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Tensorflow学习笔记之一：训练你的第一个神经网络——基础分类

前言

本教程来自Tensorflow官方教程 tensorflow.org,网站和大部分学习资源被墙，请自主进行科学上网。文章旨在记录自己学习机器学习相关知识的过程，如对您学习过程有所助益，不胜荣幸。文章是个人翻译，水平有限，希望理解。教程采用Anaconda版本的Python，是Python3代码,编辑器是Pycharm。

原文Github地址

原文colab地址(科学上网)

环境准备

本教程将会训练一个神经网络模型使它能够将衣服图片进行分类，例如鞋子和衬衣。你并不需要完全理解教程的每一处细节。此教程将会带你快速浏览一个完整的Tensorflow 程序是如何运行的。

本教程使用了tf.keras。它是Tensorflow的一个高级API，主要用于建立和训练模型。tf.keras的发明者现在在谷歌工作，并且tf.keras已经作为了Tensorflow的官方框架。tf.keras比较有利于机器学习的初学者进行机器学习具有用户友好、模块灵活、可扩展性强的特点。

你可以使用下面Python代码导入keras模块：

# TensorFlow and tf.keras
import tensorflow as tf
from tensorflow import keras

# Helper libraries
import numpy as np
import matplotlib.pyplot as plt

print(tf.__version__)

运行Python代码结果为：

1.10.0

导入Fashion MNIST 数据集

本教程将会使用的Fashion MNIST数据集包含了70000张10个不同种类衣服的灰度图。它的每一张图片都是单独的一个衣物，并且规格是 28 x 28像素，样例如下：


Tensorflow学习笔记之一：训练你的第一个神经网络——基础分类_第1张图片
fashion-mnist-sprite.png

Fashion MNIST和经典的MNIST一样是免费的数据集。MNIST数据集经常作为机器学习领域的“hello world”数据集提供给初学者。经典的MNIST数据集包含了60000个手写体的数字和他们对应的数字标签。样例如下：


Tensorflow学习笔记之一：训练你的第一个神经网络——基础分类_第2张图片
MnistExamples.png

本教程使用的是Fashion MNIST，它比MNIST数据集可能略微有一些难度，但是它和MNIST一样都是比较轻盈的数据集，有利于验证我们的算法是否如预期一样运行，是非常有利于初学者的。

我们将会使用60000张图片作为训练数据来训练神经网络，使用10000张图片作为测试数据来评估训练完成后的神经网络。现在大家可以直接使用Tensorflow的代码:

fashion_mnist = keras.datasets.fashion_mnist

(train_images, train_labels), (test_images, test_labels) = fashion_mnist.load_data()

随后开始下载(可能需要科学上网)

Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-labels-idx1-ubyte.gz
32768/29515 [=================================] - 0s 0us/step
Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/train-images-idx3-ubyte.gz
26427392/26421880 [==============================] - 1s 0us/step
Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-labels-idx1-ubyte.gz
8192/5148 [===============================================] - 0s 0us/step
Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/t10k-images-idx3-ubyte.gz
4423680/4422102 [==============================] - 0s 0us/step

我们加载数据集会返回NumPy arrays：

  • train_images和train_labels 是训练集，也就是我们的模型进行学习的数据

  • 模型通过测试数据集进行测试也就是 test_images和test_labels

  • images被当作是28x28的NumPy arrays，每个像素点值在0～255之间。

  • labels 则是0～9的数字分类，分别是以下意义：

Label class
0 T-shirt/top
1 Trouser
2 Pullover
3 Dress
4 Coat
5 Sandal
6 Shirt
7 Sneaker
8 Bag
9 Ankle boot

我们可以创建一个1x10的矩阵来保存衣服的名字：

class_names = ['T-shirt/top', 'Trouser', 'Pullover', 'Dress', 'Coat', 
               'Sandal', 'Shirt', 'Sneaker', 'Bag', 'Ankle boot']

查看数据

我们可以通过几行代码简单观察一下我们的初始数据：

print(train_images.shape)

(60000, 28, 28)

说明训练数据集是一个60000 x 28 x 28 的矩阵，也就是拥有60000张图片，每张图片的像素是 28 x 28

查看labels大小：

print(len(train_labels))

60000

并且每一个label都是一个0～9之间的数字

print(train_labels)

[9 0 0 ... 3 0 5]

同样的，我们可以查看测试数据，一样的，它有10000张图片，每张都是28 x 28 ，标签大小也是10000：

print(test_images.shape)

(10000, 28, 28)

print(len(test_labels))

10000

数据预处理

数据集在训练神经网络之前必须经过预处理。如果你直接打印第一张图片，你会看到一个矩阵，它里面的每一个像素的值都是0～255之间的值：

print(train_images[0])

[[  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   0   0]
 [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   0   0]
 [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   0   0]
 [  0   0   0   0   0   0   0   0   0   0   0   0   1   0   0  13  73   0  0   1   4   0   0   0   0   1   1   0]
 [  0   0   0   0   0   0   0   0   0   0   0   0   3   0  36 136 127  62 54   0   0   0   1   3   4   0   0   3]
 [  0   0   0   0   0   0   0   0   0   0   0   0   6   0 102 204 176 134 144 123  23   0   0   0   0  12  10  0]
 [  0   0   0   0   0   0   0   0   0   0   0   0   0   0 155 236 207 178 107 156 161 109  64  23  77 130  72  15]
 [  0   0   0   0   0   0   0   0   0   0   0   1   0  69 207 223 218 216 216 163 127 121 122 146 141  88 172  66]
 [  0   0   0   0   0   0   0   0   0   1   1   1   0 200 232 232 233 229 223 223 215 213 164 127 123 196 229   0]
 [  0   0   0   0   0   0   0   0   0   0   0   0   0 183 225 216 223 228 235 227 224 222 224 221 223 245 173   0]
 [  0   0   0   0   0   0   0   0   0   0   0   0   0 193 228 218 213 198 180 212 210 211 213 223 220 243 202   0]
 [  0   0   0   0   0   0   0   0   0   1   3   0  12 219 220 212 218 192 169 227 208 218 224 212 226 197 209  52]
 [  0   0   0   0   0   0   0   0   0   0   6   0  99 244 222 220 218 203 198 221 215 213 222 220 245 119 167  56]
 [  0   0   0   0   0   0   0   0   0   4   0   0  55 236 228 230 228 24  232 213 218 223 234 217 217 209  92   0]
 [  0   0   1   4   6   7   2   0   0   0   0   0 237 226 217 223 222 219 222 221 216 223 229 215 218 255  77   0]
 [  0   3   0   0   0   0   0   0   0  62 145 204 228 207 213 221 218 208 211 218 224 223 219 215 224 244 159   0]
 [  0   0   0   0  18  44  82 107 189 228 220 222 217 226 200 205 211 230 224 234 176 188 250 248 233 238 215   0]
 [  0  57 187 208 224 221 224 208 204 214 208 209 200 159 245 193 206 223 255 255 221 234 221 211 220 232 246   0]
 [  3 202 228 224 221 211 211 214 205 205 205 220 240  80 150 255 229 221 188 154 191 210 204 209 222 228 225   0]
 [ 98 233 198 210 222 229 229 234 249 220 194 215 217 241  65  73 106 117 168 219 221 215 217 223 223 224 229  29]
 [ 75 204 212 204 193 205 211 225 216 185 197 206 198 213 240 195 227 245 239 223 218 212 209 222 220 221 230  67]
 [ 48 203 183 194 213 197 185 190 194 192 202 214 219 221 220 236 225 216 199 206 186 181 177 172 181 205 206 115]
 [  0 122 219 193 179 171 183 196 204 210 213 207 211 210 200 196 194 191 195 191 198 192 176 156 167 177 210  92]
 [  0   0  74 189 212 191 175 172 175 181 185 188 189 188 193 198 204 209 210 210 211 188 188 194 192 216 170  0]
 [  2   0   0   0  66 200 222 237 239 242 246 243 244 221 220 193 191 179 182 182 181 176 166 168  99  58   0   0]
 [  0   0   0   0   0   0   0  40  61  44  72  41  35   0   0   0   0   0 0   0   0   0   0 0   0   0   0   0]
 [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0 0   0   0   0   0   0   0   0   0   0]
 [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0 0   0   0   0   0   0   0   0   0   0]]

我们可以用几行绘图代码来更清楚的展示它：

plt.figure()
plt.imshow(train_images[0])
plt.colorbar()
plt.gca().grid(False)
plt.show()
Tensorflow学习笔记之一：训练你的第一个神经网络——基础分类_第3张图片
train_images[0].jpg

我们需要把它转换成0～1之间的浮点数来投递给神经网络，为此我们可以将矩阵中的所有值除以255：

train_images = train_images / 255.0

test_images = test_images / 255.0

随后我们可以尝试展示25张图片和他们的对应的分类标签：

plt.figure(figsize=(10,10))
for i in range(25):
    plt.subplot(5,5,i+1)
    plt.xticks([])
    plt.yticks([])
    plt.grid('off')
    plt.imshow(train_images[i],cmap='binary')
    plt.xlabel(class_names[train_labels[I]])
plt.show()

/usr/local/lib/python3.5/dist-packages/matplotlib/cbook/deprecation.py:107: MatplotlibDeprecationWarning: Passing one of 'on', 'true', 'off', 'false' as a boolean is deprecated; use an actual boolean (True/False) instead.
  warnings.warn(message, mplDeprecation, stacklevel=1)
Tensorflow学习笔记之一：训练你的第一个神经网络——基础分类_第4张图片
25张图片

建立模型

建立神经网络需要配置神经网络的每一层，然后编译整个模型。

建立神经层

Tensorflow学习笔记之一：训练你的第一个神经网络——基础分类_第5张图片
神经网络的基本结构

神经网络是一个具有多层次结构的数学模型，其可以简单分为3部分，输入层、隐藏层、和输出层。输入层一般是需要学习的数据入口，数据由此进入神经网络，例如图片可以转化为矩阵输入。隐藏层可能包含多层，上图仅画出了一个，数据在隐藏层进行加工处理就像人类的感知过程一样。输出层往往是对数据的预测结果，例如输出图片中的数字是几，衣服的类型是什么。大多数深度学习的隐藏层数往往很多，神经网络中有许多参数，神经网络在不断学习过程中不断调整这些参数来使自身的预测更加精确。

Tensorflow的Keras模块可以使用极简的代码构建神经网络的模型结构：

model = keras.Sequential([
    keras.layers.Flatten(input_shape=(28, 28)),
    keras.layers.Dense(128, activation=tf.nn.relu),
    keras.layers.Dense(10, activation=tf.nn.softmax)
])
  • 该代码按照顺序构建了一个3层的神经网络模型
  • 该神经网络的第一层是keras.layers.Flatten，它的作用是将输入的28 x 28 矩阵展平成一个 [1 x 784]的矩阵，也就是将图片降维，虽然这样失去了二维数据的信息的意义，但有利于神经网络数据的输入和转换。
  • 神经网络的第二层是一个拥有128个神经元的全连接层，它的激活函数是relu函数。
  • 神经网络的第三层是输出层，拥有10个神经元，它的激活函数是softmax函数，它将返回10个概率分数的数组，总和为1。每个节点包含一个分数，表示当前图像属于10个类别之一的概率。

编译模型

在开始训练之前，需要进一步的进行设置，这些设置是在模型的编译步骤进行的：

  • 损失函数(Loss function) - 这可以衡量模型在训练过程中的准确程度。我们希望最小化此这个函数值，以便在正确的方向上“引导”模型。
  • 优化器 (Optimizer)- 它会根据你采用的不同种类的智能优化算法，来不断的求解损失函数的最小值。最常见的是梯度下降法，框架提供了很多种不同的优化器，需要根据问题尝试最佳的优化器
  • 性能评估(Metrics) - 用于监控培训和测试步骤。以下示例使用精度，即正确分类的图像分数。
model.compile(optimizer=tf.train.AdamOptimizer(), 
              loss='sparse_categorical_crossentropy',
              metrics=['accuracy'])
  • AdamOptimizer优化器通过使用动量（参数的移动平均数）来改善传统梯度下降，促进超参数动态调整。
  • sparse_categorical_crossentropy 是多类对数损失函数

训练模型

训练神经网络需要以下步骤：

1.将训练数据投递给神经网络，也就是train_images和train_labels矩阵
2.神经网络学习，将标签和图片关联起来
3.将测试数据test_imges投递给神经网络，神经网络给出预测值。我们可以将神经网络的输出结果和test_labels进行比对来验证预测值是否正确。

我们可以运用一行代码就可以开始神经网络的训练：

model.fit(train_images, train_labels, epochs=5)

Epoch 1/5
2018-08-15 14:32:47.708255: I tensorflow/core/platform/cpu_feature_guard.cc:141] Your CPU supports instructions that this TensorFlow binary was not compiled to use: SSE4.1 SSE4.2 AVX AVX2 FMA
2018-08-15 14:32:47.711370: I tensorflow/core/common_runtime/process_util.cc:69] Creating new thread pool with default inter op setting: 4. Tune using inter_op_parallelism_threads for best performance.
   32/60000 [..............................] - ETA: 19:56 - loss: 2.6159 - acc: 0.1250
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35136/60000 [================>.............] - ETA: 3s - loss: 0.5500 - acc: 0.8110
35552/60000 [================>.............] - ETA: 3s - loss: 0.5486 - acc: 0.8114
36032/60000 [=================>............] - ETA: 3s - loss: 0.5464 - acc: 0.8122
36480/60000 [=================>............] - ETA: 3s - loss: 0.5461 - acc: 0.8122
36864/60000 [=================>............] - ETA: 3s - loss: 0.5455 - acc: 0.8124
37184/60000 [=================>............] - ETA: 3s - loss: 0.5448 - acc: 0.8126
37600/60000 [=================>............] - ETA: 3s - loss: 0.5441 - acc: 0.8130
38048/60000 [==================>...........] - ETA: 3s - loss: 0.5426 - acc: 0.8134
38432/60000 [==================>...........] - ETA: 3s - loss: 0.5418 - acc: 0.8136
38880/60000 [==================>...........] - ETA: 3s - loss: 0.5405 - acc: 0.8139
39328/60000 [==================>...........] - ETA: 2s - loss: 0.5394 - acc: 0.8140
39808/60000 [==================>...........] - ETA: 2s - loss: 0.5389 - acc: 0.8142
40192/60000 [===================>..........] - ETA: 2s - loss: 0.5376 - acc: 0.8145
40640/60000 [===================>..........] - ETA: 2s - loss: 0.5363 - acc: 0.8150
41120/60000 [===================>..........] - ETA: 2s - loss: 0.5352 - acc: 0.8155
41504/60000 [===================>..........] - ETA: 2s - loss: 0.5337 - acc: 0.8159
41888/60000 [===================>..........] - ETA: 2s - loss: 0.5326 - acc: 0.8162
42304/60000 [====================>.........] - ETA: 2s - loss: 0.5313 - acc: 0.8168
42784/60000 [====================>.........] - ETA: 2s - loss: 0.5301 - acc: 0.8172
43264/60000 [====================>.........] - ETA: 2s - loss: 0.5288 - acc: 0.8176
43520/60000 [====================>.........] - ETA: 2s - loss: 0.5287 - acc: 0.8177
43840/60000 [====================>.........] - ETA: 2s - loss: 0.5281 - acc: 0.8180
44192/60000 [=====================>........] - ETA: 2s - loss: 0.5277 - acc: 0.8182
44576/60000 [=====================>........] - ETA: 2s - loss: 0.5264 - acc: 0.8186
44896/60000 [=====================>........] - ETA: 2s - loss: 0.5259 - acc: 0.8189
45344/60000 [=====================>........] - ETA: 2s - loss: 0.5250 - acc: 0.8193
45824/60000 [=====================>........] - ETA: 1s - loss: 0.5239 - acc: 0.8197
46272/60000 [======================>.......] - ETA: 1s - loss: 0.5233 - acc: 0.8199
46656/60000 [======================>.......] - ETA: 1s - loss: 0.5221 - acc: 0.8202
47072/60000 [======================>.......] - ETA: 1s - loss: 0.5213 - acc: 0.8206
47456/60000 [======================>.......] - ETA: 1s - loss: 0.5208 - acc: 0.8207
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48224/60000 [=======================>......] - ETA: 1s - loss: 0.5198 - acc: 0.8208
48608/60000 [=======================>......] - ETA: 1s - loss: 0.5189 - acc: 0.8209
48992/60000 [=======================>......] - ETA: 1s - loss: 0.5181 - acc: 0.8211
49440/60000 [=======================>......] - ETA: 1s - loss: 0.5174 - acc: 0.8211
49824/60000 [=======================>......] - ETA: 1s - loss: 0.5169 - acc: 0.8211
50272/60000 [========================>.....] - ETA: 1s - loss: 0.5155 - acc: 0.8216
50720/60000 [========================>.....] - ETA: 1s - loss: 0.5141 - acc: 0.8222
51168/60000 [========================>.....] - ETA: 1s - loss: 0.5127 - acc: 0.8225
51584/60000 [========================>.....] - ETA: 1s - loss: 0.5122 - acc: 0.8226
51968/60000 [========================>.....] - ETA: 1s - loss: 0.5116 - acc: 0.8229
52416/60000 [=========================>....] - ETA: 1s - loss: 0.5110 - acc: 0.8232
52864/60000 [=========================>....] - ETA: 0s - loss: 0.5101 - acc: 0.8234
53120/60000 [=========================>....] - ETA: 0s - loss: 0.5097 - acc: 0.8235
53440/60000 [=========================>....] - ETA: 0s - loss: 0.5092 - acc: 0.8236
53760/60000 [=========================>....] - ETA: 0s - loss: 0.5092 - acc: 0.8235
54080/60000 [==========================>...] - ETA: 0s - loss: 0.5085 - acc: 0.8237
54400/60000 [==========================>...] - ETA: 0s - loss: 0.5075 - acc: 0.8241
54688/60000 [==========================>...] - ETA: 0s - loss: 0.5066 - acc: 0.8242
55040/60000 [==========================>...] - ETA: 0s - loss: 0.5060 - acc: 0.8244
55488/60000 [==========================>...] - ETA: 0s - loss: 0.5053 - acc: 0.8245
55968/60000 [==========================>...] - ETA: 0s - loss: 0.5047 - acc: 0.8246
56288/60000 [===========================>..] - ETA: 0s - loss: 0.5036 - acc: 0.8249
56672/60000 [===========================>..] - ETA: 0s - loss: 0.5031 - acc: 0.8251
57152/60000 [===========================>..] - ETA: 0s - loss: 0.5024 - acc: 0.8253
57600/60000 [===========================>..] - ETA: 0s - loss: 0.5014 - acc: 0.8256
57952/60000 [===========================>..] - ETA: 0s - loss: 0.5010 - acc: 0.8257
58304/60000 [============================>.] - ETA: 0s - loss: 0.5008 - acc: 0.8258
58752/60000 [============================>.] - ETA: 0s - loss: 0.5004 - acc: 0.8259
59168/60000 [============================>.] - ETA: 0s - loss: 0.4999 - acc: 0.8260
59552/60000 [============================>.] - ETA: 0s - loss: 0.4989 - acc: 0.8263
59968/60000 [============================>.] - ETA: 0s - loss: 0.4992 - acc: 0.8263
60000/60000 [==============================] - 8s 139us/step - loss: 0.4994 - acc: 0.8263
Epoch 2/5
   32/60000 [..............................] - ETA: 10s - loss: 0.3665 - acc: 0.9062
  416/60000 [..............................] - ETA: 8s - loss: 0.3400 - acc: 0.8942 
  864/60000 [..............................] - ETA: 7s - loss: 0.3748 - acc: 0.8669
 1216/60000 [..............................] - ETA: 7s - loss: 0.3931 - acc: 0.8643
 1632/60000 [..............................] - ETA: 7s - loss: 0.3992 - acc: 0.8621
 2080/60000 [>.............................] - ETA: 7s - loss: 0.3984 - acc: 0.8596
 2528/60000 [>.............................] - ETA: 7s - loss: 0.4009 - acc: 0.8600
 2976/60000 [>.............................] - ETA: 7s - loss: 0.3920 - acc: 0.8629
 3424/60000 [>.............................] - ETA: 7s - loss: 0.3854 - acc: 0.8645
 3904/60000 [>.............................] - ETA: 6s - loss: 0.3798 - acc: 0.8668
 4320/60000 [=>............................] - ETA: 6s - loss: 0.3799 - acc: 0.8657
 4736/60000 [=>............................] - ETA: 6s - loss: 0.3779 - acc: 0.8678
 5184/60000 [=>............................] - ETA: 6s - loss: 0.3766 - acc: 0.8679
 5664/60000 [=>............................] - ETA: 6s - loss: 0.3721 - acc: 0.8676
 6144/60000 [==>...........................] - ETA: 6s - loss: 0.3746 - acc: 0.8665
 6528/60000 [==>...........................] - ETA: 6s - loss: 0.3812 - acc: 0.8655
 6944/60000 [==>...........................] - ETA: 6s - loss: 0.3820 - acc: 0.8648
 7424/60000 [==>...........................] - ETA: 6s - loss: 0.3818 - acc: 0.8660
 7872/60000 [==>...........................] - ETA: 6s - loss: 0.3831 - acc: 0.8646
 8288/60000 [===>..........................] - ETA: 6s - loss: 0.3831 - acc: 0.8643
 8704/60000 [===>..........................] - ETA: 6s - loss: 0.3838 - acc: 0.8629
 9184/60000 [===>..........................] - ETA: 6s - loss: 0.3804 - acc: 0.8652
 9664/60000 [===>..........................] - ETA: 6s - loss: 0.3804 - acc: 0.8650
10080/60000 [====>.........................] - ETA: 5s - loss: 0.3812 - acc: 0.8644
10528/60000 [====>.........................] - ETA: 5s - loss: 0.3838 - acc: 0.8633
10976/60000 [====>.........................] - ETA: 5s - loss: 0.3866 - acc: 0.8615
11424/60000 [====>.........................] - ETA: 5s - loss: 0.3869 - acc: 0.8613
11808/60000 [====>.........................] - ETA: 5s - loss: 0.3856 - acc: 0.8616
12256/60000 [=====>........................] - ETA: 5s - loss: 0.3838 - acc: 0.8623
12736/60000 [=====>........................] - ETA: 5s - loss: 0.3846 - acc: 0.8624
13152/60000 [=====>........................] - ETA: 5s - loss: 0.3846 - acc: 0.8623
13472/60000 [=====>........................] - ETA: 5s - loss: 0.3838 - acc: 0.8620
13856/60000 [=====>........................] - ETA: 5s - loss: 0.3846 - acc: 0.8614
14304/60000 [======>.......................] - ETA: 5s - loss: 0.3855 - acc: 0.8616
14752/60000 [======>.......................] - ETA: 5s - loss: 0.3866 - acc: 0.8610
15072/60000 [======>.......................] - ETA: 5s - loss: 0.3867 - acc: 0.8609
15392/60000 [======>.......................] - ETA: 5s - loss: 0.3873 - acc: 0.8605
15776/60000 [======>.......................] - ETA: 5s - loss: 0.3867 - acc: 0.8605
16224/60000 [=======>......................] - ETA: 5s - loss: 0.3871 - acc: 0.8606
16544/60000 [=======>......................] - ETA: 5s - loss: 0.3880 - acc: 0.8608
16960/60000 [=======>......................] - ETA: 5s - loss: 0.3877 - acc: 0.8607
17440/60000 [=======>......................] - ETA: 5s - loss: 0.3861 - acc: 0.8611
17888/60000 [=======>......................] - ETA: 5s - loss: 0.3855 - acc: 0.8613
18272/60000 [========>.....................] - ETA: 5s - loss: 0.3867 - acc: 0.8604
18688/60000 [========>.....................] - ETA: 5s - loss: 0.3876 - acc: 0.8600
19168/60000 [========>.....................] - ETA: 5s - loss: 0.3876 - acc: 0.8599
19648/60000 [========>.....................] - ETA: 4s - loss: 0.3874 - acc: 0.8598
20032/60000 [=========>....................] - ETA: 4s - loss: 0.3862 - acc: 0.8603
20416/60000 [=========>....................] - ETA: 4s - loss: 0.3857 - acc: 0.8605
20704/60000 [=========>....................] - ETA: 4s - loss: 0.3875 - acc: 0.8604
21024/60000 [=========>....................] - ETA: 4s - loss: 0.3883 - acc: 0.8599
21344/60000 [=========>....................] - ETA: 4s - loss: 0.3872 - acc: 0.8602
21696/60000 [=========>....................] - ETA: 4s - loss: 0.3870 - acc: 0.8604
22080/60000 [==========>...................] - ETA: 4s - loss: 0.3865 - acc: 0.8606
22496/60000 [==========>...................] - ETA: 4s - loss: 0.3871 - acc: 0.8602
22880/60000 [==========>...................] - ETA: 4s - loss: 0.3869 - acc: 0.8605
23296/60000 [==========>...................] - ETA: 4s - loss: 0.3861 - acc: 0.8608
23776/60000 [==========>...................] - ETA: 4s - loss: 0.3849 - acc: 0.8613
24224/60000 [===========>..................] - ETA: 4s - loss: 0.3846 - acc: 0.8615
24512/60000 [===========>..................] - ETA: 4s - loss: 0.3843 - acc: 0.8615
24864/60000 [===========>..................] - ETA: 4s - loss: 0.3843 - acc: 0.8611
25248/60000 [===========>..................] - ETA: 4s - loss: 0.3842 - acc: 0.8610
25600/60000 [===========>..................] - ETA: 4s - loss: 0.3827 - acc: 0.8615
25920/60000 [===========>..................] - ETA: 4s - loss: 0.3839 - acc: 0.8614
26176/60000 [============>.................] - ETA: 4s - loss: 0.3844 - acc: 0.8614
26528/60000 [============>.................] - ETA: 4s - loss: 0.3840 - acc: 0.8618
26848/60000 [============>.................] - ETA: 4s - loss: 0.3838 - acc: 0.8619
27104/60000 [============>.................] - ETA: 4s - loss: 0.3837 - acc: 0.8618
27328/60000 [============>.................] - ETA: 4s - loss: 0.3836 - acc: 0.8618
27648/60000 [============>.................] - ETA: 4s - loss: 0.3829 - acc: 0.8619
27968/60000 [============>.................] - ETA: 4s - loss: 0.3826 - acc: 0.8619
28256/60000 [=============>................] - ETA: 4s - loss: 0.3824 - acc: 0.8620
28544/60000 [=============>................] - ETA: 4s - loss: 0.3821 - acc: 0.8622
28864/60000 [=============>................] - ETA: 4s - loss: 0.3811 - acc: 0.8626
29184/60000 [=============>................] - ETA: 4s - loss: 0.3811 - acc: 0.8627
29472/60000 [=============>................] - ETA: 4s - loss: 0.3812 - acc: 0.8627
29760/60000 [=============>................] - ETA: 4s - loss: 0.3808 - acc: 0.8627
30080/60000 [==============>...............] - ETA: 4s - loss: 0.3807 - acc: 0.8630
30400/60000 [==============>...............] - ETA: 3s - loss: 0.3800 - acc: 0.8633
30752/60000 [==============>...............] - ETA: 3s - loss: 0.3807 - acc: 0.8631
31136/60000 [==============>...............] - ETA: 3s - loss: 0.3811 - acc: 0.8626
31552/60000 [==============>...............] - ETA: 3s - loss: 0.3809 - acc: 0.8627
31904/60000 [==============>...............] - ETA: 3s - loss: 0.3813 - acc: 0.8627
32256/60000 [===============>..............] - ETA: 3s - loss: 0.3822 - acc: 0.8624
32704/60000 [===============>..............] - ETA: 3s - loss: 0.3818 - acc: 0.8626
33152/60000 [===============>..............] - ETA: 3s - loss: 0.3816 - acc: 0.8626
33568/60000 [===============>..............] - ETA: 3s - loss: 0.3815 - acc: 0.8626
33952/60000 [===============>..............] - ETA: 3s - loss: 0.3819 - acc: 0.8627
34368/60000 [================>.............] - ETA: 3s - loss: 0.3818 - acc: 0.8627
34752/60000 [================>.............] - ETA: 3s - loss: 0.3817 - acc: 0.8626
35168/60000 [================>.............] - ETA: 3s - loss: 0.3817 - acc: 0.8626
35584/60000 [================>.............] - ETA: 3s - loss: 0.3811 - acc: 0.8627
36000/60000 [=================>............] - ETA: 3s - loss: 0.3802 - acc: 0.8630
36480/60000 [=================>............] - ETA: 3s - loss: 0.3802 - acc: 0.8633
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38688/60000 [==================>...........] - ETA: 2s - loss: 0.3820 - acc: 0.8626
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40000/60000 [===================>..........] - ETA: 2s - loss: 0.3819 - acc: 0.8630
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42048/60000 [====================>.........] - ETA: 2s - loss: 0.3814 - acc: 0.8634
42528/60000 [====================>.........] - ETA: 2s - loss: 0.3805 - acc: 0.8638
43008/60000 [====================>.........] - ETA: 2s - loss: 0.3799 - acc: 0.8641
43424/60000 [====================>.........] - ETA: 2s - loss: 0.3791 - acc: 0.8642
43872/60000 [====================>.........] - ETA: 2s - loss: 0.3785 - acc: 0.8644
44352/60000 [=====================>........] - ETA: 2s - loss: 0.3791 - acc: 0.8641
44832/60000 [=====================>........] - ETA: 2s - loss: 0.3789 - acc: 0.8641
45248/60000 [=====================>........] - ETA: 1s - loss: 0.3790 - acc: 0.8640
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52768/60000 [=========================>....] - ETA: 0s - loss: 0.3760 - acc: 0.8649
53248/60000 [=========================>....] - ETA: 0s - loss: 0.3755 - acc: 0.8650
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55200/60000 [==========================>...] - ETA: 0s - loss: 0.3765 - acc: 0.8645
55648/60000 [==========================>...] - ETA: 0s - loss: 0.3760 - acc: 0.8647
55968/60000 [==========================>...] - ETA: 0s - loss: 0.3763 - acc: 0.8647
56288/60000 [===========================>..] - ETA: 0s - loss: 0.3762 - acc: 0.8646
56576/60000 [===========================>..] - ETA: 0s - loss: 0.3763 - acc: 0.8645
56928/60000 [===========================>..] - ETA: 0s - loss: 0.3761 - acc: 0.8647
57248/60000 [===========================>..] - ETA: 0s - loss: 0.3758 - acc: 0.8648
57568/60000 [===========================>..] - ETA: 0s - loss: 0.3756 - acc: 0.8648
57920/60000 [===========================>..] - ETA: 0s - loss: 0.3755 - acc: 0.8648
58304/60000 [============================>.] - ETA: 0s - loss: 0.3760 - acc: 0.8646
58624/60000 [============================>.] - ETA: 0s - loss: 0.3761 - acc: 0.8646
59040/60000 [============================>.] - ETA: 0s - loss: 0.3759 - acc: 0.8648
59520/60000 [============================>.] - ETA: 0s - loss: 0.3753 - acc: 0.8650
60000/60000 [==============================] - 8s 132us/step - loss: 0.3750 - acc: 0.8649
Epoch 3/5
   32/60000 [..............................] - ETA: 11s - loss: 0.2271 - acc: 0.9062
  352/60000 [..............................] - ETA: 9s - loss: 0.3394 - acc: 0.8722 
  704/60000 [..............................] - ETA: 9s - loss: 0.3463 - acc: 0.8778
 1024/60000 [..............................] - ETA: 9s - loss: 0.3761 - acc: 0.8711
 1408/60000 [..............................] - ETA: 8s - loss: 0.3633 - acc: 0.8707
 1728/60000 [..............................] - ETA: 8s - loss: 0.3629 - acc: 0.8721
 2016/60000 [>.............................] - ETA: 9s - loss: 0.3503 - acc: 0.8770
 2304/60000 [>.............................] - ETA: 9s - loss: 0.3443 - acc: 0.8798
 2624/60000 [>.............................] - ETA: 9s - loss: 0.3391 - acc: 0.8822
 2912/60000 [>.............................] - ETA: 9s - loss: 0.3397 - acc: 0.8802
 3232/60000 [>.............................] - ETA: 9s - loss: 0.3374 - acc: 0.8815
 3584/60000 [>.............................] - ETA: 9s - loss: 0.3427 - acc: 0.8800
 3936/60000 [>.............................] - ETA: 9s - loss: 0.3395 - acc: 0.8793
 4320/60000 [=>............................] - ETA: 8s - loss: 0.3434 - acc: 0.8803
 4704/60000 [=>............................] - ETA: 8s - loss: 0.3446 - acc: 0.8778
 5184/60000 [=>............................] - ETA: 8s - loss: 0.3405 - acc: 0.8783
 5600/60000 [=>............................] - ETA: 8s - loss: 0.3404 - acc: 0.8788
 5888/60000 [=>............................] - ETA: 8s - loss: 0.3412 - acc: 0.8777
 6176/60000 [==>...........................] - ETA: 8s - loss: 0.3398 - acc: 0.8786
 6496/60000 [==>...........................] - ETA: 8s - loss: 0.3404 - acc: 0.8782
 6848/60000 [==>...........................] - ETA: 8s - loss: 0.3395 - acc: 0.8782
 7200/60000 [==>...........................] - ETA: 8s - loss: 0.3365 - acc: 0.8789
 7552/60000 [==>...........................] - ETA: 8s - loss: 0.3370 - acc: 0.8792
 8000/60000 [===>..........................] - ETA: 7s - loss: 0.3342 - acc: 0.8806
 8320/60000 [===>..........................] - ETA: 7s - loss: 0.3334 - acc: 0.8804
 8576/60000 [===>..........................] - ETA: 7s - loss: 0.3336 - acc: 0.8805
 8832/60000 [===>..........................] - ETA: 7s - loss: 0.3327 - acc: 0.8807
 9088/60000 [===>..........................] - ETA: 8s - loss: 0.3348 - acc: 0.8794
 9408/60000 [===>..........................] - ETA: 7s - loss: 0.3341 - acc: 0.8802
 9792/60000 [===>..........................] - ETA: 7s - loss: 0.3335 - acc: 0.8806
10176/60000 [====>.........................] - ETA: 7s - loss: 0.3317 - acc: 0.8812
10496/60000 [====>.........................] - ETA: 7s - loss: 0.3306 - acc: 0.8816
10880/60000 [====>.........................] - ETA: 7s - loss: 0.3292 - acc: 0.8822
11232/60000 [====>.........................] - ETA: 7s - loss: 0.3314 - acc: 0.8818
11520/60000 [====>.........................] - ETA: 7s - loss: 0.3315 - acc: 0.8818
11808/60000 [====>.........................] - ETA: 7s - loss: 0.3336 - acc: 0.8812
12192/60000 [=====>........................] - ETA: 7s - loss: 0.3330 - acc: 0.8812
12640/60000 [=====>........................] - ETA: 7s - loss: 0.3347 - acc: 0.8809
12960/60000 [=====>........................] - ETA: 7s - loss: 0.3343 - acc: 0.8810
13280/60000 [=====>........................] - ETA: 7s - loss: 0.3340 - acc: 0.8809
13728/60000 [=====>........................] - ETA: 7s - loss: 0.3346 - acc: 0.8808
14144/60000 [======>.......................] - ETA: 7s - loss: 0.3363 - acc: 0.8804
14496/60000 [======>.......................] - ETA: 6s - loss: 0.3371 - acc: 0.8798
14848/60000 [======>.......................] - ETA: 6s - loss: 0.3374 - acc: 0.8798
15232/60000 [======>.......................] - ETA: 6s - loss: 0.3383 - acc: 0.8801
15616/60000 [======>.......................] - ETA: 6s - loss: 0.3390 - acc: 0.8796
15968/60000 [======>.......................] - ETA: 6s - loss: 0.3407 - acc: 0.8787
16384/60000 [=======>......................] - ETA: 6s - loss: 0.3400 - acc: 0.8790
16864/60000 [=======>......................] - ETA: 6s - loss: 0.3395 - acc: 0.8791
17312/60000 [=======>......................] - ETA: 6s - loss: 0.3404 - acc: 0.8786
17696/60000 [=======>......................] - ETA: 6s - loss: 0.3404 - acc: 0.8784
18048/60000 [========>.....................] - ETA: 6s - loss: 0.3402 - acc: 0.8785
18464/60000 [========>.....................] - ETA: 6s - loss: 0.3405 - acc: 0.8782
18912/60000 [========>.....................] - ETA: 6s - loss: 0.3398 - acc: 0.8785
19328/60000 [========>.....................] - ETA: 5s - loss: 0.3388 - acc: 0.8786
19744/60000 [========>.....................] - ETA: 5s - loss: 0.3398 - acc: 0.8779
20224/60000 [=========>....................] - ETA: 5s - loss: 0.3399 - acc: 0.8777
20704/60000 [=========>....................] - ETA: 5s - loss: 0.3418 - acc: 0.8773
21120/60000 [=========>....................] - ETA: 5s - loss: 0.3420 - acc: 0.8770
21568/60000 [=========>....................] - ETA: 5s - loss: 0.3419 - acc: 0.8766
21952/60000 [=========>....................] - ETA: 5s - loss: 0.3433 - acc: 0.8765
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22720/60000 [==========>...................] - ETA: 5s - loss: 0.3431 - acc: 0.8768
23104/60000 [==========>...................] - ETA: 5s - loss: 0.3425 - acc: 0.8771
23488/60000 [==========>...................] - ETA: 5s - loss: 0.3406 - acc: 0.8779
23936/60000 [==========>...................] - ETA: 5s - loss: 0.3396 - acc: 0.8780
24320/60000 [===========>..................] - ETA: 5s - loss: 0.3393 - acc: 0.8782
24768/60000 [===========>..................] - ETA: 5s - loss: 0.3395 - acc: 0.8778
25248/60000 [===========>..................] - ETA: 4s - loss: 0.3393 - acc: 0.8779
25696/60000 [===========>..................] - ETA: 4s - loss: 0.3395 - acc: 0.8778
26048/60000 [============>.................] - ETA: 4s - loss: 0.3397 - acc: 0.8778
26496/60000 [============>.................] - ETA: 4s - loss: 0.3390 - acc: 0.8782
26976/60000 [============>.................] - ETA: 4s - loss: 0.3398 - acc: 0.8777
27456/60000 [============>.................] - ETA: 4s - loss: 0.3403 - acc: 0.8775
27872/60000 [============>.................] - ETA: 4s - loss: 0.3400 - acc: 0.8777
28320/60000 [=============>................] - ETA: 4s - loss: 0.3405 - acc: 0.8773
28800/60000 [=============>................] - ETA: 4s - loss: 0.3411 - acc: 0.8769
29280/60000 [=============>................] - ETA: 4s - loss: 0.3417 - acc: 0.8766
29632/60000 [=============>................] - ETA: 4s - loss: 0.3413 - acc: 0.8767
30048/60000 [==============>...............] - ETA: 4s - loss: 0.3409 - acc: 0.8770
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30912/60000 [==============>...............] - ETA: 4s - loss: 0.3430 - acc: 0.8765
31296/60000 [==============>...............] - ETA: 3s - loss: 0.3438 - acc: 0.8759
31712/60000 [==============>...............] - ETA: 3s - loss: 0.3441 - acc: 0.8756
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32992/60000 [===============>..............] - ETA: 3s - loss: 0.3437 - acc: 0.8759
33440/60000 [===============>..............] - ETA: 3s - loss: 0.3450 - acc: 0.8754
33632/60000 [===============>..............] - ETA: 3s - loss: 0.3449 - acc: 0.8752
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34080/60000 [================>.............] - ETA: 3s - loss: 0.3446 - acc: 0.8752
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35200/60000 [================>.............] - ETA: 3s - loss: 0.3442 - acc: 0.8755
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36128/60000 [=================>............] - ETA: 3s - loss: 0.3427 - acc: 0.8758
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55328/60000 [==========================>...] - ETA: 0s - loss: 0.3387 - acc: 0.8772
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56256/60000 [===========================>..] - ETA: 0s - loss: 0.3384 - acc: 0.8771
56736/60000 [===========================>..] - ETA: 0s - loss: 0.3383 - acc: 0.8770
57216/60000 [===========================>..] - ETA: 0s - loss: 0.3381 - acc: 0.8771
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58176/60000 [============================>.] - ETA: 0s - loss: 0.3382 - acc: 0.8770
58656/60000 [============================>.] - ETA: 0s - loss: 0.3380 - acc: 0.8771
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59616/60000 [============================>.] - ETA: 0s - loss: 0.3374 - acc: 0.8773
60000/60000 [==============================] - 8s 133us/step - loss: 0.3372 - acc: 0.8773
Epoch 4/5
   32/60000 [..............................] - ETA: 9s - loss: 0.3326 - acc: 0.9062
  480/60000 [..............................] - ETA: 6s - loss: 0.2988 - acc: 0.8812
  928/60000 [..............................] - ETA: 6s - loss: 0.3335 - acc: 0.8825
 1376/60000 [..............................] - ETA: 6s - loss: 0.3423 - acc: 0.8714
 1824/60000 [..............................] - ETA: 6s - loss: 0.3386 - acc: 0.8761
 2080/60000 [>.............................] - ETA: 7s - loss: 0.3433 - acc: 0.8745
 2368/60000 [>.............................] - ETA: 7s - loss: 0.3380 - acc: 0.8780
 2784/60000 [>.............................] - ETA: 7s - loss: 0.3373 - acc: 0.8786
 3232/60000 [>.............................] - ETA: 7s - loss: 0.3386 - acc: 0.8775
 3616/60000 [>.............................] - ETA: 7s - loss: 0.3318 - acc: 0.8805
 4064/60000 [=>............................] - ETA: 7s - loss: 0.3248 - acc: 0.8829
 4480/60000 [=>............................] - ETA: 7s - loss: 0.3283 - acc: 0.8799
 4928/60000 [=>............................] - ETA: 7s - loss: 0.3301 - acc: 0.8787
 5248/60000 [=>............................] - ETA: 7s - loss: 0.3269 - acc: 0.8796
 5536/60000 [=>............................] - ETA: 7s - loss: 0.3240 - acc: 0.8802
 5728/60000 [=>............................] - ETA: 7s - loss: 0.3220 - acc: 0.8809
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 6208/60000 [==>...........................] - ETA: 7s - loss: 0.3254 - acc: 0.8792
 6528/60000 [==>...........................] - ETA: 7s - loss: 0.3209 - acc: 0.8805
 6880/60000 [==>...........................] - ETA: 7s - loss: 0.3254 - acc: 0.8792
 7232/60000 [==>...........................] - ETA: 7s - loss: 0.3226 - acc: 0.8809
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 7872/60000 [==>...........................] - ETA: 7s - loss: 0.3191 - acc: 0.8824
 8256/60000 [===>..........................] - ETA: 7s - loss: 0.3207 - acc: 0.8814
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10144/60000 [====>.........................] - ETA: 7s - loss: 0.3196 - acc: 0.8825
10464/60000 [====>.........................] - ETA: 7s - loss: 0.3205 - acc: 0.8824
10816/60000 [====>.........................] - ETA: 7s - loss: 0.3206 - acc: 0.8823
11200/60000 [====>.........................] - ETA: 7s - loss: 0.3209 - acc: 0.8820
11488/60000 [====>.........................] - ETA: 7s - loss: 0.3213 - acc: 0.8824
11872/60000 [====>.........................] - ETA: 7s - loss: 0.3244 - acc: 0.8808
12352/60000 [=====>........................] - ETA: 7s - loss: 0.3238 - acc: 0.8803
12832/60000 [=====>........................] - ETA: 7s - loss: 0.3234 - acc: 0.8800
13248/60000 [=====>........................] - ETA: 7s - loss: 0.3250 - acc: 0.8795
13664/60000 [=====>........................] - ETA: 6s - loss: 0.3246 - acc: 0.8797
14144/60000 [======>.......................] - ETA: 6s - loss: 0.3265 - acc: 0.8790
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14944/60000 [======>.......................] - ETA: 6s - loss: 0.3273 - acc: 0.8786
15360/60000 [======>.......................] - ETA: 6s - loss: 0.3256 - acc: 0.8793
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16128/60000 [=======>......................] - ETA: 6s - loss: 0.3255 - acc: 0.8795
16608/60000 [=======>......................] - ETA: 6s - loss: 0.3269 - acc: 0.8789
17024/60000 [=======>......................] - ETA: 6s - loss: 0.3249 - acc: 0.8801
17472/60000 [=======>......................] - ETA: 6s - loss: 0.3250 - acc: 0.8799
17920/60000 [=======>......................] - ETA: 6s - loss: 0.3246 - acc: 0.8800
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18784/60000 [========>.....................] - ETA: 5s - loss: 0.3244 - acc: 0.8801
19232/60000 [========>.....................] - ETA: 5s - loss: 0.3234 - acc: 0.8803
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22720/60000 [==========>...................] - ETA: 5s - loss: 0.3198 - acc: 0.8822
23168/60000 [==========>...................] - ETA: 5s - loss: 0.3203 - acc: 0.8819
23616/60000 [==========>...................] - ETA: 4s - loss: 0.3207 - acc: 0.8816
23936/60000 [==========>...................] - ETA: 4s - loss: 0.3207 - acc: 0.8817
24288/60000 [===========>..................] - ETA: 4s - loss: 0.3205 - acc: 0.8818
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25120/60000 [===========>..................] - ETA: 4s - loss: 0.3199 - acc: 0.8814
25472/60000 [===========>..................] - ETA: 4s - loss: 0.3195 - acc: 0.8814
25888/60000 [===========>..................] - ETA: 4s - loss: 0.3199 - acc: 0.8814
26368/60000 [============>.................] - ETA: 4s - loss: 0.3211 - acc: 0.8814
26848/60000 [============>.................] - ETA: 4s - loss: 0.3212 - acc: 0.8816
27232/60000 [============>.................] - ETA: 4s - loss: 0.3203 - acc: 0.8821
27648/60000 [============>.................] - ETA: 4s - loss: 0.3206 - acc: 0.8821
28000/60000 [=============>................] - ETA: 4s - loss: 0.3214 - acc: 0.8816
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28832/60000 [=============>................] - ETA: 4s - loss: 0.3214 - acc: 0.8815
29280/60000 [=============>................] - ETA: 4s - loss: 0.3211 - acc: 0.8817
29760/60000 [=============>................] - ETA: 4s - loss: 0.3208 - acc: 0.8819
30240/60000 [==============>...............] - ETA: 4s - loss: 0.3211 - acc: 0.8818
30656/60000 [==============>...............] - ETA: 3s - loss: 0.3208 - acc: 0.8820
31008/60000 [==============>...............] - ETA: 3s - loss: 0.3206 - acc: 0.8823
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31712/60000 [==============>...............] - ETA: 3s - loss: 0.3199 - acc: 0.8823
32000/60000 [===============>..............] - ETA: 3s - loss: 0.3194 - acc: 0.8825
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33120/60000 [===============>..............] - ETA: 3s - loss: 0.3199 - acc: 0.8827
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60000/60000 [==============================] - 8s 134us/step - loss: 0.3136 - acc: 0.8857
Epoch 5/5
   32/60000 [..............................] - ETA: 9s - loss: 0.1876 - acc: 0.9375
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60000/60000 [==============================] - 7s 120us/step - loss: 0.2954 - acc: 0.8908

通过训练数据可以看出精确度已经达到了88%左右，实际上这并不是一个很高的值，但对于我们学习过程来说已经足够使用了。

评估精度

我们可以运用一行代码来评估整个模型相比于测试数据集的精度：

test_loss, test_acc = model.evaluate(test_images, test_labels)
print('Test accuracy:', test_acc)

输出过程已省略部分，以下是结果

10000/10000 [==============================] - 0s 20us/step
Test accuracy: 0.8693

事实证明，测试数据集的准确性略低于训练数据集的准确性。训练精度和测试精度之间的差距是过度拟合的一个例子。过度拟合是指机器学习模型在新数据上的表现比在训练数据上表现更差。

预测

运用训练后的模型，我们可以对输入数据做一些预测：

predictions = model.predict(test_images)

模型已经预测了测试集中每个图像的标签。我们来看看第一个预测：

print(predictions[0])

[2.5046500e-05, 9.4638374e-08, 2.3706765e-07, 3.2167595e-06,
       1.4285071e-06, 2.1461691e-03, 2.6124888e-05, 9.9495485e-02,
       1.7809383e-04, 8.9812416e-01]

可以看出，第9个的数值的置信度较高，但是这样观察真是太不容易了，加个函数：

print(np.argmax(predictions[0]))

9

也就是说，神经网络给出的答案是9，也就是属于第九个分类ankle boot，我们可以查看test_labels[0],看它是不是9

print(test_labels[0])

9

但是这样也太不形象了，我们可以运用一些绘图代码来更直观的表示预测结果：

plt.figure(figsize=(10,10))
for i in range(25):
    plt.subplot(5,5,i+1)
    plt.xticks([])
    plt.yticks([])
    plt.grid('off')
    plt.imshow(test_images[i], cmap=plt.cm.binary)
    predicted_label = np.argmax(predictions[I])
    true_label = test_labels[I]
    if predicted_label == true_label:
      color = 'green'
    else:
      color = 'red'
    plt.xlabel("{} ({})".format(class_names[predicted_label], 
                                  class_names[true_label]),
                                  color=color)
plt.show()
Tensorflow学习笔记之一：训练你的第一个神经网络——基础分类_第6张图片
预测结果值

最后，我们也可以尝试对单个图片的预测

# Grab an image from the test dataset
img = test_images[0]

print(img.shape)

28 x 28

tf.keras模型经过优化，可以同时对一组示例进行预测或集合。因此，即使我们使用单个图像，我们也需要将其添加到列表中：

# Add the image to a batch where it's the only member.
img = (np.expand_dims(img,0))

print(img.shape)

(1, 28, 28)

现在对这个图片进行预测：

predictions = model.predict(img)

print(predictions)

[[2.5046500e-05 9.4638374e-08 2.3706765e-07 3.2167627e-06 1.4285083e-06
  2.1461679e-03 2.6124937e-05 9.9495515e-02 1.7809383e-04 8.9812416e-01]]

它返回的是一个列表我们需要把我们的拿出来：

prediction = predictions[0]

print(np.argmax(prediction))

9

和前面一样，确实是9

#title MIT License
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# to deal in the Software without restriction, including without limitation
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# and/or sell copies of the Software, and to permit persons to whom the
# Software is furnished to do so, subject to the following conditions:
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