From then on, I understand convolutional neural network (CNN)

Convolutional neural networks It's something I couldn't figure out anyway , Mainly the name is too “ senior ” 了 , Various articles on the Internet to introduce “ What is convolution ” Especially unbearable . After listening to Wu Enda's online class , Be suddenly enlightened , Finally, I understand what this thing is and why . I will probably use 6~7 An article to explain CNN And realize some interesting applications . After reading it, you should be able to do something you like by yourself .

One 、 Introduction ： boundary detection

Let's look at the simplest example ：“ boundary detection （edge detection）”, Suppose we have such a picture , size 8×8：

The number in the picture represents the pixel value of the position , We know , The larger the pixel value , The brighter the color , So in order to signal , Let's paint the small pixel on the right dark . The dividing line between the two colors in the middle of the figure is the boundary we want to detect .

How to detect this boundary ？ We can design such a   filter （filter, Also known as kernel）, size 3×3：

then , We use this filter, On our pictures “ cover ”, Cover a piece of heel filter After the same large area , Multiply the corresponding elements , Then sum it . After calculating a region , Just move to other areas , Then calculate , Until every corner of the original image is covered . This process is  “ Convolution ”.
（ We don't care what convolution means in Mathematics , We only know in CNN How to calculate in .）
there “ Move ”, It involves a step , Suppose our step size is 1, After covering a place , Just move one space , It's easy to know , In total, it can cover 6×6 Different areas .

that , We will 6×6 Convolution results of regions , Put together a matrix ：

EH ？！ What was found ？
This picture , Light in the middle , Dark on both sides , This shows the boundary in the middle of our original picture , It is reflected here !

From the example above , We found that , We can design specific filter, Let it convolute with the picture , You can recognize some features in the picture , Like the border .
The above example is to detect the vertical boundary , We can also design to detect the horizontal boundary , Just put the just filter rotate 90° that will do . For other features , In theory, as long as we go through fine design , You can always design the right filter Of .

our CNN（convolutional neural network）, Mainly through one by one filter, Constantly extract features , From local characteristics to general characteristics , So as to carry out image recognition and other functions .

So here comes the question , How can we design so many kinds of filter ah ？ First , We may not know about a big push of pictures , What features do we need to identify , secondly , Even if you know the characteristics , Want to really design the corresponding filter, I'm afraid it's not easy , Need to know , The number of features can be thousands .

In fact, after learning neural network , We knew , these filter, We don't need to design at all , Every filter The numbers in , It's just a parameter , We can use a lot of data , Come on   Let the machine go by itself “ Study ” These parameters Well . this , Namely CNN Principle .

Two 、CNN Basic concepts of

1.padding White filling
From the introduction above , We can know , The original image is passing filter After convolution , It's getting smaller , from (8,8) Turned into (6,6). Suppose we roll it again , Then the size becomes (4,4) 了 .

What's the problem with this ？
There are two main problems ：

• Every convolution , The images are all reduced , I can't roll it for several times ;

• Compared to the middle of the picture , The number of times the edge points of the image are calculated in convolution is very small . In this case , Information on the edge is easy to lose .

To solve this problem , We can use padding Methods . Every time we convolute , Fill in the blanks around the picture first , Let the convoluted image be the same size as before , meanwhile , The original edge is also calculated more times .

such as , We put (8,8) Make up the picture of (10,10), So after (3,3) Of filter after , Namely (8,8), No change .

Let's put the above “ Let the size after convolution remain the same ” Of padding The way , be called  “Same” The way ,
Fill in the blank without any filling , be called  “Valid” The way . This is when we use some frameworks , Super parameters to be set .

2.stride step
The convolution we introduced earlier , All default steps are 1, But actually , We can set the steps to other values .
such as , about (8,8) The input of , We use it (3,3) Of filter,
If stride=1, The output of (6,6);
If stride=2, The output of (3,3);（ The example here is not very good , Divide and keep rounding down ）

3.pooling Pooling
This pooling, It is to extract the main features of a certain region , And reduce the number of parameters , Prevent model over fitting .
Like the following MaxPooling, A 2×2 The window of , And take stride=2：

except MaxPooling, also AveragePooling, As the name suggests, it is to take the average value of that area .

4. For multichannel （channels） Volume of pictures product （ important ！）
This needs to be mentioned separately . Color images , It's usually RGB Three channels （channel） Of , So there are three dimensions of input data ：（ Long , wide , passageway ）.
For example, a 28×28 Of RGB picture , Dimension is (28,28,3).

In the front Introduction , The input picture is 2 Dimensional (8,8),filter yes (3,3), The output is 2 Dimensional (6,6).

If the input image is three-dimensional （ That is to say, one more channels）, For example (8,8,3), This is the time , our filter The dimension of is going to be (3,3,3) 了 , its   The last dimension is going to follow the input channel The dimensions are the same .
Convolution at this time , It's the three one. channel All the elements of the corresponding multiplication sum , That's before 9 The sum of products , Now it is 27 The sum of products . therefore , The dimensions of output do not change . still (6,6).

however , In general , We will   More use filters Simultaneous convolution , such as , If we use 4 individual filter Words , that   The dimension of the output changes to (6,6,4).

I specially drew the following picture , To show the above process ：

The input image is (8,8,3),filter Yes 4 individual , All sizes are (3,3,3), The output is (6,6,4).
I think this picture is very clear , And gives 3 and 4 How did these two key figures come from , So I won't be wordy （ This picture made me at least 40 minute ）.

Actually , If we apply the neural network symbols we learned before to look at CNN Words ,

• Our input image is X,shape=(8,8,3);

• 4 individual filters In fact, it is the parameters of the first layer Shenjin network W1,,shape=(3,3,3,4), This 4 It means having 4 individual filters;

• Our output , Namely Z1,shape=(6,6,4);

• There should also be an activation function , such as relu, After activation ,Z1 Turn into A1,shape=(6,6,4);

therefore , In the picture above , I add an activation function , Mark the corresponding part , That's it ：

【 Personally feel , Such a good picture is not collected , What a pity 】

3、 ... and 、CNN Structure of

We already know convolution above （convolution）、 Pooling （pooling） And white filling （padding） How it works , Let's take a look CNN Overall structure , It contains 3 Seed layer （layer）：

1. Convolutional layer（ Convolution layer —CONV）
By filter filters And the activation function .
The general parameters to be set include filters The number of 、 size 、 step , as well as padding yes “valid” still “same”. Of course , It also includes choosing what activation function .

2. Pooling layer （ Pooling layer —POOL）
There are no parameters to learn , Because the parameters here are all set by us , Or Maxpooling, Or Averagepooling.
You need to specify a super parameter , It includes Max still average, Window size and step size .
Usually , What we use more is Maxpooling, And the general size is (2,2) In steps of 2 Of filter, such , after pooling after , The length and width of the input will be reduced 2 times ,channels unchanged .

3. Fully Connected layer（ Fully connected layer —FC）
This is not mentioned before , Because this is the guy we are most familiar with , It is the most common layer of neural network we learned before , It's a row of neurons . Because every unit in this layer is connected with every unit in the previous layer , So it's called “ Full connection ”.
Super parameter to be specified here , It's just the number of neurons , And activation functions .

Next , Let's look at one CNN The appearance of , To get the right CNN Some perceptual knowledge ：

Above this CNN It's the one I casually patted on the forehead . Its structure can be used ：
X→CONV(relu)→MAXPOOL→CONV(relu)→FC(relu)→FC(softmax)→Y
To express .

Here's the thing to note , After several convolutions and pooling , We   Finally, the multi-dimensional data will be processed first “ flat ”, That is the  (height,width,channel) The data is compressed to a length of  height × width × channel  One dimensional array of , And then with  FC layer Connect , After that, it is the same as the ordinary neural network .

You can see from the figure , With the development of Internet , Our image （ Strictly speaking, those in the middle can't be called images , But for convenience , Let's say so ） It's getting smaller , however channels But it's getting bigger and bigger . The representation in the figure is that the area of the cuboid facing us is getting smaller and smaller , But the length is getting longer .

Four 、 Convolutional neural networks VS. Traditional neural networks

In fact, looking back ,CNN Like the neural network we learned before , There is no big difference .
Traditional neural networks , In fact, there are many FC Layers are superimposed .
CNN, It's nothing more than putting FC Changed to CONV and POOL, It's made up of neurons layer, It's changed from filters Composed of layer.

that , Why do you want to change like this ？ What are the benefits ？
Specifically speaking, there are two points ：

1. Parameter sharing mechanism （parameters sharing）
Let's compare the layers of traditional neural networks with filters Composed of CONV layer ：
Suppose our image is 8×8 size , That is to say 64 Pixel , Suppose we use a with 9 Full connection layer of units ：

How many parameters do we need in this layer ？ need  64×9 = 576 Parameters （ Let's not consider the offset term b）. Because every link needs a weight w.

So let's see   There are also 9 Unit filter What is it like ：

In fact, you don't need to look , There are only a few parameters for a few units , So the total is 9 Parameters ！

because , For different areas , We all share the same filter, So share the same set of parameters .
And that makes sense , Through the previous explanation, we know ,filter It is used to detect features , Generally, that feature is likely to appear in more than one place , such as “ Vertical boundary ”, It may appear more in one picture , that   We share the same filter Not only is it reasonable , And it should be done .

thus it can be seen , Parameter sharing mechanism , Let us greatly reduce the number of network parameters . such , We can use fewer parameters , Train better models , The typical way is to get twice the result with half the effort , And it can effectively   Avoid overfitting .
Again , because filter Parameter sharing , Even if the picture has some translation operation , We can still recognize features , It's called  “ Translation invariance ”. therefore , The model is more robust .

2. Sparsity of connections （sparsity of connections）
It can be seen from the operation of convolution , Output any unit in the image , It is only related to a part of the input image system ：

And in the traditional neural network , Because it's all connected , So any unit of output , It's influenced by all the input units . In this way, the recognition effect of the image will be greatly reduced . Compare , Each area has its own characteristics , We don't want it to be affected by other regions .

It's because of these two advantages , bring CNN Beyond the traditional NN, It opens a new era of neural networks