吴恩达机器学习python实现3 多元分类及前馈神经网络

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我是靠谱客的博主爱撒娇衬衫，最近开发中收集的这篇文章主要介绍吴恩达机器学习python实现3 多元分类及前馈神经网络，觉得挺不错的，现在分享给大家，希望可以做个参考。

概述

多元分类

1、从images中随机选取numbers张图片

def randomly_select(images, numbers):
    m, n = images.shape[0], images.shape[1]
    res = np.zeros((1, n))
    for i in range(numbers):
        index = random.randint(0, m - 1)
        res = np.concatenate((res, images[index].reshape(1, n)), axis=0)
    return np.delete(res, 0, axis=0)  # 100*400数组

2、将若干张图片组成一张图片

def mapping(images, images_dimension):
    image_dimension = int(np.sqrt(images.shape[-1]))
    image = False
    im = False
    for i in images:
        if type(image) == bool:
            image = i.reshape(image_dimension, image_dimension)
        else:
            if image.shape[-1] == image_dimension * images_dimension:
                if type(im) == bool:
                    im = image
                else:
                    im = np.concatenate((im, image), axis=0)
                image = i.reshape(image_dimension, image_dimension)
            else:
                image = np.concatenate((image, i.reshape(image_dimension, image_dimension)), axis=1)
    return np.concatenate((im, image), axis=0) # 200*200数组

3、导入数据

使用 import scipy.io as sio

data = sio.loadmat(文件路径)
    X = data['X']
    Y = data['y']
    # X包含5000个20 * 20像素的手写字体图像  Y对应的数字
    print(X.shape, Y.shape)
    # 画图显示
    im = mapping(randomly_select(X, 100), 10)
    plt.imshow(im.T)  # 图片是镜像的需要转置让它看起来更正常
    plt.axis('off')
    plt.show()

4、梯度下降、正则化逻辑回归

def sigmoid(z):
    return 1/(1+np.exp(-z))


def cost(theta, X, y, lamda):
    m = X.shape[0]
    part1 = np.mean(-y*np.log(sigmoid(X.dot(theta)))-(1-y)*np.log(1-sigmoid(X.dot(theta))))
    part2 = (lamda/(2*m))*np.sum(np.delete((theta*theta), 0, axis=0))
    return part1+part2


def gradient(theta, X, y, lamda):
    m = X.shape[0]
    part1 = X.T.dot(sigmoid(X.dot(theta))-y)/y.shape[0]
    part2 = (lamda/m)*theta
    return part1+part2

5、将y值变化为向量来表示数字

def convert(y):
    n = len(np.unique(y))
    res = False
    for i in y:
        temp = np.zeros((1, n))
        temp[0][i[0] % 10] = 1
        if type(res) == bool:
            res = temp
        else:
            res = np.concatenate((res, temp), axis=0)
    return res  # 5000*10 数组

6、预测

def predict(theta, X):
    p = sigmoid(X.dot(theta.T))
    res = False
    for i in p:
        index = np.argmax(i)
        temp = np.zeros((1, 10))
        temp[0][index] = 1
        if type(res) == bool:
            res = temp
        else:
            res = np.concatenate((res, temp), axis=0)
    return res

y = convert(Y)
    X = np.insert(X, 0, 1, axis=1)
    m, n = X.shape[0], X.shape[1]
    theta = np.zeros((n,))
    trained_theta = False
    for i in range(y.shape[-1]):
        res = opt.minimize(fun=cost, x0=theta, args=(X, y[:, i], 1), method="TNC", jac=gradient)
        if type(trained_theta) == bool:
            trained_theta = res.x.reshape(1, n)
        else:
            trained_theta = np.concatenate((trained_theta, res.x.reshape(1, n)), axis=0)
    print(classification_report(y, predict(trained_theta, X), target_names=[str(i) for i in range(10)], digits=4))

8、结果

precision recall f1-score support

0 0.9725 0.9920 0.9822 500
1 0.9553 0.9840 0.9695 500
2 0.9444 0.9180 0.9310 500
3 0.9418 0.9060 0.9235 500
4 0.9465 0.9560 0.9512 500
5 0.9212 0.9120 0.9166 500
6 0.9683 0.9760 0.9721 500
7 0.9499 0.9480 0.9489 500
8 0.9205 0.9260 0.9232 500
9 0.9183 0.9220 0.9202 500

micro avg 0.9440 0.9440 0.9440 5000
macro avg 0.9439 0.9440 0.9438 5000
weighted avg 0.9439 0.9440 0.9438 5000
samples avg 0.9440 0.9440 0.9440 5000

前馈神经网络

1、与上文相似，将y向量化，写预测函数

def convert(y):
    n = len(np.unique(y))
    res = False
    for i in y:
        temp = np.zeros((1, n))
        temp[0][i[0] % 10] = 1
        if type(res) == bool:
            res = temp
        else:
            res = np.concatenate((res, temp), axis=0)
    return res  # 5000*10 数组


def sigmoid(z):
    return 1/(1+np.exp(-z))


def predict(theta, X):
    labels = theta[-1].shape[0]
    for t in theta:
        X = np.insert(X, 0, 1, axis=1)
        X = sigmoid(X.dot(t.T))
    p = X
    res = np.zeros((1, labels))
    for i in p:
        index = np.argmax(i)
        temp = np.zeros((1, labels))
        temp[0][index] = 1
        res = np.concatenate((res, temp), axis=0)
    return res[1:]

2、测试

theta = sio.loadmat(文件路径)
    data = sio.loadmat(文件路径)
    # print(theta.keys())
    theta1 = theta["Theta1"]  # shape(25,401)
    theta2 = theta["Theta2"]  # shape(10,26)
    y = convert(data['y'])
    # 训练集中对y的处理是 1 2 3 ... 0
    # convert处理中是 0 1 2 ... 9
    y0 = y[:, 0].reshape(y.shape[0], 1)
    y = np.concatenate((y[:, 1:], y0), axis=1)
    X = data["X"]
    print(classification_report(y, predict((theta1, theta2), X), digits=3))

3、结果

precision recall f1-score support

0 0.968 0.982 0.975 500
1 0.982 0.970 0.976 500
2 0.978 0.960 0.969 500
3 0.970 0.968 0.969 500
4 0.972 0.984 0.978 500
5 0.978 0.986 0.982 500
6 0.978 0.970 0.974 500
7 0.978 0.982 0.980 500
8 0.966 0.958 0.962 500
9 0.982 0.992 0.987 500

micro avg 0.975 0.975 0.975 5000
macro avg 0.975 0.975 0.975 5000
weighted avg 0.975 0.975 0.975 5000
samples avg 0.975 0.975 0.975 5000