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rfe.py
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# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Vincent Michel <vincent.michel@inria.fr>
# Gilles Louppe <g.louppe@gmail.com>
#
# License: BSD 3 clause
"""Recursive feature elimination for feature ranking"""
import warnings
import numpy as np
from ..utils import check_X_y, safe_sqr
from ..utils.metaestimators import if_delegate_has_method
from ..base import BaseEstimator
from ..base import MetaEstimatorMixin
from ..base import clone
from ..base import is_classifier
from ..cross_validation import _check_cv as check_cv
from ..cross_validation import _safe_split, _score
from ..metrics.scorer import check_scoring
from .base import SelectorMixin
class RFE(BaseEstimator, MetaEstimatorMixin, SelectorMixin):
"""Feature ranking with recursive feature elimination.
Given an external estimator that assigns weights to features (e.g., the
coefficients of a linear model), the goal of recursive feature elimination
(RFE) is to select features by recursively considering smaller and smaller
sets of features. First, the estimator is trained on the initial set of
features and weights are assigned to each one of them. Then, features whose
absolute weights are the smallest are pruned from the current set features.
That procedure is recursively repeated on the pruned set until the desired
number of features to select is eventually reached.
Parameters
----------
estimator : object
A supervised learning estimator with a `fit` method that updates a
`coef_` attribute that holds the fitted parameters. Important features
must correspond to high absolute values in the `coef_` array.
For instance, this is the case for most supervised learning
algorithms such as Support Vector Classifiers and Generalized
Linear Models from the `svm` and `linear_model` modules.
n_features_to_select : int or None (default=None)
The number of features to select. If `None`, half of the features
are selected.
step : int or float, optional (default=1)
If greater than or equal to 1, then `step` corresponds to the (integer)
number of features to remove at each iteration.
If within (0.0, 1.0), then `step` corresponds to the percentage
(rounded down) of features to remove at each iteration.
estimator_params : dict
Parameters for the external estimator.
Useful for doing grid searches when an `RFE` object is passed as an
argument to, e.g., a `sklearn.grid_search.GridSearchCV` object.
verbose : int, default=0
Controls verbosity of output.
Attributes
----------
n_features_ : int
The number of selected features.
support_ : array of shape [n_features]
The mask of selected features.
ranking_ : array of shape [n_features]
The feature ranking, such that ``ranking_[i]`` corresponds to the
ranking position of the i-th feature. Selected (i.e., estimated
best) features are assigned rank 1.
estimator_ : object
The external estimator fit on the reduced dataset.
Examples
--------
The following example shows how to retrieve the 5 right informative
features in the Friedman #1 dataset.
>>> from sklearn.datasets import make_friedman1
>>> from sklearn.feature_selection import RFE
>>> from sklearn.svm import SVR
>>> X, y = make_friedman1(n_samples=50, n_features=10, random_state=0)
>>> estimator = SVR(kernel="linear")
>>> selector = RFE(estimator, 5, step=1)
>>> selector = selector.fit(X, y)
>>> selector.support_ # doctest: +NORMALIZE_WHITESPACE
array([ True, True, True, True, True,
False, False, False, False, False], dtype=bool)
>>> selector.ranking_
array([1, 1, 1, 1, 1, 6, 4, 3, 2, 5])
References
----------
.. [1] Guyon, I., Weston, J., Barnhill, S., & Vapnik, V., "Gene selection
for cancer classification using support vector machines",
Mach. Learn., 46(1-3), 389--422, 2002.
"""
def __init__(self, estimator, n_features_to_select=None, step=1,
estimator_params=None, verbose=0):
self.estimator = estimator
self.n_features_to_select = n_features_to_select
self.step = step
self.estimator_params = estimator_params
self.verbose = verbose
def fit(self, X, y):
"""Fit the RFE model and then the underlying estimator on the selected
features.
Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
The training input samples.
y : array-like, shape = [n_samples]
The target values.
"""
X, y = check_X_y(X, y, "csc")
# Initialization
n_features = X.shape[1]
if self.n_features_to_select is None:
n_features_to_select = n_features / 2
else:
n_features_to_select = self.n_features_to_select
if 0.0 < self.step < 1.0:
step = int(max(1, self.step * n_features))
else:
step = int(self.step)
if step <= 0:
raise ValueError("Step must be >0")
if self.estimator_params is not None:
warnings.warn("The parameter 'estimator_params' is deprecated as of version 0.16 "
"and will be removed in 0.18. The parameter is no longer "
"necessary because the value is set via the estimator initialisation "
"or set_params function."
, DeprecationWarning)
support_ = np.ones(n_features, dtype=np.bool)
ranking_ = np.ones(n_features, dtype=np.int)
# Elimination
while np.sum(support_) > n_features_to_select:
# Remaining features
features = np.arange(n_features)[support_]
# Rank the remaining features
estimator = clone(self.estimator)
if self.estimator_params:
estimator.set_params(**self.estimator_params)
if self.verbose > 0:
print("Fitting estimator with %d features." % np.sum(support_))
estimator.fit(X[:, features], y)
if estimator.coef_.ndim > 1:
ranks = np.argsort(safe_sqr(estimator.coef_).sum(axis=0))
else:
ranks = np.argsort(safe_sqr(estimator.coef_))
# for sparse case ranks is matrix
ranks = np.ravel(ranks)
# Eliminate the worse features
threshold = min(step, np.sum(support_) - n_features_to_select)
support_[features[ranks][:threshold]] = False
ranking_[np.logical_not(support_)] += 1
# Set final attributes
self.estimator_ = clone(self.estimator)
if self.estimator_params:
self.estimator_.set_params(**self.estimator_params)
self.estimator_.fit(X[:, support_], y)
self.n_features_ = support_.sum()
self.support_ = support_
self.ranking_ = ranking_
return self
@if_delegate_has_method(delegate='estimator')
def predict(self, X):
"""Reduce X to the selected features and then predict using the
underlying estimator.
Parameters
----------
X : array of shape [n_samples, n_features]
The input samples.
Returns
-------
y : array of shape [n_samples]
The predicted target values.
"""
return self.estimator_.predict(self.transform(X))
@if_delegate_has_method(delegate='estimator')
def score(self, X, y):
"""Reduce X to the selected features and then return the score of the
underlying estimator.
Parameters
----------
X : array of shape [n_samples, n_features]
The input samples.
y : array of shape [n_samples]
The target values.
"""
return self.estimator_.score(self.transform(X), y)
def _get_support_mask(self):
return self.support_
@if_delegate_has_method(delegate='estimator')
def decision_function(self, X):
return self.estimator_.decision_function(self.transform(X))
@if_delegate_has_method(delegate='estimator')
def predict_proba(self, X):
return self.estimator_.predict_proba(self.transform(X))
@if_delegate_has_method(delegate='estimator')
def predict_log_proba(self, X):
return self.estimator_.predict_log_proba(self.transform(X))
class RFECV(RFE, MetaEstimatorMixin):
"""Feature ranking with recursive feature elimination and cross-validated
selection of the best number of features.
Parameters
----------
estimator : object
A supervised learning estimator with a `fit` method that updates a
`coef_` attribute that holds the fitted parameters. Important features
must correspond to high absolute values in the `coef_` array.
For instance, this is the case for most supervised learning
algorithms such as Support Vector Classifiers and Generalized
Linear Models from the `svm` and `linear_model` modules.
step : int or float, optional (default=1)
If greater than or equal to 1, then `step` corresponds to the (integer)
number of features to remove at each iteration.
If within (0.0, 1.0), then `step` corresponds to the percentage
(rounded down) of features to remove at each iteration.
cv : int or cross-validation generator, optional (default=None)
If int, it is the number of folds.
If None, 3-fold cross-validation is performed by default.
Specific cross-validation objects can also be passed, see
`sklearn.cross_validation module` for details.
scoring : string, callable or None, optional, default: None
A string (see model evaluation documentation) or
a scorer callable object / function with signature
``scorer(estimator, X, y)``.
estimator_params : dict
Parameters for the external estimator.
Useful for doing grid searches when an `RFE` object is passed as an
argument to, e.g., a `sklearn.grid_search.GridSearchCV` object.
verbose : int, default=0
Controls verbosity of output.
Attributes
----------
n_features_ : int
The number of selected features with cross-validation.
support_ : array of shape [n_features]
The mask of selected features.
ranking_ : array of shape [n_features]
The feature ranking, such that `ranking_[i]`
corresponds to the ranking
position of the i-th feature.
Selected (i.e., estimated best)
features are assigned rank 1.
grid_scores_ : array of shape [n_subsets_of_features]
The cross-validation scores such that
``grid_scores_[i]`` corresponds to
the CV score of the i-th subset of features.
estimator_ : object
The external estimator fit on the reduced dataset.
Notes
-----
The size of ``grid_scores_`` is equal to (n_features + step - 2) // step + 1,
where step is the number of features removed at each iteration.
Examples
--------
The following example shows how to retrieve the a-priori not known 5
informative features in the Friedman #1 dataset.
>>> from sklearn.datasets import make_friedman1
>>> from sklearn.feature_selection import RFECV
>>> from sklearn.svm import SVR
>>> X, y = make_friedman1(n_samples=50, n_features=10, random_state=0)
>>> estimator = SVR(kernel="linear")
>>> selector = RFECV(estimator, step=1, cv=5)
>>> selector = selector.fit(X, y)
>>> selector.support_ # doctest: +NORMALIZE_WHITESPACE
array([ True, True, True, True, True,
False, False, False, False, False], dtype=bool)
>>> selector.ranking_
array([1, 1, 1, 1, 1, 6, 4, 3, 2, 5])
References
----------
.. [1] Guyon, I., Weston, J., Barnhill, S., & Vapnik, V., "Gene selection
for cancer classification using support vector machines",
Mach. Learn., 46(1-3), 389--422, 2002.
"""
def __init__(self, estimator, step=1, cv=None, scoring=None,
estimator_params=None, verbose=0):
self.estimator = estimator
self.step = step
self.cv = cv
self.scoring = scoring
self.estimator_params = estimator_params
self.verbose = verbose
def fit(self, X, y):
"""Fit the RFE model and automatically tune the number of selected
features.
Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples, n_features]
Training vector, where `n_samples` is the number of samples and
`n_features` is the total number of features.
y : array-like, shape = [n_samples]
Target values (integers for classification, real numbers for
regression).
"""
X, y = check_X_y(X, y, "csr")
if self.estimator_params is not None:
warnings.warn("The parameter 'estimator_params' is deprecated as of version 0.16 "
"and will be removed in 0.18. The parameter is no longer "
"necessary because the value is set via the estimator initialisation "
"or set_params function."
, DeprecationWarning)
# Initialization
rfe = RFE(estimator=self.estimator, n_features_to_select=1,
step=self.step, estimator_params=self.estimator_params,
verbose=self.verbose - 1)
cv = check_cv(self.cv, X, y, is_classifier(self.estimator))
scorer = check_scoring(self.estimator, scoring=self.scoring)
scores = np.zeros(X.shape[1])
n_features_to_select_by_rank = np.zeros(X.shape[1])
# Cross-validation
for n, (train, test) in enumerate(cv):
X_train, y_train = _safe_split(self.estimator, X, y, train)
X_test, y_test = _safe_split(self.estimator, X, y, test, train)
# Compute a full ranking of the features
# ranking_ contains the same set of values for all CV folds,
# but perhaps reordered
ranking_ = rfe.fit(X_train, y_train).ranking_
# Score each subset of features
for k in range(0, np.max(ranking_)):
indices = np.where(ranking_ <= k + 1)[0]
estimator = clone(self.estimator)
estimator.fit(X_train[:, indices], y_train)
score = _score(estimator, X_test[:, indices], y_test, scorer)
if self.verbose > 0:
print("Finished fold with %d / %d feature ranks, score=%f"
% (k + 1, np.max(ranking_), score))
scores[k] += score
# n_features_to_select_by_rank[k] is being overwritten
# multiple times, but by the same value
n_features_to_select_by_rank[k] = indices.size
# Select the best upper bound for feature rank. It's OK to use the
# last ranking_, as np.max(ranking_) is the same over all CV folds.
scores = scores[:np.max(ranking_)]
k = np.argmax(scores)
# Re-execute an elimination with best_k over the whole set
rfe = RFE(estimator=self.estimator,
n_features_to_select=n_features_to_select_by_rank[k],
step=self.step, estimator_params=self.estimator_params)
rfe.fit(X, y)
# Set final attributes
self.support_ = rfe.support_
self.n_features_ = rfe.n_features_
self.ranking_ = rfe.ranking_
self.estimator_ = clone(self.estimator)
if self.estimator_params:
self.estimator_.set_params(**self.estimator_params)
self.estimator_.fit(self.transform(X), y)
# Fixing a normalization error, n is equal to len(cv) - 1
# here, the scores are normalized by len(cv)
self.grid_scores_ = scores / len(cv)
return self