Softmax迴歸介紹

我們知道MNIST的每一張圖片都表示一個數字，從0到9。我們希望得到給定圖片代表每個數字的概率。比如說，我們的模型可能推測一張包含9的圖片代表數字9的概率是80%但是判斷它是8的概率是5%（因為8和9都有上半部分的小圓），然後給予它代表其他數字的概率更小的值。
線性層的spftmax迴歸模型識別手寫字是一個使用softmax迴歸（softmax regression）模型的經典案例。softmax模型可以用來給不同的物件分配概率。即使在之後，我們訓練更加精細的模型時，最後一步也需要用softmax來分配概率。

溫故：
用到到tensnorflowzhong 的函式：

• tf.nn.softmax（）函式建立softmax模型
• tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)
  梯度下降優化器求解
• argmax()函式 求最大值的索引

# tensorflow做邏輯迴歸,線性層的spftmax迴歸模型識別手寫字

import tensorflow as tf
import numpy as np
import matplotlib.pylab as plt
from tensorflow.examples.tutorials.mnist import input_data

#mnist資料輸入
 

'''
在MNIST訓練資料集中，mnist.train.images 是一個形狀為 [60000, 784] 的張量，
第一個維度數字用來索引圖片，第二個維度數字用來索引每張圖片中的畫素點。
在此張量裡的每一個元素，都表示某張圖片裡的某個畫素的強度值，值介於0和1之間。
'''
mnist = input_data.read_data_sets('data/', one_hot=True)

#placeholder是一個佔位符，None表示此張量的第一個維度可以是任何長度
x = tf.placeholder("float",[None,784])
y = tf.placeholder("float"
 
,[None,10])
#定義W維度是[784，10]，初始值為0.W 和 b都是確定的，784個畫素點，需要784個權重係數
#定義b維度是[10]，初始值是0
W = tf.Variable(tf.zeros([784,10]))
b = tf.Variable(tf.zeros([10]))

#Logistic regression model 邏輯迴歸模型
#LR是二分類問題，要升級到softmax多分類問題
actv = tf.nn.softmax(tf.matmul(x,W)+ b) #預測值，每個樣本輸出10個值

#損失函式Cost Fuction -logP P是屬於真實樣本的概率值（預測值）
##以估計值y和實際值y_data之間的均方誤差作為損失
cost = tf.reduce_mean(-tf.reduce_sum(y*tf.log(actv),reduction_indices=1))

#optimize學習率
learning_rate = 0.01
#梯度下降優化器求解，訓練的過程就是最下化損失函式cost
optm = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)

#Predition argmax()函式 求最大值的索引
#其中tf.argmax(actv,1) 代表預測值第一行最大數對應的索引值 ，tf.argmax(y,1)真實值對應的索引
#其中tf.argmax(actv,0) 代表預測值第一列最大數對應的索引值 ，tf.argmax(y,0)真實值對應的索引
#預測值actv的索引和label值（真實值）的索引是否一樣，pred返回值是True 或者 False
pred = tf.equal(tf.argmax(actv,1),tf.argmax(y,1))
#accuracy準確率 tf.cast將true和false轉換為float型別，true為1和False為0，累加衡量準確率
accr = tf.reduce_mean(tf.cast(pred, "float"))

#Initializer初始化
init = tf.global_variables_initializer()

#所有訓練樣本迭代次數
train_epochs = 50
#每次迭代的樣本數
batch_size = 100
display_step = 5

#Session
sess = tf.Session()
sess.run(init)

#mini_batch Learning
#所有樣本進行50次迭代
for epoch in range(train_epochs):
    avg_cost = 0 #初始損失值為0
    num_batch = int(mnist.train.num_examples/batch_size) #取整，計算有多少簇
    #一次迭代，50個樣本
    for i in range(num_batch):
        batch_xs, batch_ys = mnist.train.next_batch(batch_size)
        # 將資料輸入給模型
        sess.run(optm, feed_dict={x: batch_xs, y: batch_ys}) 
        feeds = {x: batch_xs, y: batch_ys}
        # 損失函式值
        avg_cost += sess.run(cost, feed_dict=feeds)/num_batch #把每一小簇最小化的損失值加到一起
    #display
    if epoch % display_step == 0:       #在一個簇中每5個列印一次
        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, train_epochs, avg_cost, train_acc, test_acc))

print('Done')

output:

F:\Anaconda\python.exe D:/PycharmProjects/tensorflow邏輯迴歸實現.py
WARNING:tensorflow:From D:/PycharmProjects/tensorflow邏輯迴歸實現.py:15: read_data_sets (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use alternatives such as official/mnist/dataset.py from tensorflow/models.
WARNING:tensorflow:From F:\Anaconda\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:260: maybe_download (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.
Instructions for updating:
Please write your own downloading logic.
Extracting data/train-images-idx3-ubyte.gz
WARNING:tensorflow:From F:\Anaconda\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:262: extract_images (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use tf.data to implement this functionality.
Extracting data/train-labels-idx1-ubyte.gz
WARNING:tensorflow:From F:\Anaconda\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:267: extract_labels (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use tf.data to implement this functionality.
WARNING:tensorflow:From F:\Anaconda\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:110: dense_to_one_hot (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use tf.one_hot on tensors.
Extracting data/t10k-images-idx3-ubyte.gz
Extracting data/t10k-labels-idx1-ubyte.gz
WARNING:tensorflow:From F:\Anaconda\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:290: DataSet.__init__ (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use alternatives such as official/mnist/dataset.py from tensorflow/models.
2018-08-30 15:04:53.025707: I tensorflow/core/platform/cpu_feature_guard.cc:141] Your CPU supports instructions that this TensorFlow binary was not compiled to use: AVX AVX2
Epoch: 000/050 cost: 1.177109451 train_acc: 0.870 test_acc: 0.852
Epoch: 005/050 cost: 0.440929337 train_acc: 0.850 test_acc: 0.895
Epoch: 010/050 cost: 0.383323831 train_acc: 0.880 test_acc: 0.905
Epoch: 015/050 cost: 0.357286127 train_acc: 0.860 test_acc: 0.909
Epoch: 020/050 cost: 0.341520180 train_acc: 0.930 test_acc: 0.913
Epoch: 025/050 cost: 0.330535250 train_acc: 0.900 test_acc: 0.914
Epoch: 030/050 cost: 0.322328042 train_acc: 0.880 test_acc: 0.915
Epoch: 035/050 cost: 0.315957263 train_acc: 0.880 test_acc: 0.917
Epoch: 040/050 cost: 0.310728670 train_acc: 0.870 test_acc: 0.918
Epoch: 045/050 cost: 0.306382290 train_acc: 0.970 test_acc: 0.919
Done

Process finished with exit code 0