3. MNIST dataset classification

One 、MNIST Data sets and Softmax

1.MNIST Data sets

Most examples use handwritten digits MNIST Data sets . The dataset contains 60,000 Examples and for training 10,000 An example for testing .

Each picture contains 28*28 Pixel , stay MNIST The training data set is a shape of [60000,28,28] Tensor , We first need to convert the data set into [60000,784], Then it can be put into the network for training . The first dimension number is used to index images , The second dimension number is used to index the pixels in each image . Generally, we also need to normalize the data in the picture 0~1 Between .

MNIST The label of the dataset is between 0-9 The number of , We need to convert labels into "one-hotvectors". One one-hot A vector other than one digit is 1 Outside , The other dimension numbers are 0, Such as tag 0 Will be expressed as ([1,0,0,0,0,0,0,0,0,0]), label 3 Will be expressed as ([0,0,0,1,0,0,0,0,0,0]).
therefore ,MNIST The label of the dataset is a [60000,10] Digital matrix of .

28*28=784, Each picture has 784 Pixels , Corresponding 784 Neurons . The final output 10 Neurons correspond to 10 A digital .

2.Softmax

Softmax The function is to convert the output of neural network into probability value .
We know MNIST The result is 0-9, Our model may infer the number of a picture 9 Is the probability that 80%, It's the number. 8 Is the probability that 10%, Then the probability of other numbers is smaller , The total probability adds up to 1. This is a use of softmax Classic case of regression model .softmax The model can be used to assign probabilities to different objects .

Two 、MNIST Data set classification

The code running platform is jupyter-notebook, Code blocks in the article , According to jupyter-notebook Written in the order of division in , Run article code , Glue directly into jupyter-notebook that will do .

1. Import third-party library

import numpy as np
from keras.datasets import mnist
from keras.utils import np_utils
from keras.models import Sequential
from keras.layers import Dense
from tensorflow.keras.optimizers import SGD

2. Loading data and data preprocessing

#  Load data 
(x_train,y_train),(x_test,y_test) = mnist.load_data()
# (60000, 28, 28)
print("x_shape:\n",x_train.shape)
# (60000,)  Not yet one-hot code   You need to operate by yourself later 
print("y_shape:\n",y_train.shape)
# (60000, 28, 28) -> (60000,784) reshape() Middle parameter filling -1 Parameter results can be calculated automatically   Divide 255.0 To normalize 
x_train = x_train.reshape(x_train.shape[0],-1)/255.0
x_test = x_test.reshape(x_test.shape[0],-1)/255.0
#  in one hot Format 
y_train = np_utils.to_categorical(y_train,num_classes=10)
y_test = np_utils.to_categorical(y_test,num_classes=10)

3. Training models

#  Creating models   Input 784 Neurons , Output 10 Neurons 
model = Sequential([
        #  Define output yes 10  Input is 784, Set offset to 1, add to softmax Activation function 
        Dense(units=10,input_dim=784,bias_initializer='one',activation="softmax"),
])
#  Define optimizer 
sgd = SGD(lr=0.2)

#  Define optimizer ,loss_function, The accuracy of calculation during training 
model.compile(
    optimizer=sgd,
    loss="mse",
    metrics=['accuracy']
)
#  Training models 
model.fit(x_train,y_train,batch_size=32,epochs=10)

#  Evaluation model 
loss,accuracy = model.evaluate(x_test,y_test)

print("\ntest loss",loss)
print("accuracy:",accuracy)

The final run result ：

Be careful

• Dense(units=10,input_dim=784,bias_initializer='one',activation="softmax") It's used here softmax Activation function .
• Here we use fit Method of model training , The previous linear regression and nonlinear regression model training methods are different from this .

Code ：

model.compile(
    optimizer=sgd,
    loss="mse",
    metrics=['accuracy']
)

Add metrics=['accuracy'], You can calculate the accuracy rate during training .