吴恩达《机器学习》——第三次作业：多元分类

待我称王封你为后i 2022-01-30 07:19 256阅读 0赞

写了好长时间的驼峰命名，最近有点恶心了，决定python用下划线，C++用驼峰。

这次作业是对手写数字的数据集进行训练。多元分类的一个任务。

参考：[https://github.com/fengdu78/Coursera-ML-AndrewNg-Notes/tree/master/code][https_github.com_fengdu78_Coursera-ML-AndrewNg-Notes_tree_master_code]

import matplotlib.pyplot as plt
    import numpy as np
    import scipy.io as sio
    import matplotlib
    import scipy.optimize as opt
    from sklearn.metrics import classification_report
    
    def load_data(path, transpose=True):
        '''载入数据'''
        data = sio.loadmat(path)
        y = data.get('y')
    
        y = y.reshape(y.shape[0])
    
        X = data.get('X')
    
        if transpose:
            X = np.array([im.reshape((20, 20)).T for im in X])
    
            X = np.array([im.reshape(400) for im in X])
    
        return X, y
    
    
    
    raw_X, raw_y = load_data('ex3data1.mat')
    
    #def plot_image(image):
    # '''随机显示一张图片'''
    # fig, ax = plt.subplots(figsize=(1, 1))
    # ax.matshow(image.reshape((20, 20)), cmap=matplotlib.cm.binary)
    # plt.xticks(np.array([]))
    # plt.yticks(np.array([]))
    
    
    #pick_one = np.random.randint(0, 5000) #在(0,5000)氛围内随机取一个数
    #plot_image(X[pick_one, :])
    #plt.show()
    #print("this should be {}".format(y[pick_one]))
    
    #def plot_100_image(X):
    # '''显示100张图片'''
    # size = int(np.sqrt(X.shape[1]))
    #
    # sample_idx = np.random.choice(np.arange(X.shape[0]), 100)
    # sample_images = X[sample_idx, :]
    #
    # fig, ax_array = plt.subplots(nrows=10, ncols=10, sharey=True, sharex=True, figsize=(8, 8))
    #
    # for r in range(10):
    # for c in range(10):
    # ax_array[r, c].matshow(sample_images[10 * r + c].reshape((size, size)),
    # cmap=matplotlib.cm.binary)
    #
    # plt.xticks(np.array([]))
    # plt.yticks(np.array([]))
    
    
    #准备数据
    X = np.insert(raw_X, 0, values=np.ones(raw_X.shape[0]), axis=1)     #插入第一列，全部为1
    
    y_matrix = []
    
    for k in range(1, 11):
        y_matrix.append((raw_y == k).astype(int))
    
    y_matrix = [y_matrix[-1]] + y_matrix[:-1]
    y = np.array(y_matrix)
    
    
    #print(y.shape)
    
    #训练一维模型
    def sigmoid(z):
        '''激活函数'''
        return 1 / (1 + np.exp(-z))
    
    def gradient(theta, X, y):
        '''一次梯度下降'''
        return (1 / len(X)) * X.T @ (sigmoid(X@theta) - y)
    
    def cost(theta, X, y):
    
        '''代价函数'''
        h = sigmoid(X@theta)
        inner = y.T * np.log(h) + (1-y).T*np.log(1-h)
        return - (np.sum(inner)/len(X))
        #return np.mean(-y * np.log(sigmoid(X*theta.T)) - (1-y)*np.log(1-sigmoid(X*theta.T)))
    
    def regularized_cost(theta, X, y, l=1):
        '''正则化'''
        theta_j1_to_n = theta[1:]
        regularized_term = (1 / (2 * len(X))) * np.power(theta_j1_to_n, 2).sum()
    
        return cost(theta, X, y) + regularized_term
    
    def regularized_gradient(theta, X, y, l=1):
    
        theta_j1_to_n = theta[:-1]
        regularized_theta = (l / len(X)) * theta_j1_to_n
    
        regularized_term = np.concatenate([np.array([0]), regularized_theta])
    
        return gradient(theta, X, y) + regularized_term
    
    def logistic_regression(X, y, l=1):
    
        theta = np.zeros(X.shape[1])
        res = opt.minimize(fun=regularized_cost,
                           x0=theta,
                           args=(X, y, l),
                           method='TNC',
                           jac=regularized_gradient,
                           options={ 'disp': True})
    
        final_theta = res.x
    
        return final_theta
    
    def predict(x, theta):
        '''预测函数'''
        prob = sigmoid(X @ theta)
        return (prob >= 0.5).astype(int)
    
    t0 = logistic_regression(X, y[0])
    
    #print(t0.shape)
    #y_pred = predict(X, t0)
    #
    #print('Accuracy = {}'.format(np.mean(y[0] == y_pred)))
    
    
    #训练k维模型
    
    k_theta = np.array([logistic_regression(X, y[k]) for k in range(10)])
    #print(k_theta.shape)
    
    prob_matrix = sigmoid(X@k_theta.T)
    np.set_printoptions(suppress=True)
    
    y_pred = np.argmax(prob_matrix, axis=1)
    #返回沿轴axis最大值的索引，axis=1代表行
    
    y_answer = raw_y.copy()
    y_answer[y_answer == 10] = 0
    print(classification_report(y_answer, y_pred))

[https_github.com_fengdu78_Coursera-ML-AndrewNg-Notes_tree_master_code]: https://github.com/fengdu78/Coursera-ML-AndrewNg-Notes/tree/master/code