765 lines
25 KiB
Python
765 lines
25 KiB
Python
# 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 .utils import warn_if_not_float
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from .base import BaseEstimator, TransformerMixin
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from .utils.sparsefuncs import inplace_csr_row_normalize_l1
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from .utils.sparsefuncs import inplace_csr_row_normalize_l2
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from .utils.sparsefuncs import inplace_csr_column_scale
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from .utils.sparsefuncs import mean_variance_axis0
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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 reset to 1.0 to avoid NaNs when scaling.
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"""
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X = np.asarray(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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"""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 or CSR matrix.
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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. If 0,
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independently standardize each feature, otherwise (if 1) standardize
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each sample.
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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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Notes
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-----
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This implementation will refuse to center scipy.sparse matrices
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since it would make them non-sparse and would potentially crash the
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program with memory exhaustion problems.
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Instead the caller is expected to either set explicitly
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`with_mean=False` (in that case, only variance scaling will be
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performed on the features of the CSR matrix) or to call `X.toarray()`
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if he/she expects the materialized dense array to fit in memory.
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To avoid memory copy the caller should pass a CSR matrix.
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See also
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--------
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:class:`sklearn.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:`sklearn.pipeline.Pipeline`)
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"""
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if sp.issparse(X):
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if with_mean:
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raise ValueError(
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"Cannot center sparse matrices: pass `with_mean=False` instead"
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" See docstring for motivation and alternatives.")
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if axis != 0:
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raise ValueError("Can only scale sparse matrix on axis=0, "
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" got axis=%d" % axis)
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warn_if_not_float(X, estimator='The scale function')
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if not sp.isspmatrix_csr(X):
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X = X.tocsr()
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copy = False
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if copy:
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X = X.copy()
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_, var = mean_variance_axis0(X)
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var[var == 0.0] = 1.0
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inplace_csr_column_scale(X, 1 / np.sqrt(var))
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else:
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X = np.asarray(X)
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warn_if_not_float(X, estimator='The scale function')
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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, TransformerMixin):
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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:`sklearn.preprocessing.scale` to perform centering and
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scaling without using the ``Transformer`` object oriented API
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:class:`sklearn.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 or CSR matrix 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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if self.with_mean:
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raise ValueError(
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"Cannot center sparse matrices: pass `with_mean=False` "
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"instead See docstring for motivation and alternatives.")
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warn_if_not_float(X, estimator=self)
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copy = self.copy
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if not sp.isspmatrix_csr(X):
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X = X.tocsr()
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copy = False
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if copy:
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X = X.copy()
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self.mean_ = None
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_, var = mean_variance_axis0(X)
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self.std_ = np.sqrt(var)
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self.std_[var == 0.0] = 1.0
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inplace_csr_column_scale(X, 1 / self.std_)
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return self
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else:
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X = np.asarray(X)
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warn_if_not_float(X, estimator=self)
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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=None):
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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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if self.with_mean:
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raise ValueError(
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"Cannot center sparse matrices: pass `with_mean=False` "
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"instead See docstring for motivation and alternatives.")
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warn_if_not_float(X, estimator=self)
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if not sp.isspmatrix_csr(X):
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X = X.tocsr()
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copy = False
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if copy:
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X = X.copy()
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inplace_csr_column_scale(X, 1 / self.std_)
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else:
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X = np.asarray(X)
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warn_if_not_float(X, estimator=self)
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if copy:
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X = X.copy()
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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 inverse_transform(self, X, copy=None):
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"""Scale back the data to the original representation
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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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if self.with_mean:
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raise ValueError(
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"Cannot uncenter sparse matrices: pass `with_mean=False` "
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"instead See docstring for motivation and alternatives.")
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if not sp.isspmatrix_csr(X):
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X = X.tocsr()
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copy = False
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if copy:
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X = X.copy()
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inplace_csr_column_scale(X, self.std_)
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else:
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X = np.asarray(X)
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if copy:
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X = X.copy()
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if self.with_std:
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X *= self.std_
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if self.with_mean:
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X += self.mean_
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return X
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def normalize(X, norm='l2', axis=1, copy=True):
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"""Normalize a dataset along any axis
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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, 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 (or each non-zero
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feature if axis is 0).
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axis : 0 or 1, optional (1 by default)
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axis used to normalize the data along. If 1, independently normalize
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each sample, otherwise (if 0) normalize each feature.
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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:`sklearn.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:`sklearn.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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warn_if_not_float(X, 'The normalize function')
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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, TransformerMixin):
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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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Notes
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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:`sklearn.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, axis=1, 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 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
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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:`sklearn.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:`sklearn.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, TransformerMixin):
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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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The 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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"""Binarize each element of X
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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_label_indicator_matrix(y):
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return hasattr(y, "shape") and len(y.shape) == 2
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def _is_multilabel(y):
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return isinstance(y[0], tuple) or \
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isinstance(y[0], list) or \
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_is_label_indicator_matrix(y)
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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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|
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Parameters
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----------
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|
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neg_label: int (default: 0)
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Value with which negative labels must be encoded.
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pos_label: int (default: 1)
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Value with which positive labels must be encoded.
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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 sklearn 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(neg_label=0, pos_label=1)
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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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|
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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 __init__(self, neg_label=0, pos_label=1):
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if neg_label >= pos_label:
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raise ValueError("neg_label must be strictly less than pos_label.")
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|
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self.neg_label = neg_label
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self.pos_label = pos_label
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def _check_fitted(self):
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if not hasattr(self, "classes_"):
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raise ValueError("LabelBinarizer was not fitted yet.")
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|
|
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def fit(self, y):
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"""Fit label binarizer
|
|
|
|
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
|
|
have variable lengths.
|
|
|
|
Returns
|
|
-------
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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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self.indicator_matrix_ = _is_label_indicator_matrix(y)
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|
if self.indicator_matrix_:
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self.classes_ = np.arange(y.shape[1])
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else:
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self.classes_ = np.array(sorted(set.union(*map(set, y))))
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else:
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self.classes_ = np.unique(y)
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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_)))
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|
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
|