在之前的博文《logistic迴歸》中，我們簡單的提到了softmax迴歸。本文將首先介紹softmax迴歸的基本原理。然後比較softmax迴歸於logistic迴歸的關聯。最後用開源TensorFlow編寫演算法並應用於手寫數字（MNIST）的識別。

softmax原理

softmax與logistic

用TensorFlow實現softmax regression識別手寫數字

#!/usr/bin/env python
# @Time    : 3/28/17 11:14 PM
# @Author  : SunXiangguo
# @version : Anaconda3.6+Ubuntu_16.04_STL_64
 

# @File    : 22.py
# @Software: PyCharm
"""A very simple MNIST classifier.
"""
from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf

mnist = input_data.read_data_sets("MNIST_data", one_hot=True)
print(mnist.train.images.shape,mnist.train.labels.shape)

sess = tf.InteractiveSession()

# step1:define the algorithm for forward calculate
 

x = tf.placeholder(tf.float32, [None, 784])
W = tf.Variable(tf.zeros([784, 10]))
b = tf.Variable(tf.zeros([10]))
y = tf.nn.softmax(tf.matmul(x, W)+b)

# step2: define loss function
y_ = tf.placeholder(tf.float32, [None, 10])
cross_entropy = tf.reduce_mean(-tf.reduce_sum(y_*tf.log(y),reduction_indices=[1
 
]))

# step3: train model iterally
train_step = tf.train.GradientDescentOptimizer(0.5).minimize(cross_entropy)
tf.global_variables_initializer().run()
for i in range(1000):
    batch_xs , batch_ys = mnist.train.next_batch(100)
    train_step.run({x:batch_xs,y_:batch_ys})

# step4:test model in test_data
correct_prediction = tf.equal(tf.argmax(y,1),tf.argmax(y_,1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
print(accuracy.eval({x:mnist.test.images, y_:mnist.test.labels}))

實驗結果為：92%