机器学习&数据挖掘笔记_14（GMM-HMM语音识别简单理解）

很好，以下是第十四章的部分习题python实现： 14.1 腐蚀图像分割 ```python import numpy as np import matplotlib.pyplot as plt from scipy.misc import ascent from scipy.ndimage import grey_erosion img = ascent() # 载入一张灰度图像 selem = np.ones((50,50)) # 定义一个50x50的结构元素 eroded = grey_erosion(img, footprint=selem) # 使用结构元素进行腐蚀操作 # 显示原图和腐蚀后的图像 fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(8, 4)) ax = axes.ravel() ax[0].imshow(img, cmap=plt.cm.gray) ax[0].set_title('Original image') ax[1].imshow(eroded, cmap=plt.cm.gray) ax[1].set_title('Eroded image') plt.show() ``` 14.2 高斯混合模型 ```python import numpy as np from scipy.stats import norm class GMM: def __init__(self, n_components, max_iter=100, tol=1e-6): self.n_components = n_components self.max_iter = max_iter self.tol = tol def fit(self, X): n_samples, n_features = X.shape # 初始化参数 self.weights = np.ones(self.n_components) / self.n_components self.means = X[np.random.choice(n_samples, self.n_components, replace=False)] self.covs = [np.eye(n_features) for _ in range(self.n_components)] for i in range(self.max_iter): # E步，计算每个样本在各分模型下的后验概率 probs = np.zeros((n_samples, self.n_components)) for j in range(self.n_components): probs[:, j] = self.weights[j] * norm.pdf(X, self.means[j], self.covs[j]) probs /= probs.sum(axis=1, keepdims=True) # M步，更新参数 weights_new = probs.mean(axis=0) means_new = np.dot(probs.T, X) / probs.sum(axis=0, keepdims=True).T covs_new = [] for j in range(self.n_components): diff = X - means_new[j] cov_new = np.dot(probs[:, j] * diff.T, diff) / probs[:, j].sum() covs_new.append(cov_new) self.weights = weights_new self.means = means_new self.covs = covs_new # 判断收敛 if np.abs(weights_new - self.weights).max() < self.tol \ and np.abs(means_new - self.means).max() < self.tol \ and np.abs(covs_new - self.covs).max() < self.tol: break def predict(self, X): probs = np.zeros((X.shape[0], self.n_components)) for j in range(self.n_components): probs[:, j] = self.weights[j] * norm.pdf(X, self.means[j], self.covs[j]) return probs.argmax(axis=1) ``` 14.3 隐马尔可夫模型 ```python import numpy as np class HMM: def __init__(self, n_states, n_features): self.n_states = n_states self.n_features = n_features def fit(self, X, max_iter=100, tol=1e-6): n_samples = len(X) # 初始化参数 self.pi = np.ones(self.n_states) / self.n_states self.A = np.ones((self.n_states, self.n_states)) / self.n_states self.B = np.ones((self.n_states, self.n_features)) / self.n_features for i in range(max_iter): # E步，计算前向概率和后向概率 alpha = np.zeros((n_samples, self.n_states)) beta = np.zeros((n_samples, self.n_states)) alpha[0] = self.pi * self.B[:, X[0]] for t in range(1, n_samples): alpha[t] = np.dot(alpha[t-1], self.A) * self.B[:, X[t]] beta[-1] = 1 for t in range(n_samples-2, -1, -1): beta[t] = np.dot(self.A, self.B[:, X[t+1]] * beta[t+1]) gamma = alpha * beta / alpha[-1].sum() # M步，更新参数 self.pi = gamma[0] self.A = np.dot(gamma[:-1].T, self.A * self.B[:, X[1:]] * beta[1:]) / gamma[:-1].sum(axis=0).reshape(-1, 1) self.B = np.zeros((self.n_states, self.n_features)) for k in range(self.n_features): mask = X == k self.B[:, k] = gamma[mask].sum(axis=0) / gamma.sum(axis=0) # 判断收敛 if np.abs(alpha[-1].sum() - 1) < tol: break def predict(self, X): alpha = np.zeros((len(X), self.n_states)) alpha[0] = self.pi * self.B[:, X[0]] for t in range(1, len(X)): alpha[t] = np.dot(alpha[t-1], self.A) * self.B[:, X[t]] return alpha[-1].argmax() ``` 以上是部分习题的python实现，希望对你有所帮助。