"""Univariate features selection."""
# Authors: V. Michel, B. Thirion, G. Varoquaux, A. Gramfort, E. Duchesnay.
# L. Buitinck, A. Joly
# License: BSD 3 clause
import numpy as np
import warnings
from scipy import special, stats
from scipy.sparse import issparse
from ..base import BaseEstimator
from ..preprocessing import LabelBinarizer
from ..utils import (as_float_array, check_array, check_X_y, safe_sqr,
safe_mask)
from ..utils.extmath import safe_sparse_dot, row_norms
from ..utils.validation import check_is_fitted
from .base import SelectorMixin
def _clean_nans(scores):
"""
Fixes Issue #1240: NaNs can't be properly compared, so change them to the
smallest value of scores's dtype. -inf seems to be unreliable.
"""
# XXX where should this function be called? fit? scoring functions
# themselves?
scores = as_float_array(scores, copy=True)
scores[np.isnan(scores)] = np.finfo(scores.dtype).min
return scores
######################################################################
# Scoring functions
# The following function is a rewriting of scipy.stats.f_oneway
# Contrary to the scipy.stats.f_oneway implementation it does not
# copy the data while keeping the inputs unchanged.
def f_oneway(*args):
"""Performs a 1-way ANOVA.
The one-way ANOVA tests the null hypothesis that 2 or more groups have
the same population mean. The test is applied to samples from two or
more groups, possibly with differing sizes.
Read more in the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
sample1, sample2, ... : array_like, sparse matrices
The sample measurements should be given as arguments.
Returns
-------
F-value : float
The computed F-value of the test.
p-value : float
The associated p-value from the F-distribution.
Notes
-----
The ANOVA test has important assumptions that must be satisfied in order
for the associated p-value to be valid.
1. The samples are independent
2. Each sample is from a normally distributed population
3. The population standard deviations of the groups are all equal. This
property is known as homoscedasticity.
If these assumptions are not true for a given set of data, it may still be
possible to use the Kruskal-Wallis H-test (`scipy.stats.kruskal`_) although
with some loss of power.
The algorithm is from Heiman[2], pp.394-7.
See ``scipy.stats.f_oneway`` that should give the same results while
being less efficient.
References
----------
.. [1] Lowry, Richard. "Concepts and Applications of Inferential
Statistics". Chapter 14.
http://faculty.vassar.edu/lowry/ch14pt1.html
.. [2] Heiman, G.W. Research Methods in Statistics. 2002.
"""
n_classes = len(args)
args = [as_float_array(a) for a in args]
n_samples_per_class = np.array([a.shape[0] for a in args])
n_samples = np.sum(n_samples_per_class)
ss_alldata = sum(safe_sqr(a).sum(axis=0) for a in args)
sums_args = [np.asarray(a.sum(axis=0)) for a in args]
square_of_sums_alldata = sum(sums_args) ** 2
square_of_sums_args = [s ** 2 for s in sums_args]
sstot = ss_alldata - square_of_sums_alldata / float(n_samples)
ssbn = 0.
for k, _ in enumerate(args):
ssbn += square_of_sums_args[k] / n_samples_per_class[k]
ssbn -= square_of_sums_alldata / float(n_samples)
sswn = sstot - ssbn
dfbn = n_classes - 1
dfwn = n_samples - n_classes
msb = ssbn / float(dfbn)
msw = sswn / float(dfwn)
constant_features_idx = np.where(msw == 0.)[0]
if (np.nonzero(msb)[0].size != msb.size and constant_features_idx.size):
warnings.warn("Features %s are constant." % constant_features_idx,
UserWarning)
f = msb / msw
# flatten matrix to vector in sparse case
f = np.asarray(f).ravel()
prob = special.fdtrc(dfbn, dfwn, f)
return f, prob
def f_classif(X, y):
"""Compute the ANOVA F-value for the provided sample.
Read more in the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
X : {array-like, sparse matrix} shape = [n_samples, n_features]
The set of regressors that will be tested sequentially.
y : array of shape(n_samples)
The data matrix.
Returns
-------
F : array, shape = [n_features,]
The set of F values.
pval : array, shape = [n_features,]
The set of p-values.
See also
--------
chi2: Chi-squared stats of non-negative features for classification tasks.
f_regression: F-value between label/feature for regression tasks.
"""
X, y = check_X_y(X, y, ['csr', 'csc', 'coo'])
args = [X[safe_mask(X, y == k)] for k in np.unique(y)]
return f_oneway(*args)
def _chisquare(f_obs, f_exp):
"""Fast replacement for scipy.stats.chisquare.
Version from https://github.com/scipy/scipy/pull/2525 with additional
optimizations.
"""
f_obs = np.asarray(f_obs, dtype=np.float64)
k = len(f_obs)
# Reuse f_obs for chi-squared statistics
chisq = f_obs
chisq -= f_exp
chisq **= 2
with np.errstate(invalid="ignore"):
chisq /= f_exp
chisq = chisq.sum(axis=0)
return chisq, special.chdtrc(k - 1, chisq)
def chi2(X, y):
"""Compute chi-squared stats between each non-negative feature and class.
This score can be used to select the n_features features with the
highest values for the test chi-squared statistic from X, which must
contain only non-negative features such as booleans or frequencies
(e.g., term counts in document classification), relative to the classes.
Recall that the chi-square test measures dependence between stochastic
variables, so using this function "weeds out" the features that are the
most likely to be independent of class and therefore irrelevant for
classification.
Read more in the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
X : {array-like, sparse matrix}, shape = (n_samples, n_features_in)
Sample vectors.
y : array-like, shape = (n_samples,)
Target vector (class labels).
Returns
-------
chi2 : array, shape = (n_features,)
chi2 statistics of each feature.
pval : array, shape = (n_features,)
p-values of each feature.
Notes
-----
Complexity of this algorithm is O(n_classes * n_features).
See also
--------
f_classif: ANOVA F-value between label/feature for classification tasks.
f_regression: F-value between label/feature for regression tasks.
"""
# XXX: we might want to do some of the following in logspace instead for
# numerical stability.
X = check_array(X, accept_sparse='csr')
if np.any((X.data if issparse(X) else X) < 0):
raise ValueError("Input X must be non-negative.")
Y = LabelBinarizer().fit_transform(y)
if Y.shape[1] == 1:
Y = np.append(1 - Y, Y, axis=1)
observed = safe_sparse_dot(Y.T, X) # n_classes * n_features
feature_count = X.sum(axis=0).reshape(1, -1)
class_prob = Y.mean(axis=0).reshape(1, -1)
expected = np.dot(class_prob.T, feature_count)
return _chisquare(observed, expected)
def f_regression(X, y, center=True):
"""Univariate linear regression tests.
Linear model for testing the individual effect of each of many regressors.
This is a scoring function to be used in a feature seletion procedure, not
a free standing feature selection procedure.
This is done in 2 steps:
1. The correlation between each regressor and the target is computed,
that is, ((X[:, i] - mean(X[:, i])) * (y - mean_y)) / (std(X[:, i]) *
std(y)).
2. It is converted to an F score then to a p-value.
For more on usage see the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
X : {array-like, sparse matrix} shape = (n_samples, n_features)
The set of regressors that will be tested sequentially.
y : array of shape(n_samples).
The data matrix
center : True, bool,
If true, X and y will be centered.
Returns
-------
F : array, shape=(n_features,)
F values of features.
pval : array, shape=(n_features,)
p-values of F-scores.
See also
--------
mutual_info_regression: Mutual information for a continuous target.
f_classif: ANOVA F-value between label/feature for classification tasks.
chi2: Chi-squared stats of non-negative features for classification tasks.
SelectKBest: Select features based on the k highest scores.
SelectFpr: Select features based on a false positive rate test.
SelectFdr: Select features based on an estimated false discovery rate.
SelectFwe: Select features based on family-wise error rate.
SelectPercentile: Select features based on percentile of the highest
scores.
"""
X, y = check_X_y(X, y, ['csr', 'csc', 'coo'], dtype=np.float64)
n_samples = X.shape[0]
# compute centered values
# note that E[(x - mean(x))*(y - mean(y))] = E[x*(y - mean(y))], so we
# need not center X
if center:
y = y - np.mean(y)
if issparse(X):
X_means = X.mean(axis=0).getA1()
else:
X_means = X.mean(axis=0)
# compute the scaled standard deviations via moments
X_norms = np.sqrt(row_norms(X.T, squared=True) -
n_samples * X_means ** 2)
else:
X_norms = row_norms(X.T)
# compute the correlation
corr = safe_sparse_dot(y, X)
corr /= X_norms
corr /= np.linalg.norm(y)
# convert to p-value
degrees_of_freedom = y.size - (2 if center else 1)
F = corr ** 2 / (1 - corr ** 2) * degrees_of_freedom
pv = stats.f.sf(F, 1, degrees_of_freedom)
return F, pv
######################################################################
# Base classes
class _BaseFilter(BaseEstimator, SelectorMixin):
"""Initialize the univariate feature selection.
Parameters
----------
score_func : callable
Function taking two arrays X and y, and returning a pair of arrays
(scores, pvalues) or a single array with scores.
"""
def __init__(self, score_func):
self.score_func = score_func
def fit(self, X, y):
"""Run score function on (X, y) and get the appropriate features.
Parameters
----------
X : array-like, shape = [n_samples, n_features]
The training input samples.
y : array-like, shape = [n_samples]
The target values (class labels in classification, real numbers in
regression).
Returns
-------
self : object
Returns self.
"""
X, y = check_X_y(X, y, ['csr', 'csc'], multi_output=True)
if not callable(self.score_func):
raise TypeError("The score function should be a callable, %s (%s) "
"was passed."
% (self.score_func, type(self.score_func)))
self._check_params(X, y)
score_func_ret = self.score_func(X, y)
if isinstance(score_func_ret, (list, tuple)):
self.scores_, self.pvalues_ = score_func_ret
self.pvalues_ = np.asarray(self.pvalues_)
else:
self.scores_ = score_func_ret
self.pvalues_ = None
self.scores_ = np.asarray(self.scores_)
return self
def _check_params(self, X, y):
pass
######################################################################
# Specific filters
######################################################################
class SelectPercentile(_BaseFilter):
"""Select features according to a percentile of the highest scores.
Read more in the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
score_func : callable
Function taking two arrays X and y, and returning a pair of arrays
(scores, pvalues) or a single array with scores.
Default is f_classif (see below "See also"). The default function only
works with classification tasks.
percentile : int, optional, default=10
Percent of features to keep.
Attributes
----------
scores_ : array-like, shape=(n_features,)
Scores of features.
pvalues_ : array-like, shape=(n_features,)
p-values of feature scores, None if `score_func` returned only scores.
Notes
-----
Ties between features with equal scores will be broken in an unspecified
way.
See also
--------
f_classif: ANOVA F-value between label/feature for classification tasks.
mutual_info_classif: Mutual information for a discrete target.
chi2: Chi-squared stats of non-negative features for classification tasks.
f_regression: F-value between label/feature for regression tasks.
mutual_info_regression: Mutual information for a continuous target.
SelectKBest: Select features based on the k highest scores.
SelectFpr: Select features based on a false positive rate test.
SelectFdr: Select features based on an estimated false discovery rate.
SelectFwe: Select features based on family-wise error rate.
GenericUnivariateSelect: Univariate feature selector with configurable mode.
"""
def __init__(self, score_func=f_classif, percentile=10):
super(SelectPercentile, self).__init__(score_func)
self.percentile = percentile
def _check_params(self, X, y):
if not 0 <= self.percentile <= 100:
raise ValueError("percentile should be >=0, <=100; got %r"
% self.percentile)
def _get_support_mask(self):
check_is_fitted(self, 'scores_')
# Cater for NaNs
if self.percentile == 100:
return np.ones(len(self.scores_), dtype=np.bool)
elif self.percentile == 0:
return np.zeros(len(self.scores_), dtype=np.bool)
scores = _clean_nans(self.scores_)
treshold = stats.scoreatpercentile(scores,
100 - self.percentile)
mask = scores > treshold
ties = np.where(scores == treshold)[0]
if len(ties):
max_feats = int(len(scores) * self.percentile / 100)
kept_ties = ties[:max_feats - mask.sum()]
mask[kept_ties] = True
return mask
class SelectKBest(_BaseFilter):
"""Select features according to the k highest scores.
Read more in the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
score_func : callable
Function taking two arrays X and y, and returning a pair of arrays
(scores, pvalues) or a single array with scores.
Default is f_classif (see below "See also"). The default function only
works with classification tasks.
k : int or "all", optional, default=10
Number of top features to select.
The "all" option bypasses selection, for use in a parameter search.
Attributes
----------
scores_ : array-like, shape=(n_features,)
Scores of features.
pvalues_ : array-like, shape=(n_features,)
p-values of feature scores, None if `score_func` returned only scores.
Notes
-----
Ties between features with equal scores will be broken in an unspecified
way.
See also
--------
f_classif: ANOVA F-value between label/feature for classification tasks.
mutual_info_classif: Mutual information for a discrete target.
chi2: Chi-squared stats of non-negative features for classification tasks.
f_regression: F-value between label/feature for regression tasks.
mutual_info_regression: Mutual information for a continuous target.
SelectPercentile: Select features based on percentile of the highest scores.
SelectFpr: Select features based on a false positive rate test.
SelectFdr: Select features based on an estimated false discovery rate.
SelectFwe: Select features based on family-wise error rate.
GenericUnivariateSelect: Univariate feature selector with configurable mode.
"""
def __init__(self, score_func=f_classif, k=10):
super(SelectKBest, self).__init__(score_func)
self.k = k
def _check_params(self, X, y):
if not (self.k == "all" or 0 <= self.k <= X.shape[1]):
raise ValueError("k should be >=0, <= n_features; got %r."
"Use k='all' to return all features."
% self.k)
def _get_support_mask(self):
check_is_fitted(self, 'scores_')
if self.k == 'all':
return np.ones(self.scores_.shape, dtype=bool)
elif self.k == 0:
return np.zeros(self.scores_.shape, dtype=bool)
else:
scores = _clean_nans(self.scores_)
mask = np.zeros(scores.shape, dtype=bool)
# Request a stable sort. Mergesort takes more memory (~40MB per
# megafeature on x86-64).
mask[np.argsort(scores, kind="mergesort")[-self.k:]] = 1
return mask
class SelectFpr(_BaseFilter):
"""Filter: Select the pvalues below alpha based on a FPR test.
FPR test stands for False Positive Rate test. It controls the total
amount of false detections.
Read more in the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
score_func : callable
Function taking two arrays X and y, and returning a pair of arrays
(scores, pvalues).
Default is f_classif (see below "See also"). The default function only
works with classification tasks.
alpha : float, optional
The highest p-value for features to be kept.
Attributes
----------
scores_ : array-like, shape=(n_features,)
Scores of features.
pvalues_ : array-like, shape=(n_features,)
p-values of feature scores.
See also
--------
f_classif: ANOVA F-value between label/feature for classification tasks.
chi2: Chi-squared stats of non-negative features for classification tasks.
mutual_info_classif:
f_regression: F-value between label/feature for regression tasks.
mutual_info_regression: Mutual information between features and the target.
SelectPercentile: Select features based on percentile of the highest scores.
SelectKBest: Select features based on the k highest scores.
SelectFdr: Select features based on an estimated false discovery rate.
SelectFwe: Select features based on family-wise error rate.
GenericUnivariateSelect: Univariate feature selector with configurable mode.
"""
def __init__(self, score_func=f_classif, alpha=5e-2):
super(SelectFpr, self).__init__(score_func)
self.alpha = alpha
def _get_support_mask(self):
check_is_fitted(self, 'scores_')
return self.pvalues_ < self.alpha
class SelectFdr(_BaseFilter):
"""Filter: Select the p-values for an estimated false discovery rate
This uses the Benjamini-Hochberg procedure. ``alpha`` is an upper bound
on the expected false discovery rate.
Read more in the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
score_func : callable
Function taking two arrays X and y, and returning a pair of arrays
(scores, pvalues).
Default is f_classif (see below "See also"). The default function only
works with classification tasks.
alpha : float, optional
The highest uncorrected p-value for features to keep.
Attributes
----------
scores_ : array-like, shape=(n_features,)
Scores of features.
pvalues_ : array-like, shape=(n_features,)
p-values of feature scores.
References
----------
https://en.wikipedia.org/wiki/False_discovery_rate
See also
--------
f_classif: ANOVA F-value between label/feature for classification tasks.
mutual_info_classif: Mutual information for a discrete target.
chi2: Chi-squared stats of non-negative features for classification tasks.
f_regression: F-value between label/feature for regression tasks.
mutual_info_regression: Mutual information for a contnuous target.
SelectPercentile: Select features based on percentile of the highest scores.
SelectKBest: Select features based on the k highest scores.
SelectFpr: Select features based on a false positive rate test.
SelectFwe: Select features based on family-wise error rate.
GenericUnivariateSelect: Univariate feature selector with configurable mode.
"""
def __init__(self, score_func=f_classif, alpha=5e-2):
super(SelectFdr, self).__init__(score_func)
self.alpha = alpha
def _get_support_mask(self):
check_is_fitted(self, 'scores_')
n_features = len(self.pvalues_)
sv = np.sort(self.pvalues_)
selected = sv[sv <= float(self.alpha) / n_features *
np.arange(1, n_features + 1)]
if selected.size == 0:
return np.zeros_like(self.pvalues_, dtype=bool)
return self.pvalues_ <= selected.max()
class SelectFwe(_BaseFilter):
"""Filter: Select the p-values corresponding to Family-wise error rate
Read more in the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
score_func : callable
Function taking two arrays X and y, and returning a pair of arrays
(scores, pvalues).
Default is f_classif (see below "See also"). The default function only
works with classification tasks.
alpha : float, optional
The highest uncorrected p-value for features to keep.
Attributes
----------
scores_ : array-like, shape=(n_features,)
Scores of features.
pvalues_ : array-like, shape=(n_features,)
p-values of feature scores.
See also
--------
f_classif: ANOVA F-value between label/feature for classification tasks.
chi2: Chi-squared stats of non-negative features for classification tasks.
f_regression: F-value between label/feature for regression tasks.
SelectPercentile: Select features based on percentile of the highest scores.
SelectKBest: Select features based on the k highest scores.
SelectFpr: Select features based on a false positive rate test.
SelectFdr: Select features based on an estimated false discovery rate.
GenericUnivariateSelect: Univariate feature selector with configurable mode.
"""
def __init__(self, score_func=f_classif, alpha=5e-2):
super(SelectFwe, self).__init__(score_func)
self.alpha = alpha
def _get_support_mask(self):
check_is_fitted(self, 'scores_')
return (self.pvalues_ < self.alpha / len(self.pvalues_))
######################################################################
# Generic filter
######################################################################
# TODO this class should fit on either p-values or scores,
# depending on the mode.
class GenericUnivariateSelect(_BaseFilter):
"""Univariate feature selector with configurable strategy.
Read more in the :ref:`User Guide <univariate_feature_selection>`.
Parameters
----------
score_func : callable
Function taking two arrays X and y, and returning a pair of arrays
(scores, pvalues). For modes 'percentile' or 'kbest' it can return
a single array scores.
mode : {'percentile', 'k_best', 'fpr', 'fdr', 'fwe'}
Feature selection mode.
param : float or int depending on the feature selection mode
Parameter of the corresponding mode.
Attributes
----------
scores_ : array-like, shape=(n_features,)
Scores of features.
pvalues_ : array-like, shape=(n_features,)
p-values of feature scores, None if `score_func` returned scores only.
See also
--------
f_classif: ANOVA F-value between label/feature for classification tasks.
mutual_info_classif: Mutual information for a discrete target.
chi2: Chi-squared stats of non-negative features for classification tasks.
f_regression: F-value between label/feature for regression tasks.
mutual_info_regression: Mutual information for a continuous target.
SelectPercentile: Select features based on percentile of the highest scores.
SelectKBest: Select features based on the k highest scores.
SelectFpr: Select features based on a false positive rate test.
SelectFdr: Select features based on an estimated false discovery rate.
SelectFwe: Select features based on family-wise error rate.
"""
_selection_modes = {'percentile': SelectPercentile,
'k_best': SelectKBest,
'fpr': SelectFpr,
'fdr': SelectFdr,
'fwe': SelectFwe}
def __init__(self, score_func=f_classif, mode='percentile', param=1e-5):
super(GenericUnivariateSelect, self).__init__(score_func)
self.mode = mode
self.param = param
def _make_selector(self):
selector = self._selection_modes[self.mode](score_func=self.score_func)
# Now perform some acrobatics to set the right named parameter in
# the selector
possible_params = selector._get_param_names()
possible_params.remove('score_func')
selector.set_params(**{possible_params[0]: self.param})
return selector
def _check_params(self, X, y):
if self.mode not in self._selection_modes:
raise ValueError("The mode passed should be one of %s, %r,"
" (type %s) was passed."
% (self._selection_modes.keys(), self.mode,
type(self.mode)))
self._make_selector()._check_params(X, y)
def _get_support_mask(self):
check_is_fitted(self, 'scores_')
selector = self._make_selector()
selector.pvalues_ = self.pvalues_
selector.scores_ = self.scores_
return selector._get_support_mask()
