神经网络基础
1、"Hello World"
test = "Hello world"
print("test: " + test)
output:
test: Hello World
2、Basic_sigmoid
（math实现sigmoid函数）
import math
def basic_sigmoid(x)：
s = 1/（1+math.exp（-x））
return s
basic_sigmoid(3)
output:
0.9525741268224334
3、sigmoid()
(numpy实现sigmoid函数)
import numpy as np
def sigmoid(x):
s = 1/(1+np.exp(-x))
return s
x=np.array([1,2,3])
sigmoid(x)
output:
array([0.73105858, 0.88079708, 0.95257413])
4、sigmoid_derivative
（sigmoid()函数的导数）
def sigmoid_derivative(x)
s = 1/(1+np.exp(-x))
ds = s*(1-s)
return ds
x = np.array([1,2,3])
print("sigmoid_derivative(x) = " + str(sigmoid_derivative(x)))
output:
sigmoid_derivative(x) = [0.19661193 0.10499359 0.04517666]
5、image2vector
(reshape arrays of shape (a, b, c) into a vector of shape (a*b*c，1))
def image2vector(image):
v = image.reshape(image.shape[0]*shape[1]*shape[2] , 1)
return v
Argument:
image -- a numpy array of shape (length, height, depth)
Returns:
v -- a vector of shape (length*height*depth, 1)
image = np.array([[[ 0.67826139, 0.29380381],
[ 0.90714982, 0.52835647],
[ 0.4215251 , 0.45017551]],
[[ 0.92814219, 0.96677647],
[ 0.85304703, 0.52351845],
[ 0.19981397, 0.27417313]],
[[ 0.60659855, 0.00533165],
[ 0.10820313, 0.49978937],
[ 0.34144279, 0.94630077]]])
print ("image2vector(image) = " + str(image2vector(image)))
output:
image2vector(image) = [[0.67826139]
[0.29380381]
[0.90714982]
[0.52835647]
[0.4215251 ]
[0.45017551]
[0.92814219]
[0.96677647]
[0.85304703]
[0.52351845]
[0.19981397]
[0.27417313]
[0.60659855]
[0.00533165]
[0.10820313]
[0.49978937]
[0.34144279]
[0.94630077]]
6、normalizeRows()
changing x to x/||x||,规范化行向量
def normalizeRows(x):
x_norm = np.linalg.norm(x, ord = 2, axis = 1, keepdims = True)
x = x/x_norm
return x
Argument:
x -- A numpy matrix of shape (n, m)
Returns:
x -- The normalized (by row) numpy matrix. You are allowed to modify x.
x = np.array([
[0, 3, 4],
[1, 6, 4]])
print("normalizeRows(x) = " + str(normalizeRows(x)))
output:
normalizeRows(x) = [[0. 0.6 0.8 ]
[0.13736056 0.82416338 0.54944226]]
7、broadcasting and the softmax function
def softmax(x):
x_exp = np.exp(x)
x_sum = np.sum(x_exp, axis = 1, keepdims = True)
s = x_exp/x_sum
return s
Argument:
x -- A numpy matrix of shape (n,m)
Returns:
s -- A numpy matrix equal to the softmax of x, of shape (n,m)
x = np.array([[9,2,5,0,0],[7,5,0,0,0]])
print("softmax(x) = " + str(softmax(x)))
output:
softmax(x) = [[9.80897665e-01 8.94462891e-04 1.79657674e-02 1.21052389e-04
1.21052389e-04]
[8.78679856e-01 1.18916387e-01 8.01252314e-04 8.01252314e-04
8.01252314e-04]]
8、loss function L1
def L1 (yhat , y ):
loss = np.sum(np.abs(yhat - y))
return loss
Arguments:
yhat -- vector of size m (predicted labels)
y -- vector of size m (true labels)
Returns:
loss -- the value of the L1 loss function defined above
yhat = np.array([.9, 0.2 , 0.1 , .4 , .9])
y = np.array([1, 0 , 0 ,1 , 1])
print("L1 = " + str(L1(yhat , y)))
output:
L1 = 1.1
9、loss function L2
def L2(yhat , y):
loss = np.sum(np.dot((y - yhat) , (y - yhat)))
retutn loss
Arguments:
yhat -- vector of size m (predicted labels)
y -- vector of size m (true labels)
Returns:
loss -- the value of the L2 loss function defined above
yhat = np.array([.9, 0.2 , 0.1 , .4 , .9])
y = np.array([1, 0 , 0, 1 , 1])
print("L2 = " + str(L2(yhat,y)))
output:
L2 = 0.43