常用损失函数

客官°小女子只卖身不卖艺 2023-01-11 01:11 10阅读 0赞

## 1、均方误差（回归） ##

[https://www.cnblogs.com/gaona666/p/12302484.html][https_www.cnblogs.com_gaona666_p_12302484.html]

**MSE是真实值与预测值的差值的平方然后求和平均。**

![4e40ccfc8c012bdd3949248a20d83f91.png][]

## ##

范围\[0,+∞)，当预测值与真实值完全相同时为0，误差越大，该值越大。

**RMSE （均方根误差）（Root Mean Square Error）**

### ![01e6944ed47a8582fdd2e3e369051aca.png][] ###

**MAE （平均绝对误差）（Mean Absolute Error）**

![e3376b2e8ec52690a1e48667551ac9d0.png][]

在机器学习中均方误差可以用来作为模型的损失函数，用来预测和回归，均方误差越小，说明模型预测的越准确，反之则越不准确。总的来说，均方差是数据样本与均值的关系，而均方误差是数据样本与真实值之间的关系，在实际工作中根据需要来选择使用均方差还是均方误差。

## 2、交叉熵损失（分类） ##

[https://zhuanlan.zhihu.com/p/35709485][https_zhuanlan.zhihu.com_p_35709485]

[https://blog.csdn.net/b1055077005/article/details/100152102][https_blog.csdn.net_b1055077005_article_details_100152102]

[https://zhuanlan.zhihu.com/p/38241764][https_zhuanlan.zhihu.com_p_38241764]

# #

## 3、正则化损失 ##

[https://blog.csdn.net/u013289254/article/details/99694412][https_blog.csdn.net_u013289254_article_details_99694412]

**L1损失函数**： 基于逐像素比较差异，然后取绝对值

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTMyODkyNTQ_size_16_color_FFFFFF_t_70][]

**L2损失函数**： 基于逐像素比较差异，然后取平方

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTMyODkyNTQ_size_16_color_FFFFFF_t_70 1][]

## 4、iou损失 ##

[参考][Link 1]

iou=（box1与box2的交集）/(box1与box2的并集)

box1与box2的交集：矩形与矩形交集还是矩形只要获得该矩形的左上右下坐标即可，如下图

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3_size_16_color_FFFFFF_t_70][]

### ①、普通的iou损失 ###

**       ![L\_\{IoU\}=1-IoU][L_IoU_1-IoU]**

**         存在缺点：无法反应距离大小（IoU=0时），loss=1时，没有梯度，无法进行训练学习**

### ②、GIOU(Generalized Intersection over Union) ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3_size_16_color_FFFFFF_t_70 1][]

![202101282205446.png][]

**          Ac：两个框的最小闭包区域面积（同时包含了预测框和真实框的最小框的面积）**

**          U：两个框并集区域面积**

![20210128221220660.png][]

### ③、DIOU(Distance-IoU) ###

![20210128221630361.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3_size_16_color_FFFFFF_t_70 2][]

b,b(gt)分别表示预测框与真实框的中心点，ρ表示两个中心点的欧式距离，C表示两框闭包区域对角线距离

![20210128221706966.png][]

### ④、CIOU ###

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3_size_16_color_FFFFFF_t_70 3][]

参考：

[https://zhuanlan.zhihu.com/p/47202768][https_zhuanlan.zhihu.com_p_47202768]

[https://zhuanlan.zhihu.com/p/58883095][https_zhuanlan.zhihu.com_p_58883095]

[https_www.cnblogs.com_gaona666_p_12302484.html]: https://www.cnblogs.com/gaona666/p/12302484.html
[4e40ccfc8c012bdd3949248a20d83f91.png]: /images/20221119/99663aebb485449a97ce59e9fc7fa81c.png
[01e6944ed47a8582fdd2e3e369051aca.png]: https://img-blog.csdnimg.cn/img_convert/01e6944ed47a8582fdd2e3e369051aca.png
[e3376b2e8ec52690a1e48667551ac9d0.png]: https://img-blog.csdnimg.cn/img_convert/e3376b2e8ec52690a1e48667551ac9d0.png
[https_zhuanlan.zhihu.com_p_35709485]: https://zhuanlan.zhihu.com/p/35709485
[https_blog.csdn.net_b1055077005_article_details_100152102]: https://blog.csdn.net/b1055077005/article/details/100152102
[https_zhuanlan.zhihu.com_p_38241764]: https://zhuanlan.zhihu.com/p/38241764
[https_blog.csdn.net_u013289254_article_details_99694412]: https://blog.csdn.net/u013289254/article/details/99694412
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTMyODkyNTQ_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20190817161434452.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTMyODkyNTQ=,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTMyODkyNTQ_size_16_color_FFFFFF_t_70 1]: https://img-blog.csdnimg.cn/20190817161444696.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3UwMTMyODkyNTQ=,size_16,color_FFFFFF,t_70
[Link 1]: https://zhuanlan.zhihu.com/p/94799295
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20210117211849411.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3,size_16,color_FFFFFF,t_70
[L_IoU_1-IoU]: https://private.codecogs.com/gif.latex?L_%7BIoU%7D%3D1-IoU
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3_size_16_color_FFFFFF_t_70 1]: https://img-blog.csdnimg.cn/2021012822432995.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3,size_16,color_FFFFFF,t_70
[202101282205446.png]: https://img-blog.csdnimg.cn/202101282205446.png
[20210128221220660.png]: https://img-blog.csdnimg.cn/20210128221220660.png
[20210128221630361.png]: https://img-blog.csdnimg.cn/20210128221630361.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3_size_16_color_FFFFFF_t_70 2]: https://img-blog.csdnimg.cn/20210128225020329.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3,size_16,color_FFFFFF,t_70
[20210128221706966.png]: https://img-blog.csdnimg.cn/20210128221706966.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3_size_16_color_FFFFFF_t_70 3]: https://img-blog.csdnimg.cn/20210128221927339.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L20wXzM3MjY0Mzk3,size_16,color_FFFFFF,t_70
[https_zhuanlan.zhihu.com_p_47202768]: https://zhuanlan.zhihu.com/p/47202768
[https_zhuanlan.zhihu.com_p_58883095]: https://zhuanlan.zhihu.com/p/58883095