MNIST(Mixed National Institute of Standards and Technology)http://yann.lecun.com/exdb/mnist/ ，入门级计算机视觉数据集，美国中学生手写数字。训练集6万张图片，测试集1万张图片。数字经过预处理、格式化，大小调整并居中，图片尺寸固定28x28。数据集小，训练速度快，收敛效果好。

MNIST数据集，NIST数据集子集。4个文件。train-label-idx1-ubyte.gz 训练集标记文件(28881字节)，train-images-idx3-ubyte.gz 训练集图片文件(9912422字节)，t10k-labels-idx1-ubyte.gz，测试集标记文件(4542字节)，t10k-images-idx3-ubyte.gz 测试集图片文件(1648877字节)。测试集，前5000个样例取自原始NIST训练集，后5000个取自原始NIST测试集。

训练集标记文件 train-labels-idx1-ubyt格式：offset、type、value、description。magic number(MSB first)、number of items、label。
MSB(most significant bit，最高有效位)，二进制，MSB最高加权位。MSB位于二进制最左侧，MSB first 最高有效位在前。 magic number 写入ELF格式(Executable and Linkable Format)的ELF头文件常量，检查和自己设定是否一致判断文件是否损坏。

训练集图片文件 train-images-idx3-ubyte格式：magic number、number of images、number of rows、number of columns、pixel。
pixel(像素)取值范围0-255，0-255代表背景色(白色)，255代表前景色(黑色)。

测试集标记文件 t10k-labels-idx1-ubyte 格式：magic number(MSB first)、number of items、label。

测试集图片文件 t10k-images-idx3-ubyte格式：magic number、number of images、number of rows、number of columns、pixel。

tensor flow-1.1.0/tensorflow/examples/tutorials/mnist。mnist_softmax.py 回归训练，full_connected_feed.py Feed数据方式训练，mnist_with_summaries.py 卷积神经网络(CNN) 训练过程可视化，mnist_softmax_xla.py XLA框架。

MNIST分类问题。

Softmax回归解决两种以上分类。Logistic回归模型在分类问题推广。tensorflow-1.1.0/tensorflow/examples/tutorials/mnist/mnist_softmax.py。

加载数据。导入input_data.py文件， tensorflow.contrib.learn.read_data_sets加载数据。FLAGS.data_dir MNIST路径，可自定义。one_hot标记，长度为n数组，只有一个元素是1.0，其他元素是0.0。输出层softmax，输出概率分布，要求输入标记概率分布形式，以更计算交叉熵。

构建回归模型。输入原始真实值(group truth)，计算softmax函数拟合预测值，定义损失函数和优化器。用梯度下降算法以0.5学习率最小化交叉熵。tf.train.GradientDescentOptimizer。

训练模型。初始化创建变量，会话启动模型。模型循环训练1000次，每次循环随机抓取训练数据100个数据点，替换占位符。随机训练(stochastic training)，SGD方法梯度下降，每次从训练数据随机抓取小部分数据梯度下降训练。BGD每次对所有训练数据计算。SGD学习数据集总体特征，加速训练过程。

评估模型。tf.argmax(y,1)返回模型对任一输入x预测标记值，tf.argmax(y_,1) 正确标记值。tf.equal检测预测值和真实值是否匹配，预测布尔值转化浮点数，取平均值。

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import argparse
import sys
from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf
FLAGS = None
def main(_):
  # Import data 加载数据
  mnist = input_data.read_data_sets(FLAGS.data_dir, one_hot=True)
  # Create the model 定义回归模型
  x = tf.placeholder(tf.float32, [None, 784])
  W = tf.Variable(tf.zeros([784, 10]))
  b = tf.Variable(tf.zeros([10]))
  y = tf.matmul(x, W) + b #预测值
  # Define loss and optimizer 定义损失函数和优化器
  y_ = tf.placeholder(tf.float32, [None, 10]) # 输入真实值占位符
  # tf.nn.softmax_cross_entropy_with_logits计算预测值y与真实值y_差值，取平均值
  cross_entropy = tf.reduce_mean(
      tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=y))
  # SGD优化器
  train_step = tf.train.GradientDescentOptimizer(0.5).minimize(cross_entropy)
  # InteractiveSession()创建交互式上下文TensorFlow会话，交互式会话会成为默认会话，可以运行操作(OP)方法(tf.Tensor.eval、tf.Operation.run)
  sess = tf.InteractiveSession()
  tf.global_variables_initializer().run()
  # Train 训练模型
  for _ in range(1000):
    batch_xs, batch_ys = mnist.train.next_batch(100)
    sess.run(train_step, feed_dict={x: batch_xs, y_: batch_ys})
  # Test trained model 评估训练模型
  correct_prediction = tf.equal(tf.argmax(y, 1), tf.argmax(y_, 1))
  accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
  # 计算模型测试集准确率
  print(sess.run(accuracy, feed_dict={x: mnist.test.images,
                                      y_: mnist.test.labels}))
if __name__ == '__main__':
  parser = argparse.ArgumentParser()
  parser.add_argument('--data_dir', type=str, default='/tmp/tensorflow/mnist/input_data',
                      help='Directory for storing input data')
  FLAGS, unparsed = parser.parse_known_args()
  tf.app.run(main=main, argv=[sys.argv[0]] + unparsed)

训练过程可视化。tensorflow-1.1.0/tensorflow/examples/tutorials/mnist/mnist_summaries.py 。
TensorBoard可视化，训练过程，记录结构化数据，支行本地服务器，监听6006端口，浏览器请求页面，分析记录数据，绘制统计图表，展示计算图。
运行脚本：python mnist_with_summaries.py。
训练过程数据存储在/tmp/tensorflow/mnist目录，可命令行参数--log_dir指定。运行tree命令，ipnut_data # 存放训练数据，logs # 训练结果日志，train # 训练集结果日志。运行tensorboard命令，打开浏览器，查看训练可视化结果，logdir参数标明日志文件存储路径，命令 tensorboard --logdir=/tmp/tensorflow/mnist/logs/mnist_with_summaries 。创建摘要文件写入符(FileWriter)指定。

# sess.graph  图定义，图可视化
file_writer = tf.summary.FileWriter('/tmp/tensorflow/mnist/logs/mnist_with_summaries', sess.graph)

浏览器打开服务地址，进入可视化操作界面。

可视化实现。

给一个张量添加多个摘要描述函数variable_summaries。SCALARS面板显示每层均值、标准差、最大值、最小值。
构建网络模型，weights、biases调用variable_summaries，每层采用tf.summary.histogram绘制张量激活函数前后变化。HISTOGRAMS面板显示。
绘制准确率、交叉熵，SCALARS面板显示。

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import argparse
import os
import sys
import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
FLAGS = None
def train():
  # Import data
  mnist = input_data.read_data_sets(FLAGS.data_dir,
                                    one_hot=True,
                                    fake_data=FLAGS.fake_data)
  sess = tf.InteractiveSession()
  # Create a multilayer model.
  # Input placeholders
  with tf.name_scope('input'):
    x = tf.placeholder(tf.float32, [None, 784], name='x-input')
    y_ = tf.placeholder(tf.float32, [None, 10], name='y-input')
  with tf.name_scope('input_reshape'):
    image_shaped_input = tf.reshape(x, [-1, 28, 28, 1])
    tf.summary.image('input', image_shaped_input, 10)
  # We can't initialize these variables to 0 - the network will get stuck.
  def weight_variable(shape):
    """Create a weight variable with appropriate initialization."""
    initial = tf.truncated_normal(shape, stddev=0.1)
    return tf.Variable(initial)
  def bias_variable(shape):
    """Create a bias variable with appropriate initialization."""
    initial = tf.constant(0.1, shape=shape)
    return tf.Variable(initial)
  def variable_summaries(var):
    """Attach a lot of summaries to a Tensor (for TensorBoard visualization)."""
    """对一个张量添加多个摘要描述"""
    with tf.name_scope('summaries'):
      mean = tf.reduce_mean(var)
      tf.summary.scalar('mean', mean) # 均值
      with tf.name_scope('stddev'):
        stddev = tf.sqrt(tf.reduce_mean(tf.square(var - mean)))
      tf.summary.scalar('stddev', stddev) # 标准差
      tf.summary.scalar('max', tf.reduce_max(var)) # 最大值
      tf.summary.scalar('min', tf.reduce_min(var)) # 最小值
      tf.summary.histogram('histogram', var)
  def nn_layer(input_tensor, input_dim, output_dim, layer_name, act=tf.nn.relu):
    # Adding a name scope ensures logical grouping of the layers in the graph.
    # 确保计算图中各层分组，每层添加name_scope
    with tf.name_scope(layer_name):
      # This Variable will hold the state of the weights for the layer
      with tf.name_scope('weights'):
        weights = weight_variable([input_dim, output_dim])
        variable_summaries(weights)
      with tf.name_scope('biases'):
        biases = bias_variable([output_dim])
        variable_summaries(biases)
      with tf.name_scope('Wx_plus_b'):
        preactivate = tf.matmul(input_tensor, weights) + biases
        tf.summary.histogram('pre_activations', preactivate) # 激活前直方图
      activations = act(preactivate, name='activation')
      tf.summary.histogram('activations', activations) # 激活后直方图
      return activations
  hidden1 = nn_layer(x, 784, 500, 'layer1')
  with tf.name_scope('dropout'):
    keep_prob = tf.placeholder(tf.float32)
    tf.summary.scalar('dropout_keep_probability', keep_prob)
    dropped = tf.nn.dropout(hidden1, keep_prob)
  # Do not apply softmax activation yet, see below.
  y = nn_layer(dropped, 500, 10, 'layer2', act=tf.identity)
  with tf.name_scope('cross_entropy'):
    diff = tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=y)
    with tf.name_scope('total'):
      cross_entropy = tf.reduce_mean(diff)
  tf.summary.scalar('cross_entropy', cross_entropy) # 交叉熵
  with tf.name_scope('train'):
    train_step = tf.train.AdamOptimizer(FLAGS.learning_rate).minimize(
        cross_entropy)
  with tf.name_scope('accuracy'):
    with tf.name_scope('correct_prediction'):
      correct_prediction = tf.equal(tf.argmax(y, 1), tf.argmax(y_, 1))
    with tf.name_scope('accuracy'):
      accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
  tf.summary.scalar('accuracy', accuracy) # 准确率
  # Merge all the summaries and write them out to
  # /tmp/tensorflow/mnist/logs/mnist_with_summaries (by default)
  merged = tf.summary.merge_all()
  train_writer = tf.summary.FileWriter(FLAGS.log_dir + '/train', sess.graph)
  test_writer = tf.summary.FileWriter(FLAGS.log_dir + '/test')
  tf.global_variables_initializer().run()
  def feed_dict(train):
    """Make a TensorFlow feed_dict: maps data onto Tensor placeholders."""
    if train or FLAGS.fake_data:
      xs, ys = mnist.train.next_batch(100, fake_data=FLAGS.fake_data)
      k = FLAGS.dropout
    else:
      xs, ys = mnist.test.images, mnist.test.labels
      k = 1.0
    return {x: xs, y_: ys, keep_prob: k}
  for i in range(FLAGS.max_steps):
    if i % 10 == 0:  # Record summaries and test-set accuracy
      summary, acc = sess.run([merged, accuracy], feed_dict=feed_dict(False))
      test_writer.add_summary(summary, i)
      print('Accuracy at step %s: %s' % (i, acc))
    else:  # Record train set summaries, and train
      if i % 100 == 99:  # Record execution stats
        run_options = tf.RunOptions(trace_level=tf.RunOptions.FULL_TRACE)
        run_metadata = tf.RunMetadata()
        summary, _ = sess.run([merged, train_step],
                              feed_dict=feed_dict(True),
                              options=run_options,
                              run_metadata=run_metadata)
        train_writer.add_run_metadata(run_metadata, 'step%03d' % i)
        train_writer.add_summary(summary, i)
        print('Adding run metadata for', i)
      else:  # Record a summary
        summary, _ = sess.run([merged, train_step], feed_dict=feed_dict(True))
        train_writer.add_summary(summary, i)
  train_writer.close()
  test_writer.close()
def main(_):
  if tf.gfile.Exists(FLAGS.log_dir):
    tf.gfile.DeleteRecursively(FLAGS.log_dir)
  tf.gfile.MakeDirs(FLAGS.log_dir)
  train()
if __name__ == '__main__':
  parser = argparse.ArgumentParser()
  parser.add_argument('--fake_data', nargs='?', const=True, type=bool,
                      default=False,
                      help='If true, uses fake data for unit testing.')
  parser.add_argument('--max_steps', type=int, default=1000,
                      help='Number of steps to run trainer.')
  parser.add_argument('--learning_rate', type=float, default=0.001,
                      help='Initial learning rate')
  parser.add_argument('--dropout', type=float, default=0.9,
                      help='Keep probability for training dropout.')
  parser.add_argument(
      '--data_dir',
      type=str,
      default=os.path.join(os.getenv('TEST_TMPDIR', '/tmp'),
                           'tensorflow/mnist/input_data'),
      help='Directory for storing input data')
  parser.add_argument(
      '--log_dir',
      type=str,
      default=os.path.join(os.getenv('TEST_TMPDIR', '/tmp'),
                           'tensorflow/mnist/logs/mnist_with_summaries'),
      help='Summaries log directory')
  FLAGS, unparsed = parser.parse_known_args()
  tf.app.run(main=main, argv=[sys.argv[0]] + unparsed)

参考资料：
《TensorFlow技术解析与实战》

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