From eb61579feb2c9dcafd9647a0da7f92b74eae8740 Mon Sep 17 00:00:00 2001 From: xiaowuhu Date: Tue, 9 Apr 2019 14:49:10 +0800 Subject: [PATCH] Xiaowuhu/1202 (#186) * update * Create multiple_result_true.png * fix --- .../06.3-线性二分类结果可视化.md | 2 +- .../06.6-线性多分类结果可视化.md | 39 ++++++++++++++---- .../Images/6/multiple_result_area.png | Bin 0 -> 34129 bytes .../Images/6/multiple_result_true.png | Bin 0 -> 25410 bytes .../微软-方案1/NeuralNetwork/ch06/level4_ShowMultipleResult.py | 5 ++- 5 files changed, 34 insertions(+), 12 deletions(-) create mode 100644 B-教学案例与实践/B6-神经网络基本原理简明教程/Images/6/multiple_result_area.png create mode 100644 B-教学案例与实践/B6-神经网络基本原理简明教程/Images/6/multiple_result_true.png diff --git a/B-教学案例与实践/B6-神经网络基本原理简明教程/06.3-线性二分类结果可视化.md b/B-教学案例与实践/B6-神经网络基本原理简明教程/06.3-线性二分类结果可视化.md index 3e5bf892..a70dd27e 100644 --- a/B-教学案例与实践/B6-神经网络基本原理简明教程/06.3-线性二分类结果可视化.md +++ b/B-教学案例与实践/B6-神经网络基本原理简明教程/06.3-线性二分类结果可视化.md @@ -129,4 +129,4 @@ if __name__ == '__main__': 1. 我们用归一化前的数据画的第一张图,所以坐标范围是[0,10][0,10] 2. 我们用归一化后的数据画的第二张图,所以坐标范围是[0,1][0,1] -代码位置:ch06, Level0_BaseClassification.py, Level1_BinaryClassification.py, Level2_ShowBinaryResult.py \ No newline at end of file +代码位置:ch06, Level0, Level1, Level2 \ No newline at end of file diff --git a/B-教学案例与实践/B6-神经网络基本原理简明教程/06.6-线性多分类结果可视化.md b/B-教学案例与实践/B6-神经网络基本原理简明教程/06.6-线性多分类结果可视化.md index 528cec19..1bfe4df6 100644 --- a/B-教学案例与实践/B6-神经网络基本原理简明教程/06.6-线性多分类结果可视化.md +++ b/B-教学案例与实践/B6-神经网络基本原理简明教程/06.6-线性多分类结果可视化.md @@ -64,11 +64,11 @@ $$Z = W \cdot X+B$$ 实际上是以下计算的组合: -$$Z1 = W_1 \cdot X + B_1=w_{11} \cdot x_1 + w_{12} \cdot x_2 + b_1$$ +$$Z1 = W1 \cdot X + B1=w_{11} \cdot x_1 + w_{12} \cdot x_2 + b_1$$ -$$Z2 = W_2 \cdot X + B_2=w_{21} \cdot x_1 + w_{22} \cdot x_2 + b_2 $$ +$$Z2 = W2 \cdot X + B2=w_{21} \cdot x_1 + w_{22} \cdot x_2 + b_2 $$ -$$Z3 = W_3 \cdot X + B_3=w_{31} \cdot x_1 + w_{32} \cdot x_2 + b_3$$ +$$Z3 = W3 \cdot X + B3=w_{31} \cdot x_1 + w_{32} \cdot x_2 + b_3$$ 如何确定(Z1|Z2)之间的边界呢?那只要令Z1=Z2就行了...... @@ -136,25 +136,46 @@ if __name__ == '__main__': +【图6.6.2 想象中的一对一方式的分类结果图】 + 上图中: - 绿色线是1|2的边界,不考虑第3类 - 蓝色线是1|3的边界,不考虑第2类 - 红色线是2|3的边界,不考虑第1类 -我们只看红色的第1类,当要区分1|2和1|3时,神经网络实际是用了两条直线作为边界,它并没有画出下面这样的线来: +我们只看红色的第1类,当要区分1|2和1|3时,神经网络实际是用了两条直线(绿色和蓝色)作为边界,它并没有画出下面这样的线来: -上面这张图是所谓的一对多的方式,只看红线,它把红点和其它点一次分割成型。而实际的分类结果图中,是把每两个类别都分别分割,所以神经网络的工作方式是一对一方式! +【图6.6.3 想象中的一对多方式的分类】 -木头:嗯....那为什么从Softmax函数看,它只是取了一个最大值呢?这不是一对多的行为吗? +上面这张图是我们想象的所谓的一对多的方式,只看红线,它把红点和其它点一次分割成型。而神经网络没有画出这样的线来,这意味着神经网络不是一对多方式吗?而且 -铁柱:这就是对Softmax函数的理解不正确了。如果是max函数,对于[3,1,-3]只取[1,0,0],确实是一对多,但是Softmax在计算过程中,是考虑类每个类别的因素的,对于[3,1,-3]取值是[0.88,0.12,0.00],这可以解读为第一类 vs 第二类 = 0.88 vs 0.12,第一类 vs 第三类 = 0.88 vs 0.00,所以它是一对一的关系。 +事情还没有那么简单!有了图6.6.2,并不意味着它是一对一方式;而没有得到图6.6.3,并不意味着它就不是一对多方式。 +木头:嗯...哦...有点儿绕... -代码位置:ch06, Level0_BaseClassification.py, level3_MultipleClassification.py, level4_ShowMultipleResult.py +铁柱:图6.6.2是我们依靠令Z1=Z2, Z2=Z3, Z3=Z1三个等式得到的,但实际上神经网络的工作方式不是这样的,给定屏幕上任意点,分类器总会给你一个概率,告诉你该点分别属于三个区域的概率,比如: -注:代码中还有一个小彩蛋,ShowAreaResult()函数,有兴趣的同学可以自己试一下,放开注释即可。 +$$[0.7,0.2,0.1]$$ + +意为属于第一个区域的概率为0.7,属于后两个区域的概率为0.2与0.1。而Z1=Z2等三个等式,是我们人为地画了三条直线,而实际上,它们不应该是直线,而是线段: + + + +【图6.6.4 分段线性分类结果】 + +木头:如何证明这一点呢? + +铁柱:代码中还有一个小彩蛋,ShowAreaResult()函数,有兴趣的同学可以自己试一下,放开注释即可以看到下图: + + + +【图6.6.5】 + +由于精度较低(我们用了50x50的网格来模拟整个区域),所以看到一些锯齿,不用管它,只看趋势,完全与图6.6.4吻合,所以说明神经网络是用分段线性的方法,来做一对多的分类,而不是像我们想象的图6.6.3那样的单条直线。 + +代码位置:ch06, Level0, level3, level4 **课后作业** diff --git a/B-教学案例与实践/B6-神经网络基本原理简明教程/Images/6/multiple_result_area.png b/B-教学案例与实践/B6-神经网络基本原理简明教程/Images/6/multiple_result_area.png new file mode 100644 index 0000000000000000000000000000000000000000..797220498e9a3126d52ac5d413ff53608487b16b GIT binary patch literal 34129 zcmeFY1ydd2(k{9nBte2pfZzmocL?qfWZ~}a?(R+!+%34f26uONcX!UP_dRvacmKhy zx~ZWuEY`fzZ}-#PPxplWlo5r8#fAleK=9&XLh>LGqz?!Lu@3zS_=II*c^mi-%3eTR z5gPdC0c{Wh{0?IyrfLrYA?m*WK>Xz^Fag<^?F3Z-|*2Q9{ 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