[CV] Wu Enda machine learning course notes | Chapter 8

If there is no special explanation in this series of articles , The text explains the picture above the text
machine learning | Coursera
Wu Enda machine learning series _bilibili

8 Representation of neural networks

8-1 Nonlinear hypothesis

For an image , If the gray value of each pixel or other feature representation method is taken as a data sample , The data set will be very large , If we use the previous regression algorithm to calculate , There will be a very large computational cost

8-2 Neurons and the brain

8-3 Forward propagation - Model display I

• The figure above refers to a with Sigmoid Artificial neuron of activation function , In terms of neural networks ,$g(z)=\frac{1}{1+e^{-{\theta }^{T}X}}$ It is called activation function
  
• Neural network refers to a set of Neural Networks , first floor （Layer 1） Called the input layer （Input Layer）, The second floor （Layer 2） Called hidden layer （Hidden Layer）, The third level （Layer 3） Called output layer （Output Layer）
• use $a_i^{(j)}$ To represent the $j$ Layer of the first $i$ Activation items of neurons （“activation” of unit $i$ in layer $j$）, The so-called activation term refers to the value calculated and output by a specific neuron
• use ${\Theta }^{(j)}$ Says from the first $j$ Layer to tier $j+1$ Layer weight matrix （ Parameter matrix ）, That's what happened before $\theta$ matrix （ Previous $\theta$ It can be called parameter $parameters$ It can also be called weight $weights$）
  
• $a_1^{(2)}$、$a_2^{(2)}$ and $a_3^{(2)}$ The calculation formula of has been written in the above figure
• among ${\Theta }^{(1)}$ It's a $3\times 4$ Matrix
• If the neural network is in the $j$ Layer has a $s_j$ A unit , In the $j+1$ Layer has a $s_{j+1}$ A unit , that ${\Theta }^{(j)}$ It's a $s_{j+1}\times (s_j+1)$ Matrix

8-4 Forward propagation - Model display II

Vectorization of forward propagation ：

• Put ${\Theta }_{10}^{(1)}+{\Theta }_{11}^{(1)}+{\Theta }_{12}^{(1)}+{\Theta }_{13}^{(1)}$ Expressed as $z_1^{(2)}$
• be $a_1^{(2)}=g(z_1^{(2)})$
• Extend to the whole domain , Activation value of the second layer $a^{(2)}=g(z^{(2)})$, among $z^{(2)}={\Theta }^{(1)}{a}^{(1)}$, In addition, you need to add an offset term $a_0^{(2)}=1$

8-5 Examples and understanding I

8-6 Examples and understanding II

The figure above shows the calculation $x_1$ XNOR $x_2$ The neural network of
From the first floor to the second floor, calculate $x_1$ AND $x_2$ obtain $a_1^{(2)}$, Calculation (NOT $x_1$) AND (NOT $x_2$) obtain $a_2^{(2)}$
And then to $a_1^{(2)}$ and $a_2^{(2)}$ by $x_1$ and $x_2$ Calculation $x_1$ OR $x_2$ The result is $x_1$ XNOR $x_2$

8-7 Multivariate classification

There are four outputs ：pedestrian、car、motorcycle、truck
So there are four output units
Output $y^{(i)}$ For one 4 D matrix , May be ：
$$\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right]or\left[\begin{array}{c}0\\ 1\\ 0\\ 0\end{array}\right]or\left[\begin{array}{c}0\\ 0\\ 1\\ 0\end{array}\right]or\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]inOfItsinOneindividual$$
respectively pedestrian or car or motorcycle or truck