1. 多分类逻辑回归

自动识别手写数字

import numpy as npimport pandas as pdimport matplotlib.pyplot as pltfrom scipy.io import loadmatfrom scipy.optimize import minimize# 加载mat数据def load_data(path):data = loadmat(path)X = data['X']y = data['y']return X,ydef plot_an_image(X):"""随机打印一个数字"""pick_one = np.random.randint(0, 5000) # 随机选择行数image = X[pick_one, :]# 提取一行中400个像素点fig, ax = plt.subplots(figsize=(1, 1)) # 一行一列的图像ax.matshow(image.reshape((20, 20)), cmap='gray_r') # reshape函数将image重置为20*20的矩阵plt.xticks([]) # 去除x刻度plt.yticks([]) # 去除x刻度plt.show()print('this should be {}'.format(y[pick_one])) # 输出图像代表的值def plot_100_image(X):"""随机画100个数字"""sample_idx = np.random.choice(np.arange(X.shape[0]), 100) # 随机选100个样本sample_images = X[sample_idx, :] # (100,400)fig, ax_array = plt.subplots(nrows=10, ncols=10, sharey=True, sharex=True, figsize=(8, 8))for row in range(10):for column in range(10):ax_array[row, column].matshow(sample_images[10 * row + column].reshape((20, 20)),cmap='gray_r')plt.xticks([])plt.yticks([])plt.show()# 定义sigmoid函数def sigmoid(z):return 1 / (1 + np.exp(-z))# 代价函数 不惩罚theta0 l是正则化常数def regularized_cost(theta, X, y, l):thetaReg = theta[1:]first = (-y*np.log(sigmoid(X@theta))) + (y-1)*np.log(1-sigmoid(X@theta))reg = (thetaReg@thetaReg)*l / (2*len(X))return np.mean(first) + reg#带惩罚的梯度下降def regularized_gradient(theta, X, y, l):thetaReg = theta[1:]first = (1 / len(X)) * X.T @ (sigmoid(X @ theta) - y)# 这里人为插入一维0，使得对theta_0不惩罚，方便计算reg = np.concatenate([np.array([0]), (l / len(X)) * thetaReg])return first + reg# 多分类def one_vs_all(X, y, l, K):# k是标签数"""generalized logistic regressionargs:X: feature matrix, (m, n+1) # with incercept x0=1y: target vector, (m, )l: lambda constant for regularizationK: numbel of labelsreturn: trained parameters"""all_theta = np.zeros((K, X.shape[1])) # (10, 401)for i in range(1, K + 1):theta = np.zeros(X.shape[1])y_i = np.array([1 if label == i else 0 for label in y])ret = minimize(fun=regularized_cost, x0=theta, args=(X, y_i, l), method='TNC', # 返回一组符合十种数字的参数jac=regularized_gradient, options={'disp': True})all_theta[i - 1, :] = ret.xreturn all_thetadef predict_all(X, all_theta):h = sigmoid(X @ all_theta.T) # 注意的这里的all_theta需要转置h_argmax = np.argmax(h, axis=1) #找到每一行最大值的索引h_argmax = h_argmax + 1 #数组是0索引 需要加一个return h_argmax# X, y = load_data('ex3data1.mat')# print(X.shape, y.shape)# plot_an_image(X)# plot_100_image(X)raw_X, raw_y = load_data('ex3data1.mat')X = np.insert(raw_X, 0, 1, axis=1) # (5000, 401)y = raw_y.flatten() # 这里消除了一个维度，方便后面的计算 or .reshape(-1) （5000，）all_theta = one_vs_all(X, y, 1, 10)all_theta # 每一行是一个分类器的一组参数y_pred = predict_all(X, all_theta)accuracy = np.mean(y_pred == y)print ('accuracy = {0}%'.format(accuracy * 100))

2. 使用神经网络进行手写数字识别

import numpy as npimport pandas as pdimport matplotlib.pyplot as pltfrom scipy.io import loadmatfrom scipy.optimize import minimizedef load_weight(path):data = loadmat(path)return data['Theta1'], data['Theta2']# 1.读取已经计算好的参数theta1, theta2 = load_weight('ex3weights.mat')print(theta1.shape, theta2.shape)X, y = load_data('ex3data1.mat')y = y.flatten()X = np.insert(X, 0, values=np.ones(X.shape[0]), axis=1) #在第一列插入一列零a1 = Xz2 = a1 @ theta1.Tz2 = np.insert(z2, 0, 1, axis=1) #第二层加一列a0a2 = sigmoid(z2)z3 = a2 @ theta2.T # 第三层a3 = sigmoid(z3)y_pred = np.argmax(a3, axis=1) + 1accuracy = np.mean(y_pred == y)print ('accuracy = {0}%'.format(accuracy * 100)) # accuracy = 97.52%