让我们来看看第四幅图像。
Let’s look at the fourth image.
该图给认为是5的概率为47.12%。
It is classified as a 5 by 47.12%probability.
同时，它被认为是3的概率高达32.08%。
At the same time, it could be a 3 by apretty high probability of 32.08%.
让我们看看究竟发生了什么
Let’s see what happened.
输入图像看起来是一个被挤压的5。
The input image appears to be a squeezed 5.
此外，神经网络发现了一些类似于3特征中的水平线，因此对数字3给出了较高概率。
Furthermore, the neural network finds somehorizontal lines that resemble features of a 3, therefore giving that a highprobability.
在这种情况下，神经网络应该被训练以适应更多的多样性，以提高其分类性能。
In this case, the neural network should betrained to have more variety in the training data in order to improve itsperformance.
图4-19 为了提高神经网络的性能，神经网络可能需要通过训练以适应更多的多样性变化Theneural network may have to be trained to have more variety in the training datain order to improve its performance
最后，将第五幅图像认为是5的概率为98.18%。
Finally, the fifth image is classified as a5 by 98.18% probability.
这从第五幅图像中识别并不奇怪。
It is no wonder when we see the inputimage.
然而，这幅图像与第四幅图像几乎相同。
However, this image is almost identical tothe fourth image.
它只是在图像的顶部和底部增加了两个额外的像素。
It merely has two additional pixels on thetop and bottom of the image.
仅仅延伸水平线会导致被识别为5的概率急剧增加。
Just extending the horizontal lines resultsin a dramatic increase in the probability of being a 5.
在第四幅图像中，数字5的水平特征并不具有显著性。
The horizontal feature of a 5 is not assignificant in the fourth image.
通过增强这个水平特征，第五幅图像被正确地识别为5，如图4-20所示。
By enforcing this feature, the fifth imageis correctly classified as a 5, as shown in Figure 4-20.
图4-20 第五幅图像被正确地识别为5The fifth image iscorrectly classified as a 5
小结（Summary）
本章涵盖以下概念：
This chapter covered the followingconcepts:
对于神经网络分类器，输出节点数目和激活函数的选择通常取决于它是用于二元分类（两类）还是用于多元分类（三类或更多）。
For the neural network classifier, theselection of the number of output nodes and activation function usually dependson whether it is for a binary classification (two classes) or for a multiclassclassification (three or more classes).
对于二元分类，神经网络是由单个输出节点和sigmoid激活函数构成的。
For binary classification, the neuralnetwork is constructed with a single output node and sigmoid activationfunction.
训练数据的正确输出被转换为激活函数的最大值和最小值。
The correct output of the training data isconverted to the maximum and minimum values of the activation function.
学习规则的代价函数采用交叉熵函数。
The cost function of the learning rule employsthe cross entropy function。
对于多元分类，神经网络输出节点数目与分类类别数相同。
For a multiclass classification, the neuralnetwork includes as many output nodes as the number of classes.
——本文译自Phil Kim所著的《Matlab Deep Learning》
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