前言：
文章以Andrew Ng 的 deeplearning.ai 视频课程为主线，记录Programming Assignments 的实现过程。相对于斯坦福的CS231n课程，Andrew的视频课程更加简单易懂，适合深度学习的入门者系统学习！
这一部分主要涉及到python与numpy的一些基础知识，最重要的两个概念分别是广播和矩阵向量化的实现。具体代码如下：
1.1-sigmoid function, np.exp()
sigmoid(x) is sometimes also known as the logistic function. It is a non-linear function used not only in Machine Learning (Logistic Regression), but also in Deep Learning.
Before using np.exp(), you will use math.exp() to implement the sigmoid function. You will then see why np.exp() is preferable to math.exp()
import math
def basic_sigmoid(x):
s = 1./(1+math.exp(-x))
return s
Actually, we rarely use the "math" library in deep learning because the inputs of the functions are real numbers. In deep learning we mostly use matrices and vectors. This is why numpy is more useful.
import numpy as np
def sigmoid(x):
s = 1./(1+np.exp(-x))
return s
1.2-sigmoid grdient
The formula is: sigmoid_derivative(x)=σ′(x)=σ(x)(1−σ(x))
def sigmoid_derivative(x):
s = 1./(1+np.exp(-x))
ds = s*(1-s)
return ds
1.3 - Reshaping arrays
in computer science, an image is represented by a 3D array of shape(length,height,depth=3)(length,height,depth=3). However, when you read an image as the input of an algorithm you convert it to a vector of shape(length∗height∗3,1)(length∗height∗3,1). In other words, you "unroll", or reshape, the 3D array into a 1D vector.
def image2vector(image):
v = image.reshape(image.shape[0]*image.shape[1]*image.shape[2],1)
return v
1.4 - Normalizing rows
Another common technique we use in Machine Learning and Deep Learning is to normalize our data. It often leads to a better performance because gradient descent converges faster after normalization.
def normalizeRows(x):
x_norm = np.linalg.norm(x,axis=1,keepdims=True)
x = x/x_norm
return x
1.5 - Broadcasting and the softmax function
A very important concept to understand in numpy is "broadcasting". It is very useful for performing mathematical operations between arrays of different shapes.
def softmax(
x_exp = np.exp(x)
x_sum = np.sum(x_exp,axis=1,keepdims=True)
s = x_exp/x_sum
return s
1.6-Implement the L1 and L2 loss functions
The loss is used to evaluate the performance of your model. The bigger your loss is, the more different your predictions (ŷy^) are from the true values (yy). In deep learning, you use optimization algorithms like Gradient Descent to train your model and to minimize the cost.
L1 loss is defined as: L1(ŷ,y)=∑|y(i)−ŷ(i)|
def L1(yhat, y):
loss = np.sum(np.abs(yhat-y))
return loss
L2 loss is defined as:L2(ŷ,y)=∑(y(i)−ŷ(i))**2
def L2(yhat, y):
loss = np.sum((yhat-y)**2)
return loss
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