跟我学算法-吴恩达老师的logsitic回归

logistics回归是一种二分类问题，采用的激活函数是sigmoid函数，使得输出值转换为(0,1)之间的概率

A = sigmoid(np.dot(w.T, X) + b ) 表示预测函数

dz = A - Y ， A 表示的是预测结果， y 表示的是实际结果

cost = -y*logA - (1-y)*log(1-A)  #表示损失函数

dw = np.dot(X, dz.T)/m

db = np.sum(dz)/m

w := w - a*dw   # 更新w，a 表示学习率

b : = b - a*db     #更新b

第一步： 定义lr_utils.py 导入数据

import numpy as np
import h5py

def load_dataset():
    train_dataset = h5py.File('datasets/train_catvnoncat.h5', 'r')
    train_set_x_orig = np.array(train_dataset['train_set_x'][:])
    train_set_y = np.array(train_dataset['train_set_y'][:])

    test_dataset = h5py.File('datasets/test_catvnoncat.h5', 'r')
    test_set_x_orig = np.array(test_dataset['test_set_x'][:])
    test_set_y = np.array(test_dataset['test_set_y'][:])

    # 对矩阵预测值的维度构造成(1, train_set_x_orig.shape[0]) 即一张照片一个预测值
    train_set_y = train_set_y.reshape((1, train_set_x_orig.shape[0]))
    test_set_y = test_set_y.reshape((1, test_set_x_orig.shape[0]))

    classes = np.array(test_dataset["list_classes"][:])

    return train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes

第二步：调用函数，进行数据导入

import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
from scipy import ndimage
from lr_utils import load_dataset

train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()

# 查看图片
index = 7
plt.imshow(train_set_x_orig[7])
plt.show()

#训练集的图片个数
m_train = train_set_x_orig.shape[0]
m_test = test_set_x_orig.shape[0]
# 图片的尺寸
num_px = train_set_x_orig.shape[1]

# 对每张图片的像素点进行一个竖直排列[x1, x2, x3, x4]
train_set_x_flatten = train_set_x_orig.reshape(m_train, -1).T
test_set_x_flatten = test_set_x_orig.reshape(m_test, -1).T

# 进行像素点归一化
train_set_x = train_set_x_flatten / 255
test_set_x = test_set_x_flatten /  255

第三步：定义sigmoid函数和进行参数初始化

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

s = sigmoid(np.array([[0, 2]]))

def initialize_with_zeros(dim):

    w = np.zeros((dim, 1), dtype=float)
    b = 0.0

    return w, b

第四步：定义反向传播函数

def propgate(w, b, X, Y):
    m = X.shape[1]
    # 预测函数
    A = sigmoid(np.dot(w.T, X) + b)
    # 预测函数与真实值之差
    dz = A - Y
    # A与w的导数
    dw = 1/m * np.dot(X, dz.T)
    # b与w的导数
    db = 1/m * np.sum(dz, axis=1)
    #损失函数
    cost = np.sum(-Y  * np.log(A) - (1 - Y) * np.log(1 - A), axis=1) / m
    #更新参数的幅度
    grade = {'dw':dw, 'db':db}
    #损失函数
    cost = np.squeeze(cost)

    return cost, grade

第5步：通过反向传播函数, 训练样本

# 迭代优化

def optimize(w, b, X, Y, num_iteration, learning_rate, print_cost):
    
    # w, b 为初始参数, X, Y为训练集的变量和标签， num_iteration为训练次数, learning_rate为学习率， print_cost为是否打印
    now_num_iteration = 0
    costs = []
    for i in range(num_iteration):

        cost, grade = propgate(w, b, X, Y)

        dw = grade['dw']
        db = grade['db']

        w = w - learning_rate*dw
        b = b - learning_rate*db
        now_num_iteration += 1

        if i%100 == 0:
            costs.append(cost)

        if print_cost and i%100:
            print(cost, i)

        param = {'w':w,
                 'b':b}
        grade = {'dw':dw,
                 'db':db}

第6步：定义预测函数，使用的是前向传播函数

def predict(w, b, X):
    # w,b表示参数,X表示的是输入的图片，y轴表示图片的数目
    # m表示预测的图片的数目
    m = X.shape[1]
    Y_prediction = np.zeros((1, m))
    w = w.reshape(X.shape[0], 1)
    A = sigmoid(np.dot(w.T, X) + b)
    # 概率大于0.5，预测结果为1
    for i in range(A.shape[1]):
        if A[0, i] > 0.5:
            Y_prediction[0, i] = 1

    return Y_prediction

第7步：定义最终的训练模型， 输出训练的准确度

def model(train_set_x, train_set_y, test_set_x, test_set_y, num_iteration, learning_rate, print_cost):

    m = train_set_x.shape[0]
    # 创建初始值
    w, b = initialize_with_zeros(m)
    costs, param, grade = optimize(w, b,train_set_x, train_set_y,
                                   num_iteration, learning_rate, print_cost)
    w = param['w']
    b = param['b']

    Y_train_prediciton = predict(w, b, train_set_x)
    Y_test_prediction = predict(w, b, test_set_x)
    # 输出训练的准确度
    print('train_accuracy {}'.format(100 - np.mean(np.abs(Y_train_prediciton - train_set_y))*100))
    print('test_accuracy {}'.format(100 - np.mean(np.abs(Y_test_prediction - test_set_y ))*100))

    d = {'costs':costs,
         'Y_train_prediciton':Y_train_prediciton,
         'Y_test_prediction':Y_test_prediction,
         'w':w,
         'b':b,
         'learning_rate':learning_rate,
         'num_iteration': num_iteration}

    return  d

第8步：我们挑选一张猫的图片进行预测

# 预测图片
my_image = "cat_1.jpg"   # change this to the name of your image file
## END CODE HERE ##

# We preprocess the image to fit your algorithm.
fname = "images/" + my_image
image = np.array(ndimage.imread(fname, flatten=False))
# 重构模型大小， 使得模型的shape为(:,1)
my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((1, num_px*num_px*3)).T
# 输出预测的结果
my_predicted_image = predict(d['w'], d['b'], my_image)
plt.imshow(image)
print("y = " + str(np.squeeze(my_predicted_image)) + ", your algorithm predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") +  "\" picture.")