AI+神经网络+数字训练与识别

from __future__ import division from __future__ import print_function from __future__ import unicode_literals import numpy as np import matplotlib.pyplot as plt from scipy.io import loadmat from scipy.optimize import minimize # 加载数据 def loadData(path): data = loadmat(path) X = data['X'] y = data['y'] return X, y # 随机打印一张图片 def plot_an_image(X): pick_one = np.random.randint(0, 5000) # 随机选择一行 image = X[pick_one, :] # 从X中抽取图像数据 fig, ax = plt.subplots(figsize=(1, 1)) ax.matshow(image.reshape((20, 20)), cmap='gray_r') # 灰度图 plt.xticks([]) # 去除刻度，美观 plt.yticks([]) print('this should be {}'.format(y[pick_one])) plt.show() # 随机打印100张图 def plot_100_image(X): sample_idx = np.random.choice(np.arange(X.shape[0]), 100) sample_img = X[sample_idx, :] fig, ax_array = plt.subplots(nrows=10, ncols=10, sharey=True, sharex=True, figsize=(8, 8)) for row in range(10): for col in range(10): ax_array[row, col].matshow(sample_img[10 * row + col].reshape((20, 20)), cmap='gray_r') plt.xticks([]) plt.yticks([]) plt.show() def plot_one_type_all_image(X): sample_img = X[950:1050] fig, ax_array = plt.subplots(nrows=10, ncols=10, sharey=True, sharex=True, figsize=(8, 8)) for row in range(10): for col in range(10): ax_array[row, col].matshow(sample_img[10 * row + col].reshape((20, 20)), cmap='gray_r') plt.xticks([]) plt.yticks([]) plt.show() def sigmoid(z): return 1 / (1 + np.exp(-z)) # 正则化的代价函数 def regularized_cost(theta, X, y, l): reg = theta[1:] first = -y * np.log(sigmoid(X @ theta)) - (1 - y) * np.log(1 - sigmoid(X @ theta)) reg = (reg @ reg) * l / (2 * len(X)) return np.mean(first) + reg # 正则化的梯度下降 def regularized_gradient(theta, X, y, l): reg = theta[1:] first = (1 / len(X)) * X.T @ (sigmoid(X @ theta) - y) reg = np.concatenate([np.array([0]), (1 / len(X)) * reg]) # concatenate 数组拼接函数, 此处在前面加一个0, 即第一项不惩罚 return first + reg # 一对多分类训练 def one_vs_all(X, y, l, K): all_theta = np.zeros((K, X.shape[1])) 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', jac=regularized_gradient, options={'disp': True}) # disp为True, 则打印详细的迭代信息; all_theta[i - 1, :] = ret.x return all_theta def predict_all(X, all_theta): h = sigmoid(X @ all_theta.T) h_argmax = np.argmax(h, axis=1) h_argmax += 1 return h_argmax def main(): X, y = loadData('./ex3data1.mat') print(np.unique(y)) # 查看有几类标签 print(X.shape, y.shape) # plot_an_image(X) #plot_100_image(X) X = np.insert(X, 0, 1, axis=1) # 这里消除了一个维度，方便后面的计算 or .reshape(-1) （5000，） # 在不降维的情况下是 (5000, 1)，也就是5000维向量，转换为展平后的1维，长度是5000的向量 y = y.flatten() all_theta = one_vs_all(X, y, 1, 10) ''' 使用训练好的参数 all_theta 对训练集特征矩阵 X 进行预测，得到预测的类别标签向量 y_pred。 predict_all 函数根据输入特征矩阵 X 和参数矩阵 all_theta 进行预测，并返回预测的类别标签。 ''' y_pred = predict_all(X, all_theta) accuracy = np.mean(y_pred == y) print('accuracy = {0}%'.format(accuracy * 100)) main() def test(): X, y = loadData('./ex3data1.mat') print(np.unique(y)) # 查看有几类标签 print(X.shape, y.shape) plot_one_type_all_image(X)