Loss function

太过爱你忘了你带给我的痛 2023-02-09 13:22 25阅读 0赞

### Triplet Loss: ###

x i a x\_i^a xia是anchor,  x i p x\_i^p xip是positive ,  x i n x\_i^n xin是negtive  
 ∑ i N \[ ∣ ∣ f ( x i a ) − f ( x i p ) ∣ ∣ 2 − ∣ ∣ f ( x i a ) − f ( x i n ) ∣ ∣ 2 + α \] + \\sum\_i^N\[||f(x\_i^a)-f(x\_i^p)||^2 - || f(x\_i^a)-f(x\_i^n)||^2 + \\alpha\]\_\{+\} ∑iN\[∣∣f(xia)−f(xip)∣∣2−∣∣f(xia)−f(xin)∣∣2\+α\]\+

### Center Loss ###

在cross-entry loss的基础之上，增加同一类的均值loss.  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1RIX05VTQ_size_16_color_FFFFFF_t_70]  
 L = L S + λ L C = − ∑ i = 1 m l o g e W y i T x i + b y i ∑ j = 1 n e W y j T x i + b y j + λ 2 ∑ i = 1 m ∣ ∣ x i − c y i ∣ ∣ 2 2 L=L\_S+\\lambda L\_C = -\\sum\_\{i=1\}^m log \\frac\{e^\{W\_\{y\_i\}^T x\_i + b\_\{y\_i\}\}\}\{\\sum\_\{j=1\}^n e^\{W\_\{y\_j\}^T x\_i + b\_\{y\_j\}\}\} + \\frac\{\\lambda\}\{2\}\\sum\_\{i=1\}^m ||x\_i-c\_\{y\_i\}||^2\_2 L=LS\+λLC=−∑i=1mlog∑j=1neWyjTxi\+byjeWyiTxi\+byi\+2λ∑i=1m∣∣xi−cyi∣∣22

### A-softmax Loss ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1RIX05VTQ_size_16_color_FFFFFF_t_70 1]  
Large Angle Margin  
 L a n g = 1 N ∑ i = 1 − l o g ( e ∣ ∣ x i ∣ ∣ c o s ( m θ y i , i ) e ∣ ∣ x i ∣ ∣ c o s ( m θ y i , i ) + ∑ j ≠ y i e ∣ ∣ x i ∣ ∣ c o s ( θ y i , i ) ) L\_\{ang\}=\\frac\{1\}\{N\}\\sum\_\{i=1\}-log(\\frac\{e^\{||x\_i||cos(m \\theta\_\{y\_i\},i)\}\}\{e^\{||x\_i||cos(m \\theta\_\{y\_i\},i)\} + \\sum\_\{j \\neq y\_i\}e^\{||x\_i||cos(\\theta\_\{y\_i\},i)\}\}) Lang=N1∑i=1−log(e∣∣xi∣∣cos(mθyi,i)\+∑j=yie∣∣xi∣∣cos(θyi,i)e∣∣xi∣∣cos(mθyi,i))

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1RIX05VTQ_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20200519082629127.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1RIX05VTQ==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1RIX05VTQ_size_16_color_FFFFFF_t_70 1]: https://img-blog.csdnimg.cn/202005190829400.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L1RIX05VTQ==,size_16,color_FFFFFF,t_70