Tensorflow学习笔记

Install

Ubuntu14.04：

#安装pip
sudo apt-get install python-pip python-dev 

#安装tensorflow
sudo pip install --upgrade https://storage.googleapis.com/tensorflow/linux/cpu/tensorflow-0.8.0-cp27-none-linux_x86_64.whl

#安装python-numpy ，python-scipy，python-matplotlib
sudo apt-get install python-numpy
sudo apt-get install python-scipy
sudo apt-get install python-matplotlib

官网上的tensorflow安装命令在虚拟机里面安装不上，可能是网络的问题。

测试是否安装成功：

>>> import tensorflow as tf
>>> hello = tf.constant('Hello, TensorFlow!')
>>> sess = tf.Session()
>>> print(sess.run(hello))
Hello, TensorFlow!
>>> a = tf.constant(10)
>>> b = tf.constant(32)
>>> print(sess.run(a + b))
42

Basic Usage

TensorFlow的基本内容：

• 用图(graph)来表示计算任务
• 在会话(Session)中执行图
• 用(tensor)表示数据
• 用变量(Variable)维护状态
• 用feed和fetch来赋值或取值

构建图

构建图，首先创建源op，比如(Constant)。
TensorFlow Python 库有一个默认图(default graph), op 构造器可以为其增加节点，通常这个默认图对许多程序来说已经够用了。
图构造完成后，需要启动图才能运行操作。启动图需要创建一个Session，参数缺省启动默认图。

以下是示例代码：

import tensorflow as tf

# 创建一个常量 op, 产生一个 1x2 矩阵. 这个 op 被作为一个节点
# 加到默认图中.
#
# 构造器的返回值代表该常量 op 的返回值.
matrix1 = tf.constant([[3., 3.]])

# 创建另外一个常量 op, 产生一个 2x1 矩阵.
matrix2 = tf.constant([[2.],[2.]])

# 创建一个矩阵乘法 matmul op , 把 'matrix1' 和 'matrix2' 作为输入.
# 返回值 'product' 代表矩阵乘法的结果.
product = tf.matmul(matrix1, matrix2)

# 启动默认图.
sess = tf.Session()

# 调用 sess 的 'run()' 方法来执行矩阵乘法 op, 传入 'product' 作为该方法的参数. 
# 上面提到, 'product' 代表了矩阵乘法 op 的输出, 传入它是向方法表明, 我们希望取回
# 矩阵乘法 op 的输出.
#
# 整个执行过程是自动化的, 会话负责传递 op 所需的全部输入. op 通常是并发执行的.
# 
# 函数调用 'run(product)' 触发了图中三个 op (两个常量 op 和一个矩阵乘法 op) 的执行.
#
# 返回值 'result' 是一个 numpy `ndarray` 对象.
result = sess.run(product)
print result
# ==> [[ 12.]]

# 任务完成, 关闭会话.
sess.close()

Session对象使用完成后需要关闭释放资源。除了显示调用close以外，也可以用以下方式来代替原来方法：

with tf.Session() as sess:
  result = sess.run([product])
  print result

在实现上，TensorFlow 将图形定义转换成分布式执行的操作，以充分利用可用的计算资源(如 CPU 或 GPU)。一般不需要显式指定使用 CPU 还是 GPU，TensorFlow 能自动检测。如果检测到 GPU，TensorFlow 会尽可能地利用找到的第一个 GPU 来执行操作。

如果机器上有超过一个可用的 GPU, 除第一个外的其它 GPU 默认是不参与计算的. 为了让 TensorFlow 使用这些 GPU, 你必须将 op 明确指派给它们执行. with…Device 语句用来指派特定的 CPU 或 GPU 执行操作:

with tf.Session() as sess:
  with tf.device("/gpu:1"):
    matrix1 = tf.constant([[3., 3.]])
    matrix2 = tf.constant([[2.],[2.]])
    product = tf.matmul(matrix1, matrix2)

设备用字符串进行标识，目前支持的设备包括：

"/cpu:0": 机器的 CPU.
"/gpu:0": 机器的第一个 GPU, 如果有的话.
"/gpu:1": 机器的第二个 GPU, 以此类推.

交互式方法

文档中的 Python 示例使用一个会话 Session 来 启动图，并调用 Session.run() 方法执行操作。

为了便于使用诸如 IPython 之类的 Python 交互环境, 可以使用 InteractiveSession 代替 Session 类，使用 Tensor.eval() 和 Operation.run() 方法代替 Session.run()。这样可以避免使用一个变量来持有会话。
以下是示例代码：

# 进入一个交互式 TensorFlow 会话.
import tensorflow as tf
sess = tf.InteractiveSession()

x = tf.Variable([1.0, 2.0])
a = tf.constant([3.0, 3.0])

# 使用初始化器 initializer op 的 run() 方法初始化 'x' 
x.initializer.run()

# 增加一个减法 sub op, 从 'x' 减去 'a'. 运行减法 op, 输出结果 
sub = tf.sub(x, a)
print sub.eval()
# ==> [-2. -1.]

变量

变量维护图执行过程中的状态信息，下面的例子演示了如何使用变量实现一个简单的计数器：

# 创建一个变量, 初始化为标量 0.
state = tf.Variable(0, name="counter")

# 创建一个 op, 其作用是使 state 增加 1

one = tf.constant(1)
new_value = tf.add(state, one)
update = tf.assign(state, new_value)

# 启动图后, 变量必须先经过`初始化` (init) op 初始化,
# 首先必须增加一个`初始化` op 到图中.
init_op = tf.initialize_all_variables()

# 启动图, 运行 op
with tf.Session() as sess:
  # 运行 'init' op
  sess.run(init_op)
  # 打印 'state' 的初始值
  print sess.run(state)
  # 运行 op, 更新 'state', 并打印 'state'
  for _ in range(3):
    sess.run(update)
    print sess.run(state)

# 输出:

# 0
# 1
# 2
# 3

在调用 run() 执行表达式之前，图所描绘的表达式(assign(), add() ….)并不会真正执行赋值操作。

用[ ]可以在run的时候取回多个tensor：

input1 = tf.constant(3.0)
input2 = tf.constant(2.0)
input3 = tf.constant(5.0)
intermed = tf.add(input2, input3)
mul = tf.mul(input1, intermed)

with tf.Session():
  result = sess.run([mul, intermed])
  print result

# 输出:
# [array([ 21.], dtype=float32), array([ 7.], dtype=float32)]

还可以用一下方式来待定参数，在run的时候再设定输入：

input1 = tf.placeholder(tf.float32)
input2 = tf.placeholder(tf.float32)
output = tf.mul(input1, input2)

with tf.Session() as sess:
  print sess.run([output], feed_dict={input1:[7.], input2:[2.]})

# 输出:
# [array([ 14.], dtype=float32)]

MNIST Training

MNIST是在机器学习领域中的一个经典问题。该问题解决的是把28x28像素的灰度手写数字图片识别为相应的数字，其中数字的范围从0到9。

MNIST是ML界的’hello world’，这个比喻还挺有意思的。

MNIST Data

MNIST数据集有四个文件：

• train-images-idx3-ubyte.gz：训练集图片 - 55000 张 训练图片，5000 张 验证图片。
• train-labels-idx1-ubyte.gz：训练集图片对应的数字标签。
• t10k-images-idx3-ubyte.gz：测试集图片 - 10000 张 图片。
• t10k-labels-idx1-ubyte.gz：测试集图片对应的数字标签。

这些文件本身并没有使用标准的图片格式存储。在下面代码中extract_images()和extract_labels()函数可以手动解压他们。

图片数据将被解压成2维的tensor：[image index, pixel index] 其中每一项表示某一图片中特定像素的强度值。”image index”代表数据集中图片的编号，从0到数据集的上限值。”pixel index”代表该图片中像素点的个数, 从0到图片的像素上限值。

以train-*开头的文件中包括60000个样本，其中分割出55000个样本作为训练集，其余的5000个样本作为验证集。因为所有数据集中28x28像素的灰度图片的尺寸为784，所以训练集输出的tensor格式为[55000, 784]。

数字标签数据被解压成1维的tensor：[image index]，它定义了每个样本数值的类别分类。对于训练集的标签来说，这个数据规模就是：[55000]。

解压重构图片和标签数据之后，会得到如下数据集对象：

• data_sets.train：55000 组 图片和标签，用于训练。
• data_sets.validation：5000 组 图片和标签，用于迭代验证训练的准确性。
• data_sets.test：10000 组 图片和标签, 用于最终测试训练的准确性。

调用以下代码中的read_data_sets()函数，将会返回一个DataSet实例，其中包含了以上三个数据集。

函数DataSet.next_batch()是用于获取以batch_size为大小的一个元组，其中包含了一组图片和标签，该元组会被用于当前的TensorFlow运算会话中。

下载数据的代码：

# Copyright 2015 Google Inc. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================

"""Functions for downloading and reading MNIST data."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import gzip
import os

import tensorflow.python.platform

import numpy
from six.moves import urllib
from six.moves import xrange  # pylint: disable=redefined-builtin
import tensorflow as tf

SOURCE_URL = 'http://yann.lecun.com/exdb/mnist/'


def maybe_download(filename, work_directory):
  """Download the data from Yann's website, unless it's already here."""
  if not os.path.exists(work_directory):
    os.mkdir(work_directory)
  filepath = os.path.join(work_directory, filename)
  if not os.path.exists(filepath):
    filepath, _ = urllib.request.urlretrieve(SOURCE_URL + filename, filepath)
    statinfo = os.stat(filepath)
    print('Successfully downloaded', filename, statinfo.st_size, 'bytes.')
  return filepath


def _read32(bytestream):
  dt = numpy.dtype(numpy.uint32).newbyteorder('>')
  return numpy.frombuffer(bytestream.read(4), dtype=dt)[0]


def extract_images(filename):
  """Extract the images into a 4D uint8 numpy array [index, y, x, depth]."""
  print('Extracting', filename)
  with gzip.open(filename) as bytestream:
    magic = _read32(bytestream)
    if magic != 2051:
      raise ValueError(
          'Invalid magic number %d in MNIST image file: %s' %
          (magic, filename))
    num_images = _read32(bytestream)
    rows = _read32(bytestream)
    cols = _read32(bytestream)
    buf = bytestream.read(rows * cols * num_images)
    data = numpy.frombuffer(buf, dtype=numpy.uint8)
    data = data.reshape(num_images, rows, cols, 1)
    return data


def dense_to_one_hot(labels_dense, num_classes=10):
  """Convert class labels from scalars to one-hot vectors."""
  num_labels = labels_dense.shape[0]
  index_offset = numpy.arange(num_labels) * num_classes
  labels_one_hot = numpy.zeros((num_labels, num_classes))
  labels_one_hot.flat[index_offset + labels_dense.ravel()] = 1
  return labels_one_hot


def extract_labels(filename, one_hot=False):
  """Extract the labels into a 1D uint8 numpy array [index]."""
  print('Extracting', filename)
  with gzip.open(filename) as bytestream:
    magic = _read32(bytestream)
    if magic != 2049:
      raise ValueError(
          'Invalid magic number %d in MNIST label file: %s' %
          (magic, filename))
    num_items = _read32(bytestream)
    buf = bytestream.read(num_items)
    labels = numpy.frombuffer(buf, dtype=numpy.uint8)
    if one_hot:
      return dense_to_one_hot(labels)
    return labels


class DataSet(object):

  def __init__(self, images, labels, fake_data=False, one_hot=False,
               dtype=tf.float32):
    """Construct a DataSet.

    one_hot arg is used only if fake_data is true.  `dtype` can be either
    `uint8` to leave the input as `[0, 255]`, or `float32` to rescale into
    `[0, 1]`.
    """
    dtype = tf.as_dtype(dtype).base_dtype
    if dtype not in (tf.uint8, tf.float32):
      raise TypeError('Invalid image dtype %r, expected uint8 or float32' %
                      dtype)
    if fake_data:
      self._num_examples = 10000
      self.one_hot = one_hot
    else:
      assert images.shape[0] == labels.shape[0], (
          'images.shape: %s labels.shape: %s' % (images.shape,
                                                 labels.shape))
      self._num_examples = images.shape[0]

      # Convert shape from [num examples, rows, columns, depth]
      # to [num examples, rows*columns] (assuming depth == 1)
      assert images.shape[3] == 1
      images = images.reshape(images.shape[0],
                              images.shape[1] * images.shape[2])
      if dtype == tf.float32:
        # Convert from [0, 255] -> [0.0, 1.0].
        images = images.astype(numpy.float32)
        images = numpy.multiply(images, 1.0 / 255.0)
    self._images = images
    self._labels = labels
    self._epochs_completed = 0
    self._index_in_epoch = 0

  @property
  def images(self):
    return self._images

  @property
  def labels(self):
    return self._labels

  @property
  def num_examples(self):
    return self._num_examples

  @property
  def epochs_completed(self):
    return self._epochs_completed

  def next_batch(self, batch_size, fake_data=False):
    """Return the next `batch_size` examples from this data set."""
    if fake_data:
      fake_image = [1] * 784
      if self.one_hot:
        fake_label = [1] + [0] * 9
      else:
        fake_label = 0
      return [fake_image for _ in xrange(batch_size)], [
          fake_label for _ in xrange(batch_size)]
    start = self._index_in_epoch
    self._index_in_epoch += batch_size
    if self._index_in_epoch > self._num_examples:
      # Finished epoch
      self._epochs_completed += 1
      # Shuffle the data
      perm = numpy.arange(self._num_examples)
      numpy.random.shuffle(perm)
      self._images = self._images[perm]
      self._labels = self._labels[perm]
      # Start next epoch
      start = 0
      self._index_in_epoch = batch_size
      assert batch_size <= self._num_examples
    end = self._index_in_epoch
    return self._images[start:end], self._labels[start:end]


def read_data_sets(train_dir, fake_data=False, one_hot=False, dtype=tf.float32):
  class DataSets(object):
    pass
  data_sets = DataSets()

  if fake_data:
    def fake():
      return DataSet([], [], fake_data=True, one_hot=one_hot, dtype=dtype)
    data_sets.train = fake()
    data_sets.validation = fake()
    data_sets.test = fake()
    return data_sets

  TRAIN_IMAGES = 'train-images-idx3-ubyte.gz'
  TRAIN_LABELS = 'train-labels-idx1-ubyte.gz'
  TEST_IMAGES = 't10k-images-idx3-ubyte.gz'
  TEST_LABELS = 't10k-labels-idx1-ubyte.gz'
  VALIDATION_SIZE = 5000

  local_file = maybe_download(TRAIN_IMAGES, train_dir)
  train_images = extract_images(local_file)

  local_file = maybe_download(TRAIN_LABELS, train_dir)
  train_labels = extract_labels(local_file, one_hot=one_hot)

  local_file = maybe_download(TEST_IMAGES, train_dir)
  test_images = extract_images(local_file)

  local_file = maybe_download(TEST_LABELS, train_dir)
  test_labels = extract_labels(local_file, one_hot=one_hot)

  validation_images = train_images[:VALIDATION_SIZE]
  validation_labels = train_labels[:VALIDATION_SIZE]
  train_images = train_images[VALIDATION_SIZE:]
  train_labels = train_labels[VALIDATION_SIZE:]

  data_sets.train = DataSet(train_images, train_labels, dtype=dtype)
  data_sets.validation = DataSet(validation_images, validation_labels,
                                 dtype=dtype)
  data_sets.test = DataSet(test_images, test_labels, dtype=dtype)

  return data_sets

每一个MNIST数据单元有两部分组成：一张包含手写数字的图片和一个对应的标签。我们把这些图片设为“xs”，把这些标签设为“ys”。训练数据集和测试数据集都包含xs和ys，比如训练数据集的图片是 mnist.train.images ，训练数据集的标签是 mnist.train.labels。

其中，mnist.train.images 是一个形状为 [60000, 784] 的张量，第一个维度数字用来索引图片，第二个维度数字用来索引每张图片中的像素点。在此张量里的每一个元素，都表示某张图片里的某个像素的强度值，值介于0和1之间。
数字n将表示成一个只有在第n维度（从0开始）数字为1的10维向量。比如，标签0将表示成([1,0,0,0,0,0,0,0,0,0,0])。因此， mnist.train.labels 是一个 [60000, 10] 的数字矩阵。

Softmax

softmax模型可以用来给不同的对象分配概率。

简单版本Softmax模型实现代码：

import tensorflow as tf
import input_data

#read Data
mnist = input_data.read_data_sets("Mnist_data/", one_hot = True)

#paramete
x = tf.placeholder(tf.float32, [None, 784])
W = tf.Variable(tf.zeros([784, 10]))
b = tf.Variable(tf.zeros([10]))

#calc y
y = tf.nn.softmax(tf.matmul(x, W) + b)
#true y
y_true = tf.placeholder(tf.float32, [None, 10])
#cost function
cross_entropy = -tf.reduce_sum(y_true * tf.log(y))
#gradientDescent
train_step = tf.train.GradientDescentOptimizer(0.01).minimize(cross_entropy)
#init
init = tf.initialize_all_variables()
sess = tf.Session()
sess.run(init)

#train
for i in range(1000):
    batch_xs, batch_ys = mnist.train.next_batch(100)
    sess.run(train_step, feed_dict = {x : batch_xs, y_true : batch_ys})
    print "loop " + str(i) + " done."

correct_prediction = tf.equal(tf.argmax(y, 1), tf.argmax(y_true, 1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))

print sess.run(accuracy, feed_dict = {x : mnist.test.images, y_true : mnist.test.labels})

代码中有几个注意点：

1. tf.placeholder()相当于c/c++里面的定义的还未输入（赋值）的变量，浮点型表示用”float”或者tf.float32都可以。x = tf.placeholder(“float”, [None, 784])，第二个参数表示这个张量的形状是[None, 784]，表示第一维不定，第二维固定。
2. tf.Variable()相当于定义了带初值的变量。
3. tf.train.GradientDescentOptimizer(0.01).minimize(cross_entropy)，表示使用GD来训练，其Learning rate为0.01，cost function为cross_entropy。
4. mnist.train.next_batch(100)会每次随机读取数据中的100个数据点来批处理。
5. tf.argmax(a, b)可以返回矩阵a中，第b维中最大的数的index。
6. tf.cast()可以进行类型转换。
   最终训练结果正确率大概91%。

使用tf.InteractiveSession()实现的版本代码（别人家的代码- -，为何都如此好看）：

import input_data
import tensorflow as tf

mnist = input_data.read_data_sets("Mnist_data/", one_hot=True)

sess = tf.InteractiveSession()

# Create the model
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)

# Define loss and optimizer
y_ = tf.placeholder(tf.float32, [None, 10])
cross_entropy = -tf.reduce_sum(y_ * tf.log(y))
train_step = tf.train.GradientDescentOptimizer(0.01).minimize(cross_entropy)

# Train
tf.initialize_all_variables().run()
for i in range(1000):
  batch_xs, batch_ys = mnist.train.next_batch(100)
  train_step.run({x: batch_xs, y_: batch_ys})

# Test trained model
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}))

CNN

用CNN来训练MNIST，代码：

# load MNIST data
import input_data
mnist = input_data.read_data_sets("Mnist_data/", one_hot=True)

# start tensorflow interactiveSession
import tensorflow as tf
sess = tf.InteractiveSession()

# weight initialization
def weight_variable(shape):
    initial = tf.truncated_normal(shape, stddev=0.1)
    return tf.Variable(initial)

def bias_variable(shape):
    initial = tf.constant(0.1, shape = shape)
    return tf.Variable(initial)

# convolution
def conv2d(x, W):
    return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')
# pooling
def max_pool_2x2(x):
    return tf.nn.max_pool(x, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')

# Create the model
# placeholder
x = tf.placeholder("float", [None, 784])
y_ = tf.placeholder("float", [None, 10])
# variables
W = tf.Variable(tf.zeros([784,10]))
b = tf.Variable(tf.zeros([10]))

y = tf.nn.softmax(tf.matmul(x,W) + b)

# first convolutinal layer
w_conv1 = weight_variable([5, 5, 1, 32])
b_conv1 = bias_variable([32])

x_image = tf.reshape(x, [-1, 28, 28, 1])

h_conv1 = tf.nn.relu(conv2d(x_image, w_conv1) + b_conv1)
h_pool1 = max_pool_2x2(h_conv1)

# second convolutional layer
w_conv2 = weight_variable([5, 5, 32, 64])
b_conv2 = bias_variable([64])

h_conv2 = tf.nn.relu(conv2d(h_pool1, w_conv2) + b_conv2)
h_pool2 = max_pool_2x2(h_conv2)

# densely connected layer
w_fc1 = weight_variable([7*7*64, 1024])
b_fc1 = bias_variable([1024])

h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*64])
h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, w_fc1) + b_fc1)

# dropout
keep_prob = tf.placeholder("float")
h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

# readout layer
w_fc2 = weight_variable([1024, 10])
b_fc2 = bias_variable([10])

y_conv = tf.nn.softmax(tf.matmul(h_fc1_drop, w_fc2) + b_fc2)

# train and evaluate the model
cross_entropy = -tf.reduce_sum(y_*tf.log(y_conv))
train_step = tf.train.GradientDescentOptimizer(1e-3).minimize(cross_entropy)
#train_step = tf.train.AdagradOptimizer(1e-5).minimize(cross_entropy)
correct_prediction = tf.equal(tf.argmax(y_conv, 1), tf.argmax(y_, 1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
sess.run(tf.initialize_all_variables())
for i in range(20000):
    batch = mnist.train.next_batch(50)
    if i%100 == 0:
        train_accuracy = accuracy.eval(feed_dict={x:batch[0], y_:batch[1], keep_prob:1.0})
        print "step %d, train accuracy %g" %(i, train_accuracy)
    train_step.run(feed_dict={x:batch[0], y_:batch[1], keep_prob:0.5})

print "test accuracy %g" % accuracy.eval(feed_dict={x:mnist.test.images, y_:mnist.test.labels, keep_prob:1.0})

几个注意点：

1. tf.truncated_normal(shape, stddev=0.1)创建一个标准差为0.1，大小为shape的随机截断正态分布矩阵。
2. tf.constant(a, shape)创建一个值为a，大小为shape的矩阵。
3. tf.nn.conv2d中strides一定为strides[0] = strides[3] = 1，其余两维表示每次卷积框移动的step。

TensorFlow运作方式

Inference

其函数定义如下：

def inference(images, hidden1_units, hidden2_units):
  """Build the MNIST model up to where it may be used for inference.
  Args:
    images: Images placeholder, from inputs().
    hidden1_units: Size of the first hidden layer.
    hidden2_units: Size of the second hidden layer.
  Returns:
    softmax_linear: Output tensor with the computed logits.
  """
  # Hidden 1
  with tf.name_scope('hidden1'):
    weights = tf.Variable(
        tf.truncated_normal([IMAGE_PIXELS, hidden1_units],
                            stddev=1.0 / math.sqrt(float(IMAGE_PIXELS))),
        name='weights')
    biases = tf.Variable(tf.zeros([hidden1_units]),
                         name='biases')
    hidden1 = tf.nn.relu(tf.matmul(images, weights) + biases)
  # Hidden 2
  with tf.name_scope('hidden2'):
    weights = tf.Variable(
        tf.truncated_normal([hidden1_units, hidden2_units],
                            stddev=1.0 / math.sqrt(float(hidden1_units))),
        name='weights')
    biases = tf.Variable(tf.zeros([hidden2_units]),
                         name='biases')
    hidden2 = tf.nn.relu(tf.matmul(hidden1, weights) + biases)
  # Linear
  with tf.name_scope('softmax_linear'):
    weights = tf.Variable(
        tf.truncated_normal([hidden2_units, NUM_CLASSES],
                            stddev=1.0 / math.sqrt(float(hidden2_units))),
        name='weights')
    biases = tf.Variable(tf.zeros([NUM_CLASSES]),
                         name='biases')
    logits = tf.matmul(hidden2, weights) + biases
  return logits

这个函数主要作用说白了就是做前向传播，其中的一些库的用法也在之前也接触过了。

Loss

这个函数的定义好像新版本和旧版本的不一样。
新版本的简单多了：

def loss(logits, labels):
  """Calculates the loss from the logits and the labels.
  Args:
    logits: Logits tensor, float - [batch_size, NUM_CLASSES].
    labels: Labels tensor, int32 - [batch_size].
  Returns:
    loss: Loss tensor of type float.
  """
  labels = tf.to_int64(labels)
  cross_entropy = tf.nn.sparse_softmax_cross_entropy_with_logits(
      logits, labels, name='xentropy')
  loss = tf.reduce_mean(cross_entropy, name='xentropy_mean')
  return loss

旧版本，这个版本的代码有几个函数没有理解透彻，花了半天时间才搞懂：

def loss(logits, labels):
  """Calculates the loss from the logits and the labels.

  Args:
    logits: Logits tensor, float - [batch_size, NUM_CLASSES].
    labels: Labels tensor, int32 - [batch_size].

  Returns:
    loss: Loss tensor of type float.
  """
  # Convert from sparse integer labels in the range [0, NUM_CLASSES)
  # to 1-hot dense float vectors (that is we will have batch_size vectors,
  # each with NUM_CLASSES values, all of which are 0.0 except there will
  # be a 1.0 in the entry corresponding to the label).
  batch_size = tf.size(labels)
  labels = tf.expand_dims(labels, 1)
  indices = tf.expand_dims(tf.range(0, batch_size), 1)
  concated = tf.concat(1, [indices, labels])
  onehot_labels = tf.sparse_to_dense(
      concated, tf.pack([batch_size, NUM_CLASSES]), 1.0, 0.0)
  cross_entropy = tf.nn.softmax_cross_entropy_with_logits(logits,
                                                          onehot_labels,
                                                          name='xentropy')
  loss = tf.reduce_mean(cross_entropy, name='xentropy_mean')
  return loss

代码里面需要注意的几个点：
一是tf.expand_dims(Tensor, dim)函数，作用是为张量Tensor加一维：

sess = tf.InteractiveSession()
labels = [1,2,3]
x = tf.expand_dims(labels, 0)
print(sess.run(x))
x = tf.expand_dims(labels, 1)
print(sess.run(x))
#>>>[[1 2 3]]
#>>>[[1]
#    [2]
#    [3]]

二是tf.pack(values, axis=0, name=”pack”)函数，将一个R维张量列表沿着axis轴组合成一个R+1维的张量：

  # 'x' is [1, 4]
  # 'y' is [2, 5]
  # 'z' is [3, 6]
  pack([x, y, z]) => [[1, 4], [2, 5], [3, 6]]  # Pack along first dim.
  pack([x, y, z], axis=1) => [[1, 2, 3], [4, 5, 6]]

三是tf.concat(concat_dim, values, name=”concat”) 函数，将张量沿着指定维数拼接起来：

t1 = [[1, 2, 3], [4, 5, 6]]
t2 = [[7, 8, 9], [10, 11, 12]]
tf.concat(0, [t1, t2]) 
#==> [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
tf.concat(1, [t1, t2]) 
#==> [[1, 2, 3, 7, 8, 9], [4, 5, 6, 10, 11, 12]]

这里要注意的是，如果是两个向量，是无法调用第二个维度的：

# t1, t2为向量，只有一个维度
tf.concat(1, [t1, t2])

因此，要连接他们，只能调用tf.expand_dims来扩维：

    t1=tf.constant([1,2,3])  
    t2=tf.constant([4,5,6])  
    #concated = tf.concat(1, [t1,t2]) 错误
    t1=tf.expand_dims(tf.constant([1,2,3]),1)  
    t2=tf.expand_dims(tf.constant([4,5,6]),1)  
    concated = tf.concat(1, [t1,t2]) #正确

四是tf.sparse_to_dense，将系数矩阵转成密集矩阵，例子如下：

    import tensorflow as tf  
    import numpy  


    BATCHSIZE=6  
    label=tf.expand_dims(tf.constant([0,2,3,6,7,9]),1)  
    index=tf.expand_dims(tf.range(0, BATCHSIZE),1)  
    #use a matrix  
    concated = tf.concat(1, [index, label])  
    onehot_labels = tf.sparse_to_dense(concated, tf.pack([BATCHSIZE,10]), 1.0, 0.0)  

    #use a vector  
    concated2=tf.constant([1,3,4])  
    #onehot_labels2 = tf.sparse_to_dense(concated2, tf.pack([BATCHSIZE,10]), 1.0, 0.0)#cant use ,because output_shape is not a vector  
    onehot_labels2 = tf.sparse_to_dense(concated2, tf.pack([10]), 1.0, 0.0)#can use  

    #use a scalar  
    concated3=tf.constant(5)  
    onehot_labels3 = tf.sparse_to_dense(concated3, tf.pack([10]), 1.0, 0.0)  

    with tf.Session() as sess:  
        result1=sess.run(onehot_labels)  
        result2 = sess.run(onehot_labels2)  
        result3 = sess.run(onehot_labels3)  
        print ("This is result1:")  
        print (result1)  
        print ("This is result2:")  
        print (result2)  
        print ("This is result3:")  
        print (result3)  

结果：

    This is result1:  
    [[ 1.  0.  0.  0.  0.  0.  0.  0.  0.  0.]  
     [ 0.  0.  1.  0.  0.  0.  0.  0.  0.  0.]  
     [ 0.  0.  0.  1.  0.  0.  0.  0.  0.  0.]  
     [ 0.  0.  0.  0.  0.  0.  1.  0.  0.  0.]  
     [ 0.  0.  0.  0.  0.  0.  0.  1.  0.  0.]  
     [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  1.]]  
    This is result2:  
    [ 0.  1.  0.  1.  1.  0.  0.  0.  0.  0.]  
    This is result3:  
    [ 0.  0.  0.  0.  0.  1.  0.  0.  0.  0.]  

TensorBoard

尝试使用了一下TensorBoard来可视化。
代码如下：

import input_data
import tensorflow as tf

flags = tf.app.flags
FLAGS = flags.FLAGS
flags.DEFINE_boolean('fake_data', False, 'If true, uses fake data '
                     'for unit testing.')
flags.DEFINE_integer('max_steps', 1000, 'Number of steps to run trainer.')
flags.DEFINE_float('learning_rate', 0.01, 'Initial learning rate.')


def main(_):
  # Import data
  mnist = input_data.read_data_sets('Mnist_data/', one_hot=True,
                                    fake_data=FLAGS.fake_data)

  sess = tf.InteractiveSession()

  # Create the model
  x = tf.placeholder(tf.float32, [None, 784], name='x-input')
  W = tf.Variable(tf.zeros([784, 10]), name='weights')
  b = tf.Variable(tf.zeros([10], name='bias'))

  # Use a name scope to organize nodes in the graph visualizer
  with tf.name_scope('Wx_b'):
    y = tf.nn.softmax(tf.matmul(x, W) + b)

  # Add summary ops to collect data
  _ = tf.histogram_summary('weights', W)
  _ = tf.histogram_summary('biases', b)
  _ = tf.histogram_summary('y', y)

  # Define loss and optimizer
  y_ = tf.placeholder(tf.float32, [None, 10], name='y-input')
  # More name scopes will clean up the graph representation
  with tf.name_scope('xent'):
    cross_entropy = -tf.reduce_sum(y_ * tf.log(y))
    _ = tf.scalar_summary('cross entropy', cross_entropy)
  with tf.name_scope('train'):
    train_step = tf.train.GradientDescentOptimizer(
        FLAGS.learning_rate).minimize(cross_entropy)

  with tf.name_scope('test'):
    correct_prediction = tf.equal(tf.argmax(y, 1), tf.argmax(y_, 1))
    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
    _ = tf.scalar_summary('accuracy', accuracy)

  # Merge all the summaries and write them out to /tmp/mnist_logs
  merged = tf.merge_all_summaries()
  writer = tf.train.SummaryWriter('/tmp/mnist_logs', sess.graph_def)
  tf.initialize_all_variables().run()

  # Train the model, and feed in test data and record summaries every 10 steps

  for i in range(FLAGS.max_steps):
    if i % 10 == 0:  # Record summary data and the accuracy
      if FLAGS.fake_data:
        batch_xs, batch_ys = mnist.train.next_batch(
            100, fake_data=FLAGS.fake_data)
        feed = {x: batch_xs, y_: batch_ys}
      else:
        feed = {x: mnist.test.images, y_: mnist.test.labels}
      result = sess.run([merged, accuracy], feed_dict=feed)
      summary_str = result[0]
      acc = result[1]
      writer.add_summary(summary_str, i)
      print('Accuracy at step %s: %s' % (i, acc))
    else:
      batch_xs, batch_ys = mnist.train.next_batch(
          100, fake_data=FLAGS.fake_data)
      feed = {x: batch_xs, y_: batch_ys}
      sess.run(train_step, feed_dict=feed)

if __name__ == '__main__':
  tf.app.run()

在运行完之后，在terminal里面启动tensorboard：

tensorboard --logdir=/tmp/mnist_logs

必须与writer = tf.train.SummaryWriter(‘/tmp/mnist_logs’, sess.graph_def)中的路径相一致。
接着用浏览器打开：http://localhost:6006 就可以看到效果了。