def su_measure(X, y):
entropy_y = entropy(y)
f_ratios = np.empty(X.shape[1])
for index in range(X.shape[1]):
entropy_x = entropy(X[:, index])
cond_entropy = conditional_entropy(X[:, index], y)
f_ratios[index] = 2 * (entropy_y - cond_entropy) / (entropy_x + entropy_y)
return f_ratios
def information_gain(X, y):
"""
Calculates mutual information for each feature by formula,
I(X,Y) = H(X) - H(X|Y)
Parameters
----------
X : numpy array, shape (n_samples, n_features)
The input samples.
y : numpy array, shape (n_samples, )
The classes for the samples.
Returns
-------
Score for each feature as a numpy array, shape (n_features, )
See Also
--------
Examples
--------
>>> import sklearn.datasets as datasets
>>> from ITMO_FS.filters.univariate import information_gain
>>> X = np.array([[1, 2, 3, 3, 1],[2, 2, 3, 3, 2], [1, 3, 3, 1, 3],[3, 1, 3, 1, 4],[4, 4, 3, 1, 5]], dtype = np.integer)
>>> y = np.array([1, 2, 3, 4, 5], dtype=np.integer)
>>> scores = information_gain(X, y)
>>> print(scores)
"""
entropy_x = entropy(y)
cond_entropy = np.apply_along_axis(conditional_entropy, 0, X, y)
return entropy_x - cond_entropy
def su_measure(X, y):
"""
SU is a correlation measure between the features and the class
calculated, via formula SU(X,Y) = 2 * I(X|Y) / (H(X) + H(Y))
Parameters
----------
X : numpy array, shape (n_samples, n_features)
The input samples.
y : numpy array, shape (n_samples, )
The classes for the samples.
Returns
-------
Score for each feature as a numpy array, shape (n_features, )
See Also
--------
https://www.matec-conferences.org/articles/matecconf/pdf/2016/05/matecconf_iccma2016_06002.pdf
Examples
--------
>>> import sklearn.datasets as datasets
>>> from ITMO_FS.filters.univariate import su_measure
>>> X = np.array([[3, 3, 3, 2, 2], [3, 3, 1, 2, 3], [1, 3, 5, 1, 1], [3, 1, 4, 3, 1], [3, 1, 2, 3, 1]])
>>> y = np.array([1, 3, 2, 1, 2])
>>> scores = su_measure(X, y)
>>> print(scores)
[0.82173546 0.67908587 0.79187567 0.73717549 0.86172942]
"""
entropy_y = entropy(y)
f_ratios = np.empty(X.shape[1])
for index in range(X.shape[1]):
entropy_x = entropy(X[:, index])
cond_entropy = conditional_entropy(y, X[:, index])
f_ratios[index] = (entropy_x + entropy_y - cond_entropy) / (entropy_x +
entropy_y)
return f_ratios
def _complementarity(x_i, x_j, y):
return entropy(x_i) + entropy(x_j) + entropy(y) - entropy(list(zip(x_i, x_j))) - \
entropy(list(zip(x_i, y))) - entropy(list(zip(x_j, y))) + entropy(list(zip(x_i, x_j, y)))
def run(self, X, y):
"""
Fits filter
Parameters
----------
X : numpy array, shape (n_samples, n_features)
y : numpy array, shape (n_samples, )
Returns
----------
selected_features : numpy array
selected pool of features
"""
self.n_features = X.shape[1]
if self.expected_size is None:
self.expected_size = self.n_features / 3
free_features = np.array([], dtype=np.integer)
self.selected_features = np.arange(self.n_features, dtype=np.integer)
self._vertices = np.ones(self.n_features)
self._edges = np.zeros((self.n_features, self.n_features))
for i in range(self.n_features):
for j in range(self.n_features):
entropy_pair = entropy(list(zip(X[:, i], X[:, j])))
if entropy_pair != 0.:
self._edges[i][j] = _chained_information(
X[:, i], X[:, j], y) / entropy_pair
while self.selected_features.size != self.expected_size:
min_index = np.argmin(
np.vectorize(lambda x: self.__count_weight(x))(np.arange(
self.n_features)))
self._vertices[min_index] = 0
free_features = np.append(free_features, min_index)
self.selected_features = np.delete(self.selected_features,
min_index)
change = True
while change:
change = False
swap_index = (-1, -1)
max_difference = 0
for i in range(len(free_features)):
for j in range(len(self.selected_features)):
temp_difference = self.__count_weight(
free_features[i]) - self.__count_weight(
self.selected_features[j])
if temp_difference > max_difference:
max_difference = temp_difference
swap_index = (i, j)
if max_difference > 0:
change = True
new_selected, new_free = swap_index
free_features = np.append(free_features, new_free)
free_features = np.delete(free_features, new_selected)
self.selected_features = np.append(self.selected_features,
new_selected)
self.selected_features = np.delete(self.selected_features,
new_free)
return self.selected_features
def fit(self, X, y, feature_names=None):
"""
Fits filter
Parameters
----------
X : array-like, shape (n_samples, n_features)
The training input samples.
y : array-like, shape (n_samples, )
The target values.
feature_names : list of strings, optional
In case you want to define feature names
Returns
-------
None
"""
features = generate_features(X)
X, y, feature_names = self._check_input(X, y, feature_names)
self.feature_names = dict(zip(features, feature_names))
self.n_features = X.shape[1]
if self.expected_size is None:
self.expected_size = self.n_features // 3
free_features = np.array([], dtype='object')
self.selected_features = generate_features(X)
self._vertices = np.ones(self.n_features)
self._edges = np.zeros((self.n_features, self.n_features))
for i in range(self.n_features):
for j in range(self.n_features):
entropy_pair = entropy(list(zip(X[:, i], X[:, j])))
if entropy_pair != 0.:
self._edges[i][j] = _chained_information(
X[:, i], X[:, j], y) / entropy_pair
# TODO apply vectorize to selected_features and not arange(n_features)?
while self.selected_features.size != self.expected_size:
min_index = np.argmin(
np.vectorize(lambda x: self.__count_weight(x))(
self.selected_features))
self._vertices[min_index] = 0
free_features = np.append(free_features, min_index)
self.selected_features = np.delete(self.selected_features,
min_index)
change = True
while change:
change = False
swap_index = (-1, -1)
max_difference = 0
for i in range(len(free_features)):
for j in range(len(self.selected_features)):
temp_difference = self.__count_weight(
free_features[i]) - self.__count_weight(
self.selected_features[j])
if temp_difference > max_difference:
max_difference = temp_difference
swap_index = (i, j)
if max_difference > 0:
change = True
new_selected, new_free = swap_index
free_features = np.append(free_features, new_free)
free_features = np.delete(free_features, new_selected)
self.selected_features = np.append(self.selected_features,
new_selected)
self.selected_features = np.delete(self.selected_features,
new_free)
self.selected_features = features[self.selected_features]
