当前位置:网站首页>[CV] Wu Enda machine learning course notes | Chapter 8
[CV] Wu Enda machine learning course notes | Chapter 8
2022-07-07 07:49:00 【Fannnnf】
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
Catalog
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 ) = 1 1 + e − θ T X g(z)=\frac{1}{1+e^{-θ^TX}} g(z)=1+e−θTX1 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 ) a_i^{(j)} ai(j) To represent the j j j Layer of the first i i i Activation items of neurons (“activation” of unit i i i in layer j j j), The so-called activation term refers to the value calculated and output by a specific neuron
- use Θ ( j ) \Theta^{(j)} Θ(j) Says from the first j j j Layer to tier j + 1 j+1 j+1 Layer weight matrix ( Parameter matrix ), That's what happened before θ \theta θ matrix ( Previous θ \theta θ It can be called parameter p a r a m e t e r s parameters parameters It can also be called weight w e i g h t s weights weights)
- a 1 ( 2 ) a_1^{(2)} a1(2)、 a 2 ( 2 ) a_2^{(2)} a2(2) and a 3 ( 2 ) a_3^{(2)} a3(2) The calculation formula of has been written in the above figure
- among Θ ( 1 ) \Theta^{(1)} Θ(1) It's a 3 × 4 3×4 3×4 Matrix
- If the neural network is in the j j j Layer has a s j s_j sj A unit , In the j + 1 j+1 j+1 Layer has a s j + 1 s_{j+1} sj+1 A unit , that Θ ( j ) \Theta^{(j)} Θ(j) It's a s j + 1 × ( s j + 1 ) s_{j+1}×(s_j+1) sj+1×(sj+1) Matrix
8-4 Forward propagation - Model display II
Vectorization of forward propagation :
- Put Θ 10 ( 1 ) + Θ 11 ( 1 ) + Θ 12 ( 1 ) + Θ 13 ( 1 ) \Theta^{(1)}_{10}+\Theta^{(1)}_{11}+\Theta^{(1)}_{12}+\Theta^{(1)}_{13} Θ10(1)+Θ11(1)+Θ12(1)+Θ13(1) Expressed as z 1 ( 2 ) z_1^{(2)} z1(2)
- be a 1 ( 2 ) = g ( z 1 ( 2 ) ) a_1^{(2)}=g(z_1^{(2)}) a1(2)=g(z1(2))
- Extend to the whole domain , Activation value of the second layer a ( 2 ) = g ( z ( 2 ) ) a^{(2)}=g(z^{(2)}) a(2)=g(z(2)), among z ( 2 ) = Θ ( 1 ) a ( 1 ) z^{(2)}=\Theta^{(1)}a^{(1)} z(2)=Θ(1)a(1), In addition, you need to add an offset term a 0 ( 2 ) = 1 a^{(2)}_0=1 a0(2)=1
8-5 Examples and understanding I
8-6 Examples and understanding II
The figure above shows the calculation x 1 x_1 x1 XNOR x 2 x_2 x2 The neural network of
From the first floor to the second floor, calculate x 1 x_1 x1 AND x 2 x_2 x2 obtain a 1 ( 2 ) a_1^{(2)} a1(2), Calculation (NOT x 1 x_1 x1) AND (NOT x 2 x_2 x2) obtain a 2 ( 2 ) a_2^{(2)} a2(2)
And then to a 1 ( 2 ) a_1^{(2)} a1(2) and a 2 ( 2 ) a_2^{(2)} a2(2) by x 1 x_1 x1 and x 2 x_2 x2 Calculation x 1 x_1 x1 OR x 2 x_2 x2 The result is x 1 x_1 x1 XNOR x 2 x_2 x2
8-7 Multivariate classification
There are four outputs :pedestrian、car、motorcycle、truck
So there are four output units
Output y ( i ) y^{(i)} y(i) For one 4 D matrix , May be :
[ 1 0 0 0 ] or [ 0 1 0 0 ] or [ 0 0 1 0 ] or [ 0 0 0 1 ] in Of Its in One individual \begin{bmatrix} 1\\ 0\\ 0\\ 0\\ \end{bmatrix} or \begin{bmatrix} 0\\ 1\\ 0\\ 0\\ \end{bmatrix} or \begin{bmatrix} 0\\ 0\\ 1\\ 0\\ \end{bmatrix} or \begin{bmatrix} 0\\ 0\\ 0\\ 1\\ \end{bmatrix} One of them ⎣⎢⎢⎡1000⎦⎥⎥⎤ or ⎣⎢⎢⎡0100⎦⎥⎥⎤ or ⎣⎢⎢⎡0010⎦⎥⎥⎤ or ⎣⎢⎢⎡0001⎦⎥⎥⎤ in Of Its in One individual
respectively pedestrian or car or motorcycle or truck
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