def _fit(self, X, t, clip_min_norm=1e-10):
self._check_input(X)
self._check_target(t)
self._check_binary(t)
X0 = X[t == 0]
X1 = X[t == 1]
m0 = np.mean(X0, axis=0)
m1 = np.mean(X1, axis=0)
#equation4.28 with-in class covriance
cov_inclass = (X0 - m0).T @ (X0 - m0) + (X1 - m1).T @ (X1 - m1)
#equation4.30
self.w = np.linalg.solve(cov_inclass, m1 - m0)
self.w /= np.linalg.norm(self.w).clip(min=clip_min_norm)
#estimate variance and mean of x0 and x1
g0 = Gaussian()
g0.fit((X0 @ self.w)[:, None])
g1 = Gaussian()
g1.fit((X1 @ self.w)[:, None])
#calculate threshold
a = g1.var - g0.var
b = g0.var * g1.mu - g1.var * g0.mu
c = (
g1.var * g0.mu ** 2 - g0.var * g1.mu ** 2
- g1.var * g0.var * np.log(g1.var / g0.var)
)
self.threshold = (np.sqrt(b ** 2 - a * c) - b) / a
def fit(self, X: np.ndarray, t: np.ndarray):
"""
estimate parameter given training dataset
Parameters
----------
X : (N, D) np.ndarray
training dataset independent variable
t : (N,) np.ndarray
training dataset dependent variable
binary 0 or 1
"""
X0 = X[t == 0]
X1 = X[t == 1]
m0 = np.mean(X0, axis=0)
m1 = np.mean(X1, axis=0)
cov_inclass = np.cov(X0, rowvar=False) + np.cov(X1, rowvar=False)
self.w = np.linalg.solve(cov_inclass, m1 - m0)
self.w /= np.linalg.norm(self.w).clip(min=1e-10)
g0 = Gaussian()
g0.fit((X0 @ self.w))
g1 = Gaussian()
g1.fit((X1 @ self.w))
root = np.roots([
g1.var - g0.var, 2 * (g0.var * g1.mu - g1.var * g0.mu),
g1.var * g0.mu**2 - g0.var * g1.mu**2 -
g1.var * g0.var * np.log(g1.var / g0.var)
])
if g0.mu < root[0] < g1.mu or g1.mu < root[0] < g0.mu:
self.threshold = root[0]
else:
self.threshold = root[1]
def _fit(self, X, t, clip_min_norm=1e-10):
self._check_input(X)
self._check_target(t)
self._check_binary(t)
X0 = X[t == 0]
X1 = X[t == 1]
# (4.21)
m0 = np.mean(X0, axis=0)
m1 = np.mean(X1, axis=0)
# (4.24) s_k^2 = \sum_{n \in C_k} (y_n - m_k)^2
cov_inclass = (X0 - m0).T @ (X0 - m0) + (X1 - m1).T @ (X1 - m1)
# (4.30) w \propto S_w^{-1} (m_2 - m_1)
self.w = np.linalg.solve(cov_inclass, m1 - m0)
self.w /= np.linalg.norm(self.w).clip(min=clip_min_norm)
g0 = Gaussian()
g0.fit((X0 @ self.w)[:, None])
g1 = Gaussian()
g1.fit((X1 @ self.w)[:, None])
a = g1.var - g0.var
b = g0.var * g1.mu - g1.var * g0.mu
c = (g1.var * g0.mu**2 - g0.var * g1.mu**2 -
g1.var * g0.var * np.log(g1.var / g0.var))
self.threshold = (np.sqrt(b**2 - a * c) - b) / a
def fit(self, x_train: np.ndarray, y_train: np.ndarray):
"""Estimate parameter given training dataset.
Parameters
----------
x_train : np.ndarray
training dataset independent variable (N, D)
y_train : np.ndarray
training dataset dependent variable (N,)
binary 0 or 1
"""
x0 = x_train[y_train == 0]
x1 = x_train[y_train == 1]
m0 = np.mean(x0, axis=0)
m1 = np.mean(x1, axis=0)
cov_inclass = np.cov(x0, rowvar=False) + np.cov(x1, rowvar=False)
self.w = np.linalg.solve(cov_inclass, m1 - m0)
self.w /= np.linalg.norm(self.w).clip(min=1e-10)
g0 = Gaussian()
g0.fit((x0 @ self.w))
g1 = Gaussian()
g1.fit((x1 @ self.w))
root = np.roots([
g1.var - g0.var,
2 * (g0.var * g1.mu - g1.var * g0.mu),
g1.var * g0.mu**2 - g0.var * g1.mu**2 -
g1.var * g0.var * np.log(g1.var / g0.var),
])
if g0.mu < root[0] < g1.mu or g1.mu < root[0] < g0.mu:
self.threshold = root[0]
else:
self.threshold = root[1]
def _fit(self, X, t, clip_min_norm=1e-10):
self._check_input(X)
self._check_target(t)
self._check_binary(t)
X0 = X[t == 0]
X1 = X[t == 1]
m0 = np.mean(X0, axis=0)
m1 = np.mean(X1, axis=0)
cov_inclass = (X0 - m0).T @ (X0 - m0) + (X1 - m1).T @ (X1 - m1)
self.w = np.linalg.solve(cov_inclass, m1 - m0)
self.w /= np.linalg.norm(self.w).clip(min=clip_min_norm)
g0 = Gaussian()
g0.fit((X0 @ self.w)[:, None])
g1 = Gaussian()
g1.fit((X1 @ self.w)[:, None])
a = g1.var - g0.var
b = g0.var * g1.mu - g1.var * g0.mu
c = (g1.var * g0.mu**2 - g0.var * g1.mu**2 -
g1.var * g0.var * np.log(g1.var / g0.var))
self.threshold = (np.sqrt(b**2 - a * c) - b) / a
def _fit(self, X, t, clip_min_norm = 1e-10): self._check_input(X) self._check_target(t) self._check_binary(t) X0 = X[t == 0] X1 = X[t == 1] m0 = np.mean(X0, axis = 0) m1 = np.mean(X1, axis = 0) cov_inclass = (X0 - m0).T @ (X0 - m0) + (X1 - m1).T @ (X1 - m1) # 类内散度矩阵 self.w = np.linalg.solve(cov_inclass, m1 - m0) # 找特征向量 #solve函数有两个参数a和b。a是一个N*N的二维数组，而b是一个长度为N的一维数组，solve函数找到一个长度为N的一维数组x，使得a和x的矩阵乘积正好等于b，数组x就是多元一次方程组的解。 self.w /= np.linalg.norm(self.w)clip(min = clip_min_norm) # 正则化 # 以上是参数拟合，也就是得到w， # 下面是得到输出X · w，变换后的变量Z ， 并对这个输出做高斯拟合 g0 = Gaussian() g0.fit((X0 @ self.w)[:, None]) g1 = Gaussian() g1.fit((X1 @ self.w)[:, None]) a = g1.var - g0.var b = g0.var * g1.mu - g1.var * g0.mu c = (g1.var * g0.mu**2 - g0.var * g1.mu**2 - g1.var * g0.var * np.log(g1.var / g0.var)) self.threshold = (np.sqrt(b**2 - a * c) - b) / a # 这个公式有点像求根公式， 以上几行都是求为了求threshold，这个方法，等以后问问作者吧，自己不研究了 """
def _fit(self, X, t, clip_min_norm=1e-10):
self._check_input(X)
self._check_target(t)
self._check_binary(t)
X0 = X[t == 0]
X1 = X[t == 1]
m0 = np.mean(X0, axis=0)
m1 = np.mean(X1, axis=0)
cov_inclass = (X0 - m0).T @ (X0 - m0) + (X1 - m1).T @ (X1 - m1)
self.w = np.linalg.solve(cov_inclass, m1 - m0)
self.w /= np.linalg.norm(self.w).clip(min=clip_min_norm)
g0 = Gaussian()
g0.fit((X0 @ self.w)[:, None])
g1 = Gaussian()
g1.fit((X1 @ self.w)[:, None])
a = g1.var - g0.var
b = g0.var * g1.mu - g1.var * g0.mu
c = (
g1.var * g0.mu ** 2 - g0.var * g1.mu ** 2
- g1.var * g0.var * np.log(g1.var / g0.var)
)
self.threshold = (np.sqrt(b ** 2 - a * c) - b) / a