我就废话不多说了，大家还是直接看代码吧~
注释讲解版：
# Classifier example
import numpy as np
# for reproducibility
np.random.seed(1337)
# from keras.datasets import mnist
from keras.utils import np_utils
from keras.models import Sequential
from keras.layers import Dense, Activation
from keras.optimizers import RMSprop
# 程序中用到的数据是经典的手写体识别mnist数据集
# download the mnist to the path if it is the first time to be called
# X shape (60,000 28x28), y
# (X_train, y_train), (X_test, y_test) = mnist.load_data()
# 下载minst.npz：
# 链接: https://pan.baidu.com/s/1b2ppKDOdzDJxivgmyOoQsA
# 提取码: y5ir
# 将下载好的minst.npz放到当前目录下
path='./mnist.npz'
f = np.load(path)
X_train, y_train = f['x_train'], f['y_train']
X_test, y_test = f['x_test'], f['y_test']
f.close()
# data pre-processing
# 数据预处理
# normalize
# X shape (60,000 28x28)，表示输入数据 X 是个三维的数据
# 可以理解为 60000行数据，每一行是一张28 x 28 的灰度图片
# X_train.reshape(X_train.shape[0], -1)表示：只保留第一维，其余的纬度，不管多少纬度，重新排列为一维
# 参数-1就是不知道行数或者列数多少的情况下使用的参数
# 所以先确定除了参数-1之外的其他参数，然后通过(总参数的计算) / (确定除了参数-1之外的其他参数) = 该位置应该是多少的参数
# 这里用-1是偷懒的做法,等同于 28*28
# reshape后的数据是：共60000行，每一行是784个数据点（feature）
# 输入的 x 变成 60,000*784 的数据，然后除以 255 进行标准化
# 因为每个像素都是在 0 到 255 之间的，标准化之后就变成了 0 到 1 之间
X_train = X_train.reshape(X_train.shape[0], -1) / 255
X_test = X_test.reshape(X_test.shape[0], -1) / 255
# 分类标签编码
# 将y转化为one-hot vector
y_train = np_utils.to_categorical(y_train, num_classes = 10)
y_test = np_utils.to_categorical(y_test, num_classes = 10)
# Another way to build your neural net
# 建立神经网络
# 应用了2层的神经网络，前一层的激活函数用的是relu，后一层的激活函数用的是softmax
#32是输出的维数
model = Sequential([
Dense(32, input_dim=784),
Activation('relu'),
Dense(10),
Activation('softmax')
])
# Another way to define your optimizer
# 优化函数
# 优化算法用的是RMSprop
rmsprop = RMSprop(lr=0.001, rho=0.9, epsilon=1e-08, decay=0.0)
# We add metrics to get more results you want to see
# 不自己定义，直接用内置的优化器也行，optimizer='rmsprop'
#激活模型：接下来用 model.compile 激励神经网络
model.compile(
optimizer=rmsprop,
loss='categorical_crossentropy',
metrics=['accuracy']
)
print('Training------------')
# Another way to train the model
# 训练模型
# 上一个程序是用train_on_batch 一批一批的训练 X_train, Y_train
# 默认的返回值是 cost，每100步输出一下结果
# 输出的样式与上一个程序的有所不同，感觉用model.fit()更清晰明了
# 上一个程序是Python实现Keras搭建神经网络训练回归模型：
# https://blog.csdn.net/weixin_45798684/article/details/106503685
model.fit(X_train, y_train, nb_epoch=2, batch_size=32)
print('\nTesting------------')
# Evaluate the model with the metrics we defined earlier
# 测试
loss, accuracy = model.evaluate(X_test, y_test)
print('test loss:', loss)
print('test accuracy:', accuracy)
运行结果：
Using TensorFlow backend. Training------------ Epoch 1/2 32/60000 [..............................] - ETA: 5:03 - loss: 2.4464 - accuracy: 0.0625 864/60000 [..............................] - ETA: 14s - loss: 1.8023 - accuracy: 0.4850 1696/60000 [..............................] - ETA: 9s - loss: 1.5119 - accuracy: 0.6002 2432/60000 [>.............................] - ETA: 7s - loss: 1.3151 - accuracy: 0.6637 3200/60000 [>.............................] - ETA: 6s - loss: 1.1663 - accuracy: 0.7056 3968/60000 [>.............................] - ETA: 5s - loss: 1.0533 - accuracy: 0.7344 4704/60000 [=>............................] - ETA: 5s - loss: 0.9696 - accuracy: 0.7564 5408/60000 [=>............................] - ETA: 5s - loss: 0.9162 - accuracy: 0.7681 6112/60000 [==>...........................] - ETA: 5s - loss: 0.8692 - accuracy: 0.7804 6784/60000 [==>...........................] - ETA: 4s - loss: 0.8225 - accuracy: 0.7933 7424/60000 [==>...........................] - ETA: 4s - loss: 0.7871 - accuracy: 0.8021 8128/60000 [===>..........................] - ETA: 4s - loss: 0.7546 - accuracy: 0.8099 8960/60000 [===>..........................] - ETA: 4s - loss: 0.7196 - accuracy: 0.8183 9568/60000 [===>..........................] - ETA: 4s - loss: 0.6987 - accuracy: 0.8230 10144/60000 [====>.........................] - ETA: 4s - loss: 0.6812 - accuracy: 0.8262 10784/60000 [====>.........................] - ETA: 4s - loss: 0.6640 - accuracy: 0.8297 11456/60000 [====>.........................] - ETA: 4s - loss: 0.6462 - accuracy: 0.8329 12128/60000 [=====>........................] - ETA: 4s - loss: 0.6297 - accuracy: 0.8366 12704/60000 [=====>........................] - ETA: 4s - loss: 0.6156 - accuracy: 0.8405 13408/60000 [=====>........................] - ETA: 3s - loss: 0.6009 - accuracy: 0.8430 14112/60000 [======>.......................] - ETA: 3s - loss: 0.5888 - accuracy: 0.8457 14816/60000 [======>.......................] - ETA: 3s - loss: 0.5772 - accuracy: 0.8487 15488/60000 [======>.......................] - ETA: 3s - loss: 0.5685 - accuracy: 0.8503 16192/60000 [=======>......................] - ETA: 3s - loss: 0.5576 - accuracy: 0.8534 16896/60000 [=======>......................] - ETA: 3s - loss: 0.5477 - accuracy: 0.8555 17600/60000 [=======>......................] - ETA: 3s - loss: 0.5380 - accuracy: 0.8576 18240/60000 [========>.....................] - ETA: 3s - loss: 0.5279 - accuracy: 0.8600 18976/60000 [========>.....................] - ETA: 3s - loss: 0.5208 - accuracy: 0.8617 19712/60000 [========>.....................] - ETA: 3s - loss: 0.5125 - accuracy: 0.8634 20416/60000 [=========>....................] - ETA: 3s - loss: 0.5046 - accuracy: 0.8654 21088/60000 [=========>....................] - ETA: 3s - loss: 0.4992 - accuracy: 0.8669 21792/60000 [=========>....................] - ETA: 3s - loss: 0.4932 - accuracy: 0.8684 22432/60000 [==========>...................] - ETA: 3s - loss: 0.4893 - accuracy: 0.8693 23072/60000 [==========>...................] - ETA: 2s - loss: 0.4845 - accuracy: 0.8703 23648/60000 [==========>...................] - ETA: 2s - loss: 0.4800 - accuracy: 0.8712 24096/60000 [===========>..................] - ETA: 2s - loss: 0.4776 - accuracy: 0.8718 24576/60000 [===========>..................] - ETA: 2s - loss: 0.4733 - accuracy: 0.8728 25056/60000 [===========>..................] - ETA: 2s - loss: 0.4696 - accuracy: 0.8736 25568/60000 [===========>..................] - ETA: 2s - loss: 0.4658 - accuracy: 0.8745 26080/60000 [============>.................] - ETA: 2s - loss: 0.4623 - accuracy: 0.8753 26592/60000 [============>.................] - ETA: 2s - loss: 0.4600 - accuracy: 0.8756 27072/60000 [============>.................] - ETA: 2s - loss: 0.4566 - accuracy: 0.8763 27584/60000 [============>.................] - ETA: 2s - loss: 0.4532 - accuracy: 0.8771 28032/60000 [=============>................] - ETA: 2s - loss: 0.4513 - accuracy: 0.8775 28512/60000 [=============>................] - ETA: 2s - loss: 0.4477 - accuracy: 0.8784 28992/60000 [=============>................] - ETA: 2s - loss: 0.4464 - accuracy: 0.8786 29472/60000 [=============>................] - ETA: 2s - loss: 0.4439 - accuracy: 0.8791 29952/60000 [=============>................] - ETA: 2s - loss: 0.4404 - accuracy: 0.8800 30464/60000 [==============>...............] - ETA: 2s - loss: 0.4375 - accuracy: 0.8807 30784/60000 [==============>...............] - ETA: 2s - loss: 0.4349 - accuracy: 0.8813 31296/60000 [==============>...............] - ETA: 2s - loss: 0.4321 - accuracy: 0.8820 31808/60000 [==============>...............] - ETA: 2s - loss: 0.4301 - accuracy: 0.8827 32256/60000 [===============>..............] - ETA: 2s - loss: 0.4279 - accuracy: 0.8832 32736/60000 [===============>..............] - ETA: 2s - loss: 0.4258 - accuracy: 0.8838 33280/60000 [===============>..............] - ETA: 2s - loss: 0.4228 - accuracy: 0.8844 33920/60000 [===============>..............] - ETA: 2s - loss: 0.4195 - accuracy: 0.8849 34560/60000 [================>.............] - ETA: 2s - loss: 0.4179 - accuracy: 0.8852 35104/60000 [================>.............] - ETA: 2s - loss: 0.4165 - accuracy: 0.8854 35680/60000 [================>.............] - ETA: 2s - loss: 0.4139 - accuracy: 0.8860 36288/60000 [=================>............] - ETA: 2s - loss: 0.4111 - accuracy: 0.8870 36928/60000 [=================>............] - ETA: 2s - loss: 0.4088 - accuracy: 0.8874 37504/60000 [=================>............] - ETA: 2s - loss: 0.4070 - accuracy: 0.8878 38048/60000 [==================>...........] - ETA: 1s - loss: 0.4052 - accuracy: 0.8882 38656/60000 [==================>...........] - ETA: 1s - loss: 0.4031 - accuracy: 0.8888 39264/60000 [==================>...........] - ETA: 1s - loss: 0.4007 - accuracy: 0.8894 39840/60000 [==================>...........] - ETA: 1s - loss: 0.3997 - accuracy: 0.8896 40416/60000 [===================>..........] - ETA: 1s - loss: 0.3978 - accuracy: 0.8901 40960/60000 [===================>..........] - ETA: 1s - loss: 0.3958 - accuracy: 0.8906 41504/60000 [===================>..........] - ETA: 1s - loss: 0.3942 - accuracy: 0.8911 42016/60000 [====================>.........] - ETA: 1s - loss: 0.3928 - accuracy: 0.8915 42592/60000 [====================>.........] - ETA: 1s - loss: 0.3908 - accuracy: 0.8920 43168/60000 [====================>.........] - ETA: 1s - loss: 0.3889 - accuracy: 0.8924 43744/60000 [====================>.........] - ETA: 1s - loss: 0.3868 - accuracy: 0.8931 44288/60000 [=====================>........] - ETA: 1s - loss: 0.3864 - accuracy: 0.8931 44832/60000 [=====================>........] - ETA: 1s - loss: 0.3842 - accuracy: 0.8938 45408/60000 [=====================>........] - ETA: 1s - loss: 0.3822 - accuracy: 0.8944 45984/60000 [=====================>........] - ETA: 1s - loss: 0.3804 - accuracy: 0.8949 46560/60000 [======================>.......] - ETA: 1s - loss: 0.3786 - accuracy: 0.8953 47168/60000 [======================>.......] - ETA: 1s - loss: 0.3767 - accuracy: 0.8958 47808/60000 [======================>.......] - ETA: 1s - loss: 0.3744 - accuracy: 0.8963 48416/60000 [=======================>......] - ETA: 1s - loss: 0.3732 - accuracy: 0.8966 48928/60000 [=======================>......] - ETA: 0s - loss: 0.3714 - accuracy: 0.8971 49440/60000 [=======================>......] - ETA: 0s - loss: 0.3701 - accuracy: 0.8974 50048/60000 [========================>.....] - ETA: 0s - loss: 0.3678 - accuracy: 0.8979 50688/60000 [========================>.....] - ETA: 0s - loss: 0.3669 - accuracy: 0.8983 51264/60000 [========================>.....] - ETA: 0s - loss: 0.3654 - accuracy: 0.8988 51872/60000 [========================>.....] - ETA: 0s - loss: 0.3636 - accuracy: 0.8992 52608/60000 [=========================>....] - ETA: 0s - loss: 0.3618 - accuracy: 0.8997 53376/60000 [=========================>....] - ETA: 0s - loss: 0.3599 - accuracy: 0.9003 54048/60000 [==========================>...] - ETA: 0s - loss: 0.3583 - accuracy: 0.9006 54560/60000 [==========================>...] - ETA: 0s - loss: 0.3568 - accuracy: 0.9010 55296/60000 [==========================>...] - ETA: 0s - loss: 0.3548 - accuracy: 0.9016 56064/60000 [===========================>..] - ETA: 0s - loss: 0.3526 - accuracy: 0.9021 56736/60000 [===========================>..] - ETA: 0s - loss: 0.3514 - accuracy: 0.9026 57376/60000 [===========================>..] - ETA: 0s - loss: 0.3499 - accuracy: 0.9029 58112/60000 [============================>.] - ETA: 0s - loss: 0.3482 - accuracy: 0.9033 58880/60000 [============================>.] - ETA: 0s - loss: 0.3459 - accuracy: 0.9039 59584/60000 [============================>.] - ETA: 0s - loss: 0.3444 - accuracy: 0.9043 60000/60000 [==============================] - 5s 87us/step - loss: 0.3435 - accuracy: 0.9046 Epoch 2/2 32/60000 [..............................] - ETA: 11s - loss: 0.0655 - accuracy: 1.0000 736/60000 [..............................] - ETA: 4s - loss: 0.2135 - accuracy: 0.9389 1408/60000 [..............................] - ETA: 4s - loss: 0.2217 - accuracy: 0.9361 1984/60000 [..............................] - ETA: 4s - loss: 0.2316 - accuracy: 0.9390 2432/60000 [>.............................] - ETA: 4s - loss: 0.2280 - accuracy: 0.9379 3040/60000 [>.............................] - ETA: 4s - loss: 0.2374 - accuracy: 0.9368 3808/60000 [>.............................] - ETA: 4s - loss: 0.2251 - accuracy: 0.9386 4576/60000 [=>............................] - ETA: 4s - loss: 0.2225 - accuracy: 0.9379 5216/60000 [=>............................] - ETA: 4s - loss: 0.2208 - accuracy: 0.9377 5920/60000 [=>............................] - ETA: 4s - loss: 0.2173 - accuracy: 0.9383 6656/60000 [==>...........................] - ETA: 4s - loss: 0.2217 - accuracy: 0.9370 7392/60000 [==>...........................] - ETA: 4s - loss: 0.2224 - accuracy: 0.9360 8096/60000 [===>..........................] - ETA: 4s - loss: 0.2234 - accuracy: 0.9363 8800/60000 [===>..........................] - ETA: 3s - loss: 0.2235 - accuracy: 0.9358 9408/60000 [===>..........................] - ETA: 3s - loss: 0.2196 - accuracy: 0.9365 10016/60000 [====>.........................] - ETA: 3s - loss: 0.2207 - accuracy: 0.9363 10592/60000 [====>.........................] - ETA: 3s - loss: 0.2183 - accuracy: 0.9369 11168/60000 [====>.........................] - ETA: 3s - loss: 0.2177 - accuracy: 0.9377 11776/60000 [====>.........................] - ETA: 3s - loss: 0.2154 - accuracy: 0.9385 12544/60000 [=====>........................] - ETA: 3s - loss: 0.2152 - accuracy: 0.9393 13216/60000 [=====>........................] - ETA: 3s - loss: 0.2163 - accuracy: 0.9390 13920/60000 [=====>........................] - ETA: 3s - loss: 0.2155 - accuracy: 0.9391 14624/60000 [======>.......................] - ETA: 3s - loss: 0.2150 - accuracy: 0.9391 15424/60000 [======>.......................] - ETA: 3s - loss: 0.2143 - accuracy: 0.9398 16032/60000 [=======>......................] - ETA: 3s - loss: 0.2122 - accuracy: 0.9405 16672/60000 [=======>......................] - ETA: 3s - loss: 0.2096 - accuracy: 0.9409 17344/60000 [=======>......................] - ETA: 3s - loss: 0.2091 - accuracy: 0.9411 18112/60000 [========>.....................] - ETA: 3s - loss: 0.2086 - accuracy: 0.9416 18784/60000 [========>.....................] - ETA: 3s - loss: 0.2084 - accuracy: 0.9418 19392/60000 [========>.....................] - ETA: 3s - loss: 0.2076 - accuracy: 0.9418 20000/60000 [=========>....................] - ETA: 3s - loss: 0.2067 - accuracy: 0.9421 20608/60000 [=========>....................] - ETA: 3s - loss: 0.2071 - accuracy: 0.9419 21184/60000 [=========>....................] - ETA: 3s - loss: 0.2056 - accuracy: 0.9423 21856/60000 [=========>....................] - ETA: 3s - loss: 0.2063 - accuracy: 0.9419 22624/60000 [==========>...................] - ETA: 2s - loss: 0.2059 - accuracy: 0.9421 23328/60000 [==========>...................] - ETA: 2s - loss: 0.2056 - accuracy: 0.9422 23936/60000 [==========>...................] - ETA: 2s - loss: 0.2051 - accuracy: 0.9423 24512/60000 [===========>..................] - ETA: 2s - loss: 0.2041 - accuracy: 0.9424 25248/60000 [===========>..................] - ETA: 2s - loss: 0.2036 - accuracy: 0.9426 26016/60000 [============>.................] - 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accuracy: 0.9438 50304/60000 [========================>.....] - ETA: 0s - loss: 0.1965 - accuracy: 0.9437 51072/60000 [========================>.....] - ETA: 0s - loss: 0.1967 - accuracy: 0.9437 51744/60000 [========================>.....] - ETA: 0s - loss: 0.1961 - accuracy: 0.9439 52480/60000 [=========================>....] - ETA: 0s - loss: 0.1957 - accuracy: 0.9439 53248/60000 [=========================>....] - ETA: 0s - loss: 0.1959 - accuracy: 0.9438 54016/60000 [==========================>...] - ETA: 0s - loss: 0.1963 - accuracy: 0.9437 54592/60000 [==========================>...] - ETA: 0s - loss: 0.1965 - accuracy: 0.9436 55168/60000 [==========================>...] - ETA: 0s - loss: 0.1962 - accuracy: 0.9436 55776/60000 [==========================>...] - ETA: 0s - loss: 0.1959 - accuracy: 0.9437 56448/60000 [===========================>..] - ETA: 0s - loss: 0.1965 - accuracy: 0.9437 57152/60000 [===========================>..] - ETA: 0s - loss: 0.1958 - accuracy: 0.9439 57824/60000 [===========================>..] - ETA: 0s - loss: 0.1956 - accuracy: 0.9438 58560/60000 [============================>.] - ETA: 0s - loss: 0.1951 - accuracy: 0.9440 59360/60000 [============================>.] - ETA: 0s - loss: 0.1947 - accuracy: 0.9440 60000/60000 [==============================] - 5s 76us/step - loss: 0.1946 - accuracy: 0.9440 Testing------------ 32/10000 [..............................] - ETA: 15s 1248/10000 [==>...........................] - ETA: 0s 2656/10000 [======>.......................] - ETA: 0s 4064/10000 [===========>..................] - ETA: 0s 5216/10000 [==============>...............] - ETA: 0s 6464/10000 [==================>...........] - ETA: 0s 7744/10000 [======================>.......] - ETA: 0s 9056/10000 [==========================>...] - ETA: 0s 9984/10000 [============================>.] - ETA: 0s 10000/10000 [==============================] - 0s 47us/step test loss: 0.17407772153392434 test accuracy: 0.9513000249862671
补充知识：Keras 搭建简单神经网络：顺序模型+回归问题
多层全连接神经网络
每层神经元个数、神经网络层数、激活函数等可自由修改
使用不同的损失函数可适用于其他任务，比如：分类问题
这是Keras搭建神经网络模型最基础的方法之一，Keras还有其他进阶的方法，官网给出了一些基本使用方法：Keras官网
# 这里搭建了一个4层全连接神经网络（不算输入层），传入函数以及函数内部的参数均可自由修改
def ann(X, y):
'''
X: 输入的训练集数据
y: 训练集对应的标签
'''
'''初始化模型'''
# 首先定义了一个顺序模型作为框架，然后往这个框架里面添加网络层
# 这是最基础搭建神经网络的方法之一
model = Sequential()
'''开始添加网络层'''
# Dense表示全连接层，第一层需要我们提供输入的维度 input_shape
# Activation表示每层的激活函数，可以传入预定义的激活函数，也可以传入符合接口规则的其他高级激活函数
model.add(Dense(64, input_shape=(X.shape[1],)))
model.add(Activation('sigmoid'))
model.add(Dense(256))
model.add(Activation('relu'))
model.add(Dense(256))
model.add(Activation('tanh'))
model.add(Dense(32))
model.add(Activation('tanh'))
# 输出层，输出的维度大小由具体任务而定
# 这里是一维输出的回归问题
model.add(Dense(1))
model.add(Activation('linear'))
'''模型编译'''
# optimizer表示优化器（可自由选择），loss表示使用哪一种
model.compile(optimizer='rmsprop', loss='mean_squared_error')
# 自定义学习率，也可以使用原始的基础学习率
reduce_lr = ReduceLROnPlateau(monitor='loss', factor=0.1, patience=10,
verbose=0, mode='auto', min_delta=0.001,
cooldown=0, min_lr=0)
'''模型训练'''
# 这里的模型也可以先从函数返回后，再进行训练
# epochs表示训练的轮数，batch_size表示每次训练的样本数量（小批量学习），validation_split表示用作验证集的训练数据的比例
# callbacks表示回调函数的集合，用于模型训练时查看模型的内在状态和统计数据，相应的回调函数方法会在各自的阶段被调用
# verbose表示输出的详细程度，值越大输出越详细
model.fit(X, y, epochs=100,
batch_size=50, validation_split=0.0,
callbacks=[reduce_lr],
verbose=0)
# 打印模型结构
print(model.summary())
return model
下图是此模型的结构图，其中下划线后面的数字是根据调用次数而定
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