深度学习入门之温故而知新

目录

 

 

目录

 

前言

一、感知机.

二、神经网络

 

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前言

写作目的： 回顾《深度学习入门》的内容， 捋一下思路， 看到后面需要理清思路。

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提示：以下是本篇文章正文内容，下面案例可供参考

一、感知机.

 

 

import numpy as np

x = np.array([0, 1]) #输入
w = np.array([0.5, 0.5]) #权重
b = -0.7 #偏置 就是阈值的相反数
print(w*x)
print(np.sum(w*x) + b)

[0.  0.5]
-0.19999999999999996

 相异为True

 

def AND(x1, x2): #与门
    '''
    w1, w2, theta = 0.5, 0.5, 0.7
    tmp = x1*w1 + x2*w2
    if tmp <= theta:
        return 0
    elif tmp > theta:
        return 1
    '''
    x = np.array([x1, x2])
    w = np.array([0.5, 0.5])
    b = -0.7
    tmp = np.sum(x*w) + b
    if tmp > 0:
        return 1
    else:
        return 0

    
print(AND(0, 0))
print(AND(1, 0))
print(AND(0, 1))
print(AND(1, 1))


0
0
0
1

 

def NAND(x1, x2): #与非门
    '''
    w1, w2, theta = -0.5, -0.5, -0.7
    tmp = x1*w1 + x2*w2
    if tmp <= theta:
        return 0
    elif tmp > theta:
        return 1
    '''
    x = np.array([x1, x2])
    w = np.array([-0.5, -0.5])
    b = 0.7
    tmp = np.sum(x*w) + b
    if tmp > 0:
        return 1
    else:
        return 0

print(NAND(0, 0))
print(NAND(1, 0))
print(NAND(0, 1))
print(NAND(1, 1))


1
1
1
0

 

def OR(x1, x2): #非门
    '''
    w1, w2, theta = 0.5, 0.5, 0.4
    tmp = x1*w1 + x2*w2
    if tmp <= theta:
        return 0
    elif tmp > theta:
        return 1
    '''
    x = np.array([x1, x2])
    w = np.array([0.5, 0.5])
    b = -0.2
    tmp = np.sum(w*x) + b
    if tmp > 0:
        return 1
    else:
        return 0
    
print(OR(0, 0))
print(OR(1, 0))
print(OR(0, 1))
print(OR(1, 1))


0
1
1
1

  代码如下：

def XOR(x1, x2): #异或门
    s1 = NAND(x1, x2)
    s2 = OR(x1, x2)
    y = AND(s1, s2)
    return y

print(XOR(1, 1))
print(XOR(1, 0))
print(XOR(0, 1))
print(XOR(0, 0))


0
1
1
0

 

 

二、神经网络

 

**函数-->，

 

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

# x = np.array([-1.0, 1.0, 2.0]) #由于numpy的广播功能, np.array也可以进行计算
x = np.arange(-5.0, 5.0, 0.1)
y = sigmoid(x)

plt.plot(x, y)
plt.ylim(-0.1, 1.1) #指定y轴的范围
plt.show()

import numpy as np
import matplotlib.pylab as plt

def step_function(x):
    return np.array(x > 0, dtype=np.int)

x = np.arange(-5.0, 5.0, 0.1)
y = step_function(x)

plt.plot(x, y)
plt.ylim(-0.1, 1.1) #指定y轴的范围
plt.show()

import numpy as np

def relu(x):
    return np.maximum(0, x)

 

，

，

 

，

import numpy as np

#输入层到第1层的信号传递
X = np.array([1.0, 0.5]) 
W1 = np.array([[0.1, 0.3, 0.5], [0.2, 0.4, 0.6]]) #权重
B1 = np.array([0.1, 0.2, 0.3]) #偏置

print(W1.shape)
print(X.shape)
print(B1.shape)

A1 = np.dot(X, W1) + B1
print(A1)
Z1 = sigmoid(A1)
print(Z1)

，，，

#第1层到第2层的信号传递
W2 = np.array([[0.1, 0.4], [0.2, 0.5], [0.3, 0.6]])
B2 = np.array([0.1, 0.2])

print(Z1.shape)
print(W2.shape)
print(B2.shape)

A2 = np.dot(Z1, W2) + B2
Z2 = sigmoid(A2)
print(A2)
print(Z2)

，，

def identify_function(x): #恒等函数, 一般回归问题使用
    return x

#第2层到输出层
W3 = np.array([[0.1, 0.3], [0.2, 0.4]])
B3 = np.array([0.1, 0.2])

A3 = np.dot(Z2, W3) + B3
Y = identify_function(A3)

print(Y)

，

，

，，，，

def softmax(a): #输出层
    c = np.max(a)
    exp_a = np.exp(a - c) # 溢出对策
    sum_exp_a = np.sum(exp_a)
    y = exp_a / sum_exp_a
    
    return y

整合代码：

#综合整理
def init_network():
    network = {}
    network['W1'] = np.array([[0.1, 0.3, 0.5], [0.2, 0.4, 0.6]])
    network['b1'] = np.array([0.1, 0.2, 0.3])
    network['W2'] = np.array([[0.1, 0.4], [0.2, 0.5], [0.3, 0.6]])
    network['b2'] = np.array([0.1, 0.2])
    network['W3'] = np.array([[0.1, 0.3], [0.2, 0.4]])
    network['b3'] = np.array([0.1, 0.2])
    
    return network



def forward(network, x):
    W1, W2, W3 = network['W1'], network['W2'], network['W3']
    b1, b2, b3 = network['b1'], network['b2'], network['b3']
    
    a1 = np.dot(x, W1) + b1
    z1 = sigmoid(a1)
    a2 = np.dot(z1, W2) + b2
    z2 = sigmoid(a2)
    a3 = np.dot(z2, W3) + b3
    y = identify_function(a3)
    
    return y

network = init_network()
x = np.array([1.0, 0.5])
y = forward(network, x)
print(y)

手写数字识别：

，，

import sys, os
sys.path.append(os.pardir) #为了导入父目录的文件而进行的设定
from sourceCode.dataset.mnist import load_mnist

# 第一次调用会花费几分钟
# load_mnist以 (训练图像, 训练标签), (测试图像, 测试标签) 返回读入的MNIST数据
(x_train, t_train), (x_test, t_test) = load_mnist(flatten=True, normalize=False)

# 输出各个数据的形状
print(x_train.shape)
print(t_train.shape)
print(x_test.shape)
print(t_test.shape)


(60000, 784)
(60000,)
(10000, 784)
(10000,)

 

import sys, os
sys.path.append(os.pardir)
import numpy as np
from dataset.mnist import load_mnist
from PIL import Image


def img_show(img):
    # 把保存为Numpy数组的图像数据转换为PIL用的数据对象
    pil_img = Image.fromarray(np.uint8(img)) 
    pil_img.show() # 再显示它
  

(x_train, t_train), (x_test, t_test) = load_mnist(flatten=True, normalize=False)
# x_train的形状是（6000,784），即6000行728列的矩阵，所以x_train[0]表示第一列的784个数据
img = x_train[0]
# t_train的形状是（6000，），即一行或者一列数据6000个，所以t_train[0]是第一个数据，这里它的值是5
label = t_train[0]

print(label) # 5
print(img.shape) # (784,)
img = img.reshape(28, 28) # 把图像的形状变成原来的尺寸
print(img.shape) # (28, 28)
img_show(img)

import sys, os
sys.path.append(os.pardir)  # 为了导入父目录的文件而进行的设定
import numpy as np
import pickle
from dataset.mnist import load_mnist


def get_data():
    (x_train, t_train), (x_test, t_test) = load_mnist(normalize=True, flatten=True, one_hot_label=False)
    return x_test, t_test # 返回(测试图像, 测试标签)


def init_network():
    with open("sourceCode//ch03//sample_weight.pkl", 'rb') as f:
        network = pickle.load(f)
    return network


def predict(network, x):
    W1, W2, W3 = network['W1'], network['W2'], network['W3']
    b1, b2, b3 = network['b1'], network['b2'], network['b3']

    a1 = np.dot(x, W1) + b1
    z1 = sigmoid(a1)
    a2 = np.dot(z1, W2) + b2
    z2 = sigmoid(a2)
    a3 = np.dot(z2, W3) + b3
    y = softmax(a3)

    return y


# 神经网络的推理处理
x, t = get_data()
network = init_network()
accuracy_cnt = 0
for i in range(len(x)):
    y = predict(network, x[i])
    p = np.argmax(y) # 获取概率最高的元素的索引
    if p == t[i]:
        accuracy_cnt += 1

print("Accuracy:" + str(float(accuracy_cnt) / len(x)))

 

x, _ = get_data()
network = init_network()
W1, W2, W3 = network['W1'], network['W2'], network['W3']

print(x.shape)
print(x[0].shape)
print(W1.shape)
print(W2.shape)
print(W3.shape)


(10000, 784)
(784,)
(784, 50)
(50, 100)
(100, 10)

# 批处理方式
x, t = get_data()
network = init_network()

batch_size = 100 # 批数量
accuracy_cnt = 0

for i in range(0, len(x), batch_size):
    x_batch = x[i : i + batch_size]
    y_batch = predict(network, x_batch)
    p = np.argmax(y_batch, axis = 1) # 沿着第1维找到最大元素的索引; 第0维对应第一个维度; 第1维对应第二个维度
    accuracy_cnt += np.sum(p == t[i : i + batch_size])
    
    
print("Accuracy:" + str(float(accuracy_cnt) / len(x)))


Accuracy:0.9352