def predict_sample_generate_proba(self, X):
# 返回样本的生成概率
W = np.asarray([
utils.gaussian_nd(X, u, sigma) * alpha
for alpha, u, sigma in self.params
]).T
return np.sum(W, axis=1)
def predict_proba(self, X):
# 预测样本在几个高斯模型上的概率分布
W = np.asarray([
utils.gaussian_nd(X, u, sigma) * alpha
for alpha, u, sigma in self.params
]).T
W = W / np.sum(W, axis=1, keepdims=True)
return W
def fit(self, X):
n_sample, _ = X.shape
# 初始化参数
u = np.mean(X, axis=0)
sigma = np.cov(X.T)
alpha = 1.0 / self.n_components
max_value = X.max()
min_value = X.min()
for _ in range(0, self.n_components):
# 每个高斯模型的权重初始化一样
# 每个高斯模型的均值在整体均值的基础上添加一个随机的bias
# 方差初始化一样，使用整体的方差
self.params.append([alpha, u + np.random.random() * (max_value + min_value) / 2, sigma])
# 计算当前的隐变量
W = np.asarray([utils.gaussian_nd(X, u, sigma) * alpha for alpha, u, sigma in self.params]).T
# 记录当前的log like hold
current_log_loss = np.log(W.sum(axis=1)).sum() / n_sample
W = W / np.sum(W, axis=1, keepdims=True)
# 迭代训练
for _ in range(0, self.n_iter):
if self.verbose is True:
utils.plot_contourf(X, lambda x: self.predict_sample_generate_proba(x), lines=5)
utils.plt.pause(0.1)
utils.plt.clf()
# 更新高斯模型参数
for k in range(0, self.n_components):
self.params[k][0] = W[:, k].sum() / n_sample # 更新alpha
self.params[k][1] = np.sum(W[:, [k]] * X, axis=0) / W[:, k].sum() # 更新均值
self.params[k][2] = np.sum(
[W[i, k] * (X[[i]] - self.params[k][1]).T.dot(X[[i]] - self.params[k][1]) for i in
range(0, n_sample)], axis=0) / W[:, k].sum() # 更新方差
# 更新当前的隐变量
W = np.asarray([utils.gaussian_nd(X, u, sigma) * alpha for alpha, u, sigma in self.params]).T
# 计算log like hold
new_log_loss = np.log(W.sum(axis=1)).sum() / n_sample
W = W / np.sum(W, axis=1, keepdims=True)
if new_log_loss - current_log_loss > self.tol:
current_log_loss = new_log_loss
else:
break
if self.verbose:
utils.plot_contourf(X, lambda x: self.predict_sample_generate_proba(x), lines=5)
utils.plt.show()