SA_mRMR.py

# 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 numpy as np
from sklearn.feature_selection.base import SelectorMixin
from sklearn.feature_selection import mutual_info_
from sklearn.base import BaseEstimator
from sklearn.base import MetaEstimatorMixin
from sklearn.base import clone
from sklearn.base import is_classifier
from sklearn.externals.joblib import Parallel, delayed
from sklearn.model_selection import check_cv
from sklearn.model_selection._validation import _safe_split, _score
from sklearn.metrics.scorer import check_scoring
from sklearn.utils import check_X_y, safe_sqr
from sklearn.utils.metaestimators import if_delegate_has_method


def _rfe_single_fit(rfe, estimator, X, y, train, test, scorer):
    """
    Return the score for a fit across one fold.
    """
    X_train, y_train = _safe_split(estimator, X, y, train)
    X_test, y_test = _safe_split(estimator, X, y, test, train)
    return rfe._fit(
        X_train, y_train, lambda estimator, features:
        _score(estimator, X_test[:, features], y_test, scorer)).scores_


class SA_mRMR(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.

    Read more in the :ref:`User Guide <rfe>`.

    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.

    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,
                 verbose=0):
        self.estimator = estimator
        self.n_features_to_select = n_features_to_select
        self.step = step
        self.verbose = verbose

    @property
    def _estimator_type(self):
        return self.estimator._estimator_type

    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.
        """
        return self._fit(X, y)

    def _fit(self, X, y, step_score=None):
        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")

        support_ = np.ones(n_features, dtype=np.bool)
        ranking_ = np.ones(n_features, dtype=np.int)

        if step_score:
            self.scores_ = []

        # Elimination
        iter = 0
        while np.sum(support_) > n_features_to_select:
            iter += 1
            # Remaining features, features为剩余特征的索引列表
            features = np.arange(n_features)[support_]

            # Rank the remaining features
            # estimator = clone(self.estimator)
            if self.verbose > 0:
                print("Fitting estimator with %d features." % np.sum(support_))

            # estimator.fit(X[:, features], y)  # 每次循环都重新训练一次

            # Get coefs 此处得到就是SVM中的权重w
            # if hasattr(estimator, 'coef_'):
            #     coefs = estimator.coef_
            # else:
            #     coefs = getattr(estimator, 'feature_importances_', None)
            # if coefs is None:
            #     raise RuntimeError('The classifier does not expose '
            #                        '"coef_" or "feature_importances_" '
            #                        'attributes')

            # ----------------------代码修改处-----------------------
            # rfe_rank = safe_sqr(coefs).sum(axis=0)  # rfe算法得到的特征打分
            mrmr_rank = []  # mrmr算法得到的特征打分
            combine_rank = []  # 两种算法结合的特征打分
            beta = 0.5

            D = []
            R = []
            for fea in features:
                D.append(mutual_info_._compute_mi(X[:, fea], y, True, True))    # 后两个参数是不是传True????
            # D = D / len(features)

            for fea_i in features:
                R_sum = 0
                for fea_j in features:
                    if fea_j == fea_i:
                        continue
                    R_sum += mutual_info_._compute_mi(X[:, fea_i], X[:, fea_j], True, True)
                R.append(R_sum / len(features))

            for i in range(len(D)):
                mrmr_rank.append(D[i] / R[i])

            mrmr_rank = np.asarray(mrmr_rank)
            # combine_rank = 0.6 * rfe_rank + 0.4 * mrmr_rank

            combine_ranks = np.argsort(combine_rank)
            # rfe_ranks = np.argsort(rfe_rank)

            # Get ranks, 求权值平方w^2， -----ranks存储的元素的索引位置的排序
            # [[0.4, -0.3,...,0.4]]
            # if coefs.ndim > 1:
            ranks = np.argsort(mrmr_rank)
            # else:
            #     ranks = np.argsort(safe_sqr(coefs))

            # for sparse case ranks is matrix
            ranks = np.ravel(ranks)

            # Eliminate the worse features, ----得到要移除的特征个数
            step = 1 / (iter + 1) * np.sum(support_)  # 模拟退火的思想，每次去除1/(iter+1)个特征
            step = max(step, 1)  # 防止step小于1时，下面的式子中强转后为0
            threshold = int(min(step, np.sum(support_) - n_features_to_select))

            # Compute step score on the previous selection iteration
            # because 'estimator' must use features
            # that have not been eliminated yet
            # if step_score:
            #     self.scores_.append(step_score(estimator, features))
            support_[features[ranks][:threshold]] = False
            ranking_[np.logical_not(support_)] += 1  # False对应的特征加一

        # Set final attributes
        features = np.arange(n_features)[support_]
        # self.estimator_ = clone(self.estimator)
        # self.estimator_.fit(X[:, features], y)

        # Compute step score when only n_features_to_select features left
        if step_score:
            self.scores_.append(step_score(self.estimator_, features))
        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(SA_mRMR, MetaEstimatorMixin):
    """Feature ranking with recursive feature elimination and cross-validated
    selection of the best number of features.

    Read more in the :ref:`User Guide <rfe>`.

    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, cross-validation generator or an iterable, optional
        Determines the cross-validation splitting strategy.
        Possible inputs for cv are:

        - None, to use the default 3-fold cross-validation,
        - integer, to specify the number of folds.
        - An object to be used as a cross-validation generator.
        - An iterable yielding train/test splits.

        For integer/None inputs, if ``y`` is binary or multiclass,
        :class:`sklearn.model_selection.StratifiedKFold` is used. If the 
        estimator is a classifier or if ``y`` is neither binary nor multiclass, 
        :class:`sklearn.model_selection.KFold` is used.

        Refer :ref:`User Guide <cross_validation>` for the various
        cross-validation strategies that can be used here.

    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)``.

    verbose : int, default=0
        Controls verbosity of output.

    n_jobs : int, default 1
        Number of cores to run in parallel while fitting across folds.
        Defaults to 1 core. If `n_jobs=-1`, then number of jobs is set
        to number of cores.

    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 ceil((n_features - 1) / 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, verbose=0,
                 n_jobs=1):
        self.estimator = estimator
        self.step = step
        self.cv = cv
        self.scoring = scoring
        self.verbose = verbose
        self.n_jobs = n_jobs

    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")

        # Initialization
        cv = check_cv(self.cv, y, is_classifier(self.estimator))
        scorer = check_scoring(self.estimator, scoring=self.scoring)
        n_features = X.shape[1]
        n_features_to_select = 1

        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")

        rfe = SA_mRMR(estimator=self.estimator,
                      n_features_to_select=n_features_to_select,
                      step=self.step, verbose=self.verbose)

        # Determine the number of subsets of features by fitting across
        # the train folds and choosing the "features_to_select" parameter
        # that gives the least averaged error across all folds.

        # Note that joblib raises a non-picklable error for bound methods
        # even if n_jobs is set to 1 with the default multiprocessing
        # backend.
        # This branching is done so that to
        # make sure that user code that sets n_jobs to 1
        # and provides bound methods as scorers is not broken with the
        # addition of n_jobs parameter in version 0.18.

        if self.n_jobs == 1:
            parallel, func = list, _rfe_single_fit
        else:
            parallel, func, = Parallel(n_jobs=self.n_jobs), delayed(_rfe_single_fit)

        scores = parallel(
            func(rfe, self.estimator, X, y, train, test, scorer)
            for train, test in cv.split(X, y))

        scores = np.sum(scores, axis=0)
        n_features_to_select = max(
            n_features - (np.argmax(scores) * step),
            n_features_to_select)

        # Re-execute an elimination with best_k over the whole set
        rfe = SA_mRMR(estimator=self.estimator,
                      n_features_to_select=n_features_to_select, step=self.step)

        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)
        self.estimator_.fit(self.transform(X), y)

        # Fixing a normalization error, n is equal to get_n_splits(X, y) - 1
        # here, the scores are normalized by get_n_splits(X, y)
        self.grid_scores_ = scores[::-1] / cv.get_n_splits(X, y)
        return self