深度學習-1

躍遷函數
簡單說就是大於0返回1，否則返回0
import numpy as np
0
def setp_function(x):
    y = x > 0
    return y.astype(np.int)
x = np.array([-1,1,2])
p
setp_function(x)
array([0, 1, 1])
import matplotlib.pylab as plt
x = np.arange(-5.0,5.0,0.1)
y = setp_function(x)
plt.plot(x,y)
plt.ylim(-0.1,1.1)
plt.show()
x = np.arange(-5.0,5.0,0.1)
y = setp_function(x)
plt.plot(x,y)
plt.ylim(-0.1,1.1)
plt.show()

sigmoid函數
h(x) = 1/(1+exp(-x))
def sigmoid(x):
    return 1/(1+np.exp(-x))
x = np.array([-1,1,2])
x = np.array([-1,1,2])
sigmoid
sigmoid(x)
array([0.26894142, 0.73105858, 0.88079708])
x = np.arange(-5.0,5.0,0.1)
y = sigmoid(x)
plt.plot(x,y)
plt.ylim(-0.1,1.1)
plt.show()

Relu函數
Relu函數在輸出大於0時直接輸出該值，在輸入小於等於0時，輸出0
relu
def relu(x):
    return np.maximum(0,x)
x = np.array([-1,1,2])
x
relu(x)
array([0, 1, 2])
x = np.arange(-5.0,5.0,0.1)
y = relu(x)
plt.plot(x,y)
#plt.ylim(-0.1,1.1)
plt.show()

def init_work():
    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
x
def identity_function(x):
    return x
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(a1, W2) + b2
    z2 = sigmoid(a2)
    z3 = np.dot(z2, W3) + b3
    y = identity_function(z3)
    
    return y
network = init_work()
x = np.array([1.0,0.5])
y = forward(network, x)
print(y)
[0.32273376 0.71003315]
softmax函數
exp_a = np.exp(a)
sum_exp_a = np.sum(exp_a)
y = exp_a/sum_exp_a
a = np.array([0.3,2.9,4.0])
exp_a = np.exp(a)
sum_exp_a = np.sum(exp_a)
y = exp_a/sum_exp_a
print(y)
[0.01821127 0.24519181 0.73659691]
定義函數
def softmax(a):
    exp_a = np.exp(a)
    sum_exp_a = np.sum(exp_a)
    y = exp_a/sum_exp_a
    
    return y
def softmax(a):
    exp_a = np.exp(a)
    sum_exp_a = np.sum(exp_a)
    y = exp_a/sum_exp_a
    
    return y
a = np.array([1010,1000,990])
softmax(a)
a = np.array([1010,1000,990])
softmax(a)
C:\Users\Administrator\Anaconda3\lib\site-packages\ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in true_divide
  after removing the cwd from sys.path.
array([nan, nan, nan])
，需要減去數組中最大的數值，如下
#### e的一千次會返回一個無窮大的一個值 ，需要減去數組中最大的數值，如下
c = np.max(a) #1010
a - c
array([  0, -10, -20])
c
softmax(a-c)
array([9.99954600e-01, 4.53978686e-05, 2.06106005e-09])
於是我們的到這樣的softmax函數
softmax
def softmax(a):
    c = np.max(a)
    exp_a = np.exp(a-c) #溢出對策
    sum_exp_a = np.sum(exp_a)
    y = exp_a/sum_exp_a
    
    return y
a = np.array([1010,1000,990])
softmax(a)
array([9.99954600e-01, 4.53978686e-05, 2.06106005e-09])
#輸出值和總是1
np.sum(softmax(a))#輸出值和總是1
1.0​
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