Notes for Deep Learning Lessons of Pro. Hung-yi Lee (3)

1737-汪同学

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To be honest, I did not fully understand the process of developing perceptron to nerual network. Today, Pro. Lee help me solve this problem. Well, feel good. Maybe I have not gotten that point, haha.

As we all know, the perceptron model is a linear model. For the following task in which we want to divide these points into two groups (the red go to one group and the blue go to the other), we need to make the output of Class 1 larger than 0.5 and the output of Class 2 smaller than 0.5. However, we can not finish this task by using a linear.
Notes for Deep Learning Lessons of Pro. Hung-yi Lee (3)
How can we finish this task? We can use feature transformation to do that. In other words, using a specific way to change the value of

(

x

1

,

x

2

)

(x_1,x_2)

(x1,x2) to

(

x

1

,

x

2

)

(x_1^{'},x_2^{'})

(x1,x2) with the aim of making them seperable by a linear model.

Notes for Deep Learning Lessons of Pro. Hung-yi Lee (3)
But finding a suitbale transformation is always difficult. We can use neural network to help us finish it. For example, taking the following figure as inllustration, we use the upper perceptron to transfer

     x


     1




   x_1


</span><span class="katex-html"><span class="base"><span class="strut" style="height: 0.58056em; vertical-align: -0.15em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span></span></span> to <span class="katex--inline"><span class="katex"><span class="katex-mathml">





     x


     1




      ′





   x_1^{&#39;}


</span><span class="katex-html"><span class="base"><span class="strut" style="height: 1.19059em; vertical-align: -0.248108em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.94248em;"><span class="" style="top: -2.45189em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class=""></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.827829em;"><span class="" style="top: -2.931em; margin-right: 0.0714286em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.248108em;"><span class=""></span></span></span></span></span></span></span></span></span></span> and the bottom perceptron to transfer <span class="katex--inline"><span class="katex"><span class="katex-mathml">





     x


     2




   x_2


</span><span class="katex-html"><span class="base"><span class="strut" style="height: 0.58056em; vertical-align: -0.15em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.301108em;"><span class="" style="top: -2.55em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.15em;"><span class=""></span></span></span></span></span></span></span></span></span></span> to <span class="katex--inline"><span class="katex"><span class="katex-mathml">





     x


     2




      ′





   x_2^{&#39;}


</span><span class="katex-html"><span class="base"><span class="strut" style="height: 1.19059em; vertical-align: -0.248108em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 0.94248em;"><span class="" style="top: -2.45189em; margin-left: 0em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span class="" style="top: -3.063em; margin-right: 0.05em;"><span class="pstrut" style="height: 2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class=""></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height: 0.827829em;"><span class="" style="top: -2.931em; margin-right: 0.0714286em;"><span class="pstrut" style="height: 2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">′</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height: 0.248108em;"><span class=""></span></span></span></span></span></span></span></span></span></span>, and then these points become seperable by perceptron. All we have to do is to train the parameters to make the transformation suitable for our current dataset. And this task can be done by sorts of optimization algorithm.<br /> <img src="https://img-blog.csdnimg.cn/c73b0493bbe344daa7e5fb1ff2724392.PNG?x-oss-process&#61;image/watermark,type_ZHJvaWRzYW5zZmFsbGJhY2s,shadow_50,text_Q1NETiBAaGVsbG9fSmVyZW15V2FuZw&#61;&#61;,size_20,color_FFFFFF,t_70,g_se,x_16#pic_center" alt="在这里插入图片描述" /><br /> <img src="https://img-blog.csdnimg.cn/66fd1a349e7c4e33a34174983ff4678e.PNG?x-oss-process&#61;image/watermark,type_ZHJvaWRzYW5zZmFsbGJhY2s,shadow_50,text_Q1NETiBAaGVsbG9fSmVyZW15V2FuZw&#61;&#61;,size_20,color_FFFFFF,t_70,g_se,x_16#pic_center" alt="在这里插入图片描述" />

未经允许不得转载:作者:1737-汪同学, 转载或复制请以 超链接形式 并注明出处 拜师资源博客
原文地址:《Notes for Deep Learning Lessons of Pro. Hung-yi Lee (3)》 发布于2021-10-12

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