# Authors: Alexandre Gramfort # Vincent Michel # Gilles Louppe # # License: BSD Style. """Recursive feature elimination for feature ranking""" import numpy as np from ..utils import check_arrays, safe_sqr, safe_mask from ..base import BaseEstimator from ..base import MetaEstimatorMixin from ..base import clone from ..base import is_classifier from ..cross_validation import check_cv class RFE(BaseEstimator, MetaEstimatorMixin): """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. 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={}, 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_arrays(X, y, sparse_format="csr") # 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(self.step * n_features) else: step = int(self.step) if step <= 0: raise ValueError("Step must be >0") 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) 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) 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 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(X[:, safe_mask(X, self.support_)]) 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(X[:, safe_mask(X, self.support_)], y) def transform(self, X): """Reduce X to the selected features during the elimination. Parameters ---------- X : array of shape [n_samples, n_features] The input samples. Returns ------- X_r : array of shape [n_samples, n_selected_features] The input samples with only the features selected during the \ elimination. """ return X[:, safe_mask(X, self.support_)] def decision_function(self, X): return self.estimator_.decision_function(self.transform(X)) def predict_proba(self, X): return self.estimator_.predict_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. loss_function : function, optional (default=None) The loss function to minimize by cross-validation. If None, then the score function of the estimator is maximized. estimator_params : dict Parameters for the external estimator. Useful for doing grid searches. 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. `cv_scores_` : array of shape [n_subsets_of_features] The cross-validation scores such that `cv_scores_[i]` corresponds to the CV score of the i-th subset of features. `estimator_` : object The external estimator fit on the reduced dataset. 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, loss_func=None, estimator_params={}, verbose=0): self.estimator = estimator self.step = step self.cv = cv self.loss_func = loss_func 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_arrays(X, y, sparse_format="csr") # 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)) scores = np.zeros(X.shape[1]) # Cross-validation n = 0 for train, test in cv: # Compute a full ranking of the features ranking_ = rfe.fit(X[train], y[train]).ranking_ # Score each subset of features for k in xrange(0, max(ranking_)): mask = np.where(ranking_ <= k + 1)[0] estimator = clone(self.estimator) estimator.fit(X[train][:, mask], y[train]) if self.loss_func is None: loss_k = 1.0 - estimator.score(X[test][:, mask], y[test]) else: loss_k = self.loss_func( y[test], estimator.predict(X[test][:, mask])) if self.verbose > 0: print("Finished fold with %d / %d feature ranks, loss=%f" % (k, max(ranking_), loss_k)) scores[k] += loss_k n += 1 # Pick the best number of features on average best_score = np.inf best_k = None for k, score in enumerate(scores): if score < best_score: best_score = score best_k = k + 1 # Re-execute an elimination with best_k over the whole set rfe = RFE(estimator=self.estimator, n_features_to_select=best_k, step=self.step, estimator_params=self.estimator_params) rfe.fit(X, y) # Set final attributes self.estimator_ = clone(self.estimator) self.estimator_.set_params(**self.estimator_params) self.estimator_.fit(X[:, safe_mask(X, rfe.support_)], y) self.n_features_ = rfe.n_features_ self.support_ = rfe.support_ self.ranking_ = rfe.ranking_ self.cv_scores_ = scores / n return self