def test_qda():
# QDA classification.
# This checks that QDA implements fit and predict and returns
# correct values for a simple toy dataset.
clf = QuadraticDiscriminantAnalysis()
y_pred = clf.fit(X6, y6).predict(X6)
assert_array_equal(y_pred, y6)
# Assure that it works with 1D data
y_pred1 = clf.fit(X7, y6).predict(X7)
assert_array_equal(y_pred1, y6)
# Test probas estimates
y_proba_pred1 = clf.predict_proba(X7)
assert_array_equal((y_proba_pred1[:, 1] > 0.5) + 1, y6)
y_log_proba_pred1 = clf.predict_log_proba(X7)
assert_array_almost_equal(np.exp(y_log_proba_pred1), y_proba_pred1, 8)
y_pred3 = clf.fit(X6, y7).predict(X6)
# QDA shouldn't be able to separate those
assert np.any(y_pred3 != y7)
# Classes should have at least 2 elements
with pytest.raises(ValueError):
clf.fit(X6, y4)
class QDA(object):
def __init__(self,
priors=None,
reg_param=0.,
store_covariance=False,
tol=1.0e-4):
"""
:param priors: 分来优先级， array, 可选项， shape=[n_classes]
:param reg_param: float, 可选项，将协方差估计正规化
:param store_covariance: boolean 如果为真，则计算并存储协方差矩阵到self.covariance_中
:param tol: 使用排序评估的阈值
"""
self.model = QuadraticDiscriminantAnalysis(
priors=priors,
reg_param=reg_param,
store_covariance=store_covariance,
tol=tol)
def fit(self, x, y):
self.model.fit(X=x, y=y)
def get_params(self, deep=True):
return self.model.get_params(deep=deep)
def predict(self, x):
return self.model.predict(X=x)
def predict_log_dict(self, x):
return self.model.predict_log_proba(X=x)
def predict_proba(self, x):
return self.model.predict_proba(X=x)
def score(self, x, y, sample_weight=None):
return self.model.score(X=x, y=y, sample_weight=sample_weight)
def set_params(self, **params):
self.model.set_params(**params)
def decision_function(self, x): # 将决策函数应用于样本数组。
return self.model.decision_function(X=x)
def get_attribute(self):
covariance = self.model.covariance_ # 每个种类的协方差矩阵， list of array-like of shape (n_features, n_features)
means = self.model.means # 种类均值， array-like of shape (n_classes, n_features)
priors = self.model.priors_ # 种类占比， 求和为1， array-like of shape (n_classes)
rotations = self.model.rotations_ # n_k = min(n_features, number of elements in class k) list_array,
# 高斯分布的旋转
scalings = self.model.scalings_ # list_array, 每个种类k，shape[n_k]的数组，包含高斯分布的缩放，
# 如，旋转坐标系中的方差
classes = self.model.classes_ # array-like, shape(n_classes,), 不同种类标签
return covariance, means, priors, rotations, scalings, classes
def test_qda():
# QDA classification.
# This checks that QDA implements fit and predict and returns
# correct values for a simple toy dataset.
clf = QuadraticDiscriminantAnalysis()
y_pred = clf.fit(X6, y6).predict(X6)
assert_array_equal(y_pred, y6)
# Assure that it works with 1D data
y_pred1 = clf.fit(X7, y6).predict(X7)
assert_array_equal(y_pred1, y6)
# Test probas estimates
y_proba_pred1 = clf.predict_proba(X7)
assert_array_equal((y_proba_pred1[:, 1] > 0.5) + 1, y6)
y_log_proba_pred1 = clf.predict_log_proba(X7)
assert_array_almost_equal(np.exp(y_log_proba_pred1), y_proba_pred1, 8)
y_pred3 = clf.fit(X6, y7).predict(X6)
# QDA shouldn't be able to separate those
assert np.any(y_pred3 != y7)
# Classes should have at least 2 elements
assert_raises(ValueError, clf.fit, X6, y4)
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.contour(xx, yy, Z, cmap=plt.cm.Blues)
plt.xlabel('$x_1$')
plt.ylabel('$x_2$')
plt.grid()
# In[51]:
x, y = np.random.multivariate_normal(Mean, Cov, N).T
x2, y2 = np.random.multivariate_normal(Mean2, Cov2, N).T
X = np.r_[np.c_[x, y], np.c_[x2, y2]]
Y = np.r_[np.ones((N, 1)), np.zeros((N, 1))]
Y = Y.flatten()
y_pred = clf.predict(X)
y_pred2 = clf.predict_log_proba(X)
score = y_pred2[:, 0] - y_pred2[:, 1]
#TruePositive
indi_TP = np.logical_and((y_pred == Y), (Y == 1))
#TrueNegative
indi_TN = np.logical_and((y_pred == Y), (Y == 0))
#FalsePositive
indi_FP = np.logical_and((y_pred != Y), (Y == 1))
#FalseNegative
indi_FN = np.logical_and((y_pred != Y), (Y == 0))
TP = score[indi_TP]
TN = score[indi_TN]
FP = score[indi_FP]
FN = score[indi_FN]
_ = plt.hist(TP, bins=30, rwidth=0.9, label='TP', alpha=0.5)
