]
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The standard deviation for each feature in the training set.
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See also
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--------
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:func:`scikits.learn.preprocessing.scale` to perform centering and
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scaling without using the ``Transformer`` object oriented API
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:class:`scikits.learn.decomposition.RandomizedPCA` with `whiten=True`
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to further remove the linear correlation across features.
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"""
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def __init__(self, copy=True, with_mean=True, with_std=True):
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self.with_mean = with_mean
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self.with_std = with_std
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self.copy = copy
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def fit(self, X, y=None):
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"""Compute the mean and std to be used for later scaling
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Parameters
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----------
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X : array-like with shape [n_samples, n_features]
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The data used to compute the mean and standard deviation
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used for later scaling along the features axis.
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"""
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if sp.issparse(X):
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raise NotImplementedError(
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"Scaling is not yet implement for sparse matrices")
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self.mean_, self.std_ = _mean_and_std(
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X, axis=0, with_mean=self.with_mean, with_std=self.with_std)
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return self
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def transform(self, X, y=None, copy=True):
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"""Perform standardization by centering and scaling
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Parameters
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----------
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X : array-like with shape [n_samples, n_features]
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The data used to scale along the features axis.
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"""
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copy = copy if copy is not None else self.copy
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if sp.issparse(X):
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raise NotImplementedError(
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"Scaling is not yet implement for sparse matrices")
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X = np.asanyarray(X)
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if copy:
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X = X.copy()
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# We are taking a view of the X array and modifying it
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if self.with_mean:
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X -= self.mean_
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if self.with_std:
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X /= self.std_
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return X
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def normalize(X, norm='l2', axis=1, copy=True):
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"""Normalize rows of a 2D array or scipy.sparse matrix
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Parameters
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----------
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X : array or scipy.sparse matrix with shape [n_samples, n_features]
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The data to binarize, element by element.
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scipy.sparse matrices should be in CSR format to avoid an
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un-necessary copy.
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norm : 'l1' or 'l2', optional ('l2' by default)
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the norm to use to normalize each non zero sample
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axis : 0 or 1, optional (1 by default)
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if 1, normalize the columns instead of the rows
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copy : boolean, optional, default is True
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set to False to perform inplace row normalization and avoid a
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copy (if the input is already a numpy array or a scipy.sparse
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CSR matrix and if axis is 1).
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See also
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--------
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:class:`scikits.learn.preprocessing.Normalizer` to perform normalization
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using the ``Transformer`` API (e.g. as part of a preprocessing
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:class:`scikits.learn.pipeline.Pipeline`)
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"""
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if norm not in ('l1', 'l2'):
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raise ValueError("'%s' is not a supported norm" % norm)
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if axis == 0:
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sparse_format = 'csc'
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elif axis == 1:
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sparse_format = 'csr'
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else:
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raise ValueError("'%d' is not a supported axis" % axis)
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X = check_arrays(X, sparse_format=sparse_format, copy=copy)[0]
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if axis == 0:
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X = X.T
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if sp.issparse(X):
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if norm == 'l1':
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inplace_csr_row_normalize_l1(X)
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elif norm == 'l2':
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inplace_csr_row_normalize_l2(X)
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else:
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if norm == 'l1':
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norms = np.abs(X).sum(axis=1)[:, np.newaxis]
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norms[norms == 0.0] = 1.0
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elif norm == 'l2':
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norms = np.sqrt(np.sum(X ** 2, axis=1))[:, np.newaxis]
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norms[norms == 0.0] = 1.0
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X /= norms
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if axis == 0:
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X = X.T
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return X
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class Normalizer(BaseEstimator):
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"""Normalize samples individually to unit norm
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Each sample (i.e. each row of the data matrix) with at least one
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non zero component is rescaled independently of other samples so
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that its norm (l1 or l2) equals one.
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This transformer is able to work both with dense numpy arrays and
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scipy.sparse matrix (use CSR format if you want to avoid the burden of
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a copy / conversion).
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Scaling inputs to unit norms is a common operation for text
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classification or clustering for instance. For instance the dot
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product of two l2-normalized TF-IDF vectors is the cosine similarity
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of the vectors and is the base similarity metric for the Vector
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Space Model commonly used by the Information Retrieval community.
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Parameters
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----------
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norm : 'l1' or 'l2', optional ('l2' by default)
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the norm to use to normalize each non zero sample
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copy : boolean, optional, default is True
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set to False to perform inplace row normalization and avoid a
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copy (if the input is already a numpy array or a scipy.sparse
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CSR matrix).
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Note
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----
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This estimator is stateless (besides constructor parameters), the
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fit method does nothing but is useful when used in a pipeline.
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See also
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--------
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:func:`scikits.learn.preprocessing.normalize` equivalent function
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without the object oriented API
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"""
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def __init__(self, norm='l2', copy=True):
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self.norm = norm
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self.copy = copy
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def fit(self, X, y=None):
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"""Do nothing and return the estimator unchanged
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This method is just there to implement the usual API and hence
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work in pipelines.
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"""
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return self
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def transform(self, X, y=None, copy=None):
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"""Scale each non zero row of X to unit norm
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Parameters
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----------
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X : array or scipy.sparse matrix with shape [n_samples, n_features]
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The data to normalize, row by row. scipy.sparse matrices should be
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in CSR format to avoid an un-necessary copy.
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"""
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copy = copy if copy is not None else self.copy
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return normalize(X, norm=self.norm, copy=copy)
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def binarize(X, threshold=0.0, copy=True):
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"""Boolean thresholding of array-like or scipy.sparse matrix
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Parameters
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----------
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X : array or scipy.sparse matrix with shape [n_samples, n_features]
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The data to binarize, element by element.
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scipy.sparse matrices should be in CSR format to avoid an
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un-necessary copy.
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threshold : float, optional (0.0 by default)
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The
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copy : boolean, optional, default is True
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set to False to perform inplace binarization and avoid a copy
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(if the input is already a numpy array or a scipy.sparse CSR
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matrix and if axis is 1).
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See also
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--------
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:class:`scikits.learn.preprocessing.Binarizer` to perform binarization
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using the ``Transformer`` API (e.g. as part of a preprocessing
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:class:`scikits.learn.pipeline.Pipeline`)
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"""
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X = check_arrays(X, sparse_format='csr', copy=copy)[0]
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if sp.issparse(X):
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cond = X.data > threshold
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not_cond = np.logical_not(cond)
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X.data[cond] = 1
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# FIXME: if enough values became 0, it may be worth changing
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# the sparsity structure
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X.data[not_cond] = 0
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else:
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cond = X > threshold
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not_cond = np.logical_not(cond)
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X[cond] = 1
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X[not_cond] = 0
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return X
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class Binarizer(BaseEstimator):
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"""Binarize data (set feature values to 0 or 1) according to a threshold
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The default threshold is 0.0 so that any non-zero values are set to 1.0
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and zeros are left untouched.
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Binarization is a common operation on text count data where the
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analyst can decide to only consider the presence or absence of a
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feature rather than a quantified number of occurences for instance.
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It can also be used as a pre-processing step for estimators that
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consider boolean random variables (e.g. modeled using the Bernoulli
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distribution in a Bayesian setting).
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Parameters
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----------
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threshold : float, optional (0.0 by default)
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Lower bound that triggers feature values to be replaced by 1.0
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copy : boolean, optional, default is True
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set to False to perform inplace binarization and avoid a copy (if
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the input is already a numpy array or a scipy.sparse CSR matrix).
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Notes
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-----
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If the input is a sparse matrix, only the non-zero values are subject
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to update by the Binarizer class.
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This estimator is stateless (besides constructor parameters), the
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fit method does nothing but is useful when used in a pipeline.
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"""
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def __init__(self, threshold=0.0, copy=True):
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self.threshold = threshold
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self.copy = copy
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def fit(self, X, y=None):
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"""Do nothing and return the estimator unchanged
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This method is just there to implement the usual API and hence
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work in pipelines.
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"""
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return self
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def transform(self, X, y=None, copy=None):
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"""Scale each non zero row of X to unit norm
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Parameters
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----------
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X : array or scipy.sparse matrix with shape [n_samples, n_features]
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The data to binarize, element by element.
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scipy.sparse matrices should be in CSR format to avoid an
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un-necessary copy.
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"""
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copy = copy if copy is not None else self.copy
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return binarize(X, threshold=self.threshold, copy=copy)
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def _is_multilabel(y):
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return isinstance(y[0], tuple) or isinstance(y[0], list)
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class LabelBinarizer(BaseEstimator, TransformerMixin):
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"""Binarize labels in a one-vs-all fashion.
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Several regression and binary classification algorithms are
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available in the scikit. A simple way to extend these algorithms
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to the multi-class classification case is to use the so-called
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one-vs-all scheme.
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At learning time, this simply consists in learning one regressor
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or binary classifier per class. In doing so, one needs to convert
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multi-class labels to binary labels (belong or does not belong
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to the class). LabelBinarizer makes this process easy with the
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transform method.
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At prediction time, one assigns the class for which the corresponding
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model gave the greatest confidence. LabelBinarizer makes this easy
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with the inverse_transform method.
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Attributes
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----------
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classes_ : array of shape [n_class]
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Holds the label for each class.
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Examples
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--------
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>>> from scikits.learn import preprocessing
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>>> clf = preprocessing.LabelBinarizer()
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>>> clf.fit([1, 2, 6, 4, 2])
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LabelBinarizer()
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>>> clf.classes_
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array([1, 2, 4, 6])
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>>> clf.transform([1, 6])
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array([[ 1., 0., 0., 0.],
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[ 0., 0., 0., 1.]])
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>>> clf.fit_transform([(1, 2), (3,)])
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array([[ 1., 1., 0.],
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[ 0., 0., 1.]])
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>>> clf.classes_
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array([1, 2, 3])
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"""
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def fit(self, y):
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"""Fit label binarizer
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Parameters
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----------
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y : numpy array of shape [n_samples] or sequence of sequences
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Target values. In the multilabel case the nested sequences can
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have variable lengths.
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Returns
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-------
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self : returns an instance of self.
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"""
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self.multilabel = _is_multilabel(y)
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if self.multilabel:
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# concatenation of the sub-sequences
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self.classes_ = np.unique(reduce(lambda a, b: a + b, y))
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else:
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self.classes_ = np.unique(y)
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return self
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def transform(self, y):
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"""Transform multi-class labels to binary labels
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The output of transform is sometimes referred to by some authors as the
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1-of-K coding scheme.
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Parameters
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----------
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y : numpy array of shape [n_samples] or sequence of sequences
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Target values. In the multilabel case the nested sequences can
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have variable lengths.
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Returns
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-------
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Y : numpy array of shape [n_samples, n_classes]
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"""
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if len(self.classes_) == 2:
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Y = np.zeros((len(y), 1))
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else:
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Y = np.zeros((len(y), len(self.classes_)))
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if self.multilabel:
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if not _is_multilabel(y):
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raise ValueError("y should be a list of label lists/tuples,"
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"got %r" % (y,))
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# inverse map: label => column index
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imap = dict((v, k) for k, v in enumerate(self.classes_))
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for i, label_tuple in enumerate(y):
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for label in label_tuple:
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Y[i, imap[label]] = 1
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return Y
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elif len(self.classes_) == 2:
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Y[y == self.classes_[1], 0] = 1
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return Y
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elif len(self.classes_) >= 2:
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for i, k in enumerate(self.classes_):
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Y[y == k, i] = 1
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return Y
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else:
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raise ValueError("Wrong number of classes: %d"
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% len(self.classes_))
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def inverse_transform(self, Y):
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"""Transform binary labels back to multi-class labels
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Parameters
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----------
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Y : numpy array of shape [n_samples, n_classes]
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Target values
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Returns
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-------
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y : numpy array of shape [n_samples] or sequence of sequences
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Target values. In the multilabel case the nested sequences can
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have variable lengths.
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Note
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-----
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In the case when the binary labels are fractional
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(probabilistic), inverse_transform chooses the class with the
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greatest value. Typically, this allows to use the output of a
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linear model's decision_function method directly as the input
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of inverse_transform.
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|
"""
|
|
if self.multilabel:
|
|
Y = np.array(Y > 0, dtype=int)
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|
return [tuple(self.classes_[np.flatnonzero(Y[i])])
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|
for i in range(Y.shape[0])]
|
|
|
|
if len(Y.shape) == 1 or Y.shape[1] == 1:
|
|
y = np.array(Y.ravel() > 0, 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
|
|
scikits.learn.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 = K.sum() / (n_samples ** 2)
|
|
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
|