首先，邏輯迴歸是一個二分類，而mnist是一個十分類，因此我們要做一個多分類的任務，引入一個知識softmax分類器。

softmax分類器公式如下：

舉個例子：

一、接下來準備資料集。

import numpy as np
import tensorflow as tf
import matplotlib.pyplot as plt
import input_data  
mnist      = input_data.read_data_sets('data/', one_hot=True)
trainimg   = mnist.train.images
trainlabel = mnist.train.labels
testimg    = mnist.test.images
testlabel  = mnist.test.labels
print ("MNIST loaded")
 

二、看一下資料集的資料尺寸大小。

print (trainimg.shape)
print (trainlabel.shape)
print (testimg.shape)
print (testlabel.shape)
#print (trainimg)
print (trainlabel[0])

結果：

三、建立tensorflow框架。

x = tf.placeholder("float", [None, 784]) 
y = tf.placeholder("float", [None, 10])  # None is for infinite 
W = tf.Variable(tf.zeros([784, 10]))
b = tf.Variable(tf.zeros([10]))
# LOGISTIC REGRESSION MODEL
actv = tf.nn.softmax(tf.matmul(x, W) + b) 
# COST FUNCTION
cost = tf.reduce_mean(-tf.reduce_sum(y*tf.log(actv), reduction_indices=1)) 
# OPTIMIZER
learning_rate = 0.01
optm = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)
# PREDICTION
pred = tf.equal(tf.argmax(actv, 1), tf.argmax(y, 1))   
# ACCURACY
accr = tf.reduce_mean(tf.cast(pred, "float"))
# INITIALIZER
init = tf.global_variables_initializer()
sess = tf.InteractiveSession()
 

y*tf.log(actv)中y是，所以相乘之後就是對應正確類別的概率值。

四、進行迭代。

training_epochs = 50
batch_size      = 100
display_step    = 5
# SESSION
sess = tf.Session()
sess.run(init)
# MINI-BATCH LEARNING
for epoch in range(training_epochs):
    avg_cost = 0.
    num_batch = int(mnist.train.num_examples/batch_size)
    for i in range(num_batch): 
        batch_xs, batch_ys = mnist.train.next_batch(batch_size)
        sess.run(optm, feed_dict={x: batch_xs, y: batch_ys})
        feeds = {x: batch_xs, y: batch_ys}
        avg_cost += sess.run(cost, feed_dict=feeds)/num_batch
    # DISPLAY
    if epoch % display_step == 0:
        #feeds_train = {x: batch_xs, y: batch_ys}
        #feeds_test = {x: mnist.test.images, y: mnist.test.labels}
        train_acc = sess.run(accr, feed_dict=feeds_train)
        test_acc = sess.run(accr, feed_dict=feeds_test)
        print ("Epoch: %03d/%03d cost: %.9f train_acc: %.3f test_acc: %.3f" 
               % (epoch, training_epochs, avg_cost, train_acc, test_acc))
print ("DONE")
 

結果：