神经网络思维的逻辑回归python代码_np.zeros(dim,1)

一、工具包

• numpy是Python科学计算的基本包。
• h5py是一个与存储在H5文件中的数据集交互的常用包。
• matplotlib是一个著名的Python绘图库。
• PIL和scipy在这里用来测试模型。

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
 
%matplotlib inline

二、问题概述

一个数据集(“data.h5”)包含:训练集训练图像标记为cat(y = 1)或non-cat(y = 0),测试集测试图像标记为cat或non-cat,图像大小为(num px, num px, 3) 。因此，每个图像是正方形(height =num px)和(width=num px)。构建一个简单的图像识别算法，可以正确地将图片分类为猫或非猫。

# Loading the data (cat/non-cat)
train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()

# Example of a picture
index = 25
plt.imshow(train_set_x_orig[index])
print ("y = " + str(train_set_y[:, index]) + ", it's a '" + classes[np.squeeze(train_set_y[:, index])].decode("utf-8") +  "' picture.")

 index=25的训练集图像：

### START CODE HERE ### (≈ 3 lines of code)
m_train = train_set_x_orig.shape[0]
m_test = test_set_x_orig.shape[0]
num_px = train_set_x_orig.shape[1]
### END CODE HERE ###
 
print ("Number of training examples: m_train = " + str(m_train))
print ("Number of testing examples: m_test = " + str(m_test))
print ("Height/Width of each image: num_px = " + str(num_px))
print ("Each image is of size: (" + str(num_px) + ", " + str(num_px) + ", 3)")
print ("train_set_x shape: " + str(train_set_x_orig.shape))
print ("train_set_y shape: " + str(train_set_y.shape))
print ("test_set_x shape: " + str(test_set_x_orig.shape))
print ("test_set_y shape: " + str(test_set_y.shape))

 输出：

# Reshape the training and test examples
 
### START CODE HERE ### (≈ 2 lines of code)
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
### END CODE HERE ###
 
print ("train_set_x_flatten shape: " + str(train_set_x_flatten.shape))
print ("train_set_y shape: " + str(train_set_y.shape))
print ("test_set_x_flatten shape: " + str(test_set_x_flatten.shape))
print ("test_set_y shape: " + str(test_set_y.shape))
print ("sanity check after reshaping: " + str(train_set_x_flatten[0:5,0]))

Reshape the training and test data sets so that images of size (num_px, num_px, 3) are flattened into single vectors of shape (num_px∗num_px∗3, 1).

输出：

 标准化数据集：

train_set_x = train_set_x_flatten/255.
test_set_x = test_set_x_flatten/255.

三、学习算法的总体架构

逻辑回归其实就是一个非常简单的神经网络。

四、算法构建部分

建立神经网络的主要步骤是:

1. 定义模型结构(例如输入特性的数量)

2. 初始化模型的参数

3.循环:

• 计算电流损耗(正向传播)
• 计算电流梯度(反向传播)
• 更新参数(梯度下降)

通常分别构建1-3个函数，并将它们集成到一个称为model()的函数中。

定义sigmoid函数

# GRADED FUNCTION: sigmoid
 
def sigmoid(z):
    """
    Compute the sigmoid of z
    Arguments:
    z -- A scalar or numpy array of any size.
    Return:
    s -- sigmoid(z)
    """
 
    ### START CODE HERE ### (≈ 1 line of code)
    s = 1.0 / (1.0 + np.exp(-1.0 * z))
    ### END CODE HERE ###
    
    return s

初始化参数

# GRADED FUNCTION: initialize_with_zeros
 
def initialize_with_zeros(dim):
    """
    This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.
    
    Argument:
    dim -- size of the w vector we want (or number of parameters in this case)
    
    Returns:
    w -- initialized vector of shape (dim, 1)
    b -- initialized scalar (corresponds to the bias)
    """
    
    ### START CODE HERE ### (≈ 1 line of code)
    w = np.zeros((dim,1))
    b = 0
    ### END CODE HERE ###
 
    assert(w.shape == (dim, 1))
    assert(isinstance(b, float) or isinstance(b, int))
    
    return w, b

前向和后向传播

# GRADED FUNCTION: propagate
 
def propagate(w, b, X, Y):
    """
    Implement the cost function and its gradient for the propagation explained above
    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of size (num_px * num_px * 3, number of examples)
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)
    Return:
    cost -- negative log-likelihood cost for logistic regression
    dw -- gradient of the loss with respect to w, thus same shape as w
    db -- gradient of the loss with respect to b, thus same shape as b
    
    Tips:
    - Write your code step by step for the propagation. np.log(), np.dot()
    """
    
    m = X.shape[1]
    
    # FORWARD PROPAGATION (FROM X TO COST)
    ### START CODE HERE ### (≈ 2 lines of code)
    A = sigmoid(np.dot(w.T, X) + b)                                    # compute activation
    cost = -(1.0 / m) * np.sum(Y * np.log(A) + (1 - Y) * np.log(1 - A))                                # compute cost
    ### END CODE HERE ###
    
    # BACKWARD PROPAGATION (TO FIND GRAD)
    ### START CODE HERE ### (≈ 2 lines of code)
    dw = (1.0 / m) * np.dot(X, (A - Y).T)
    db = (1.0 / m) * np.sum(A - Y)
    ### END CODE HERE ###
 
    assert(dw.shape == w.shape)
    assert(db.dtype == float)
    cost = np.squeeze(cost)
    assert(cost.shape == ())
    
    grads = {"dw": dw,
             "db": db}
    
    return grads, cost

优化参数

Write down the optimization function. The goal is to learn