tensenflow入门学习-1

Tensorflow MNIST

本文主要是自己在入门TensorFlow时候的对其中概念的一些理解。可能有不对的地方。谢谢。

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MNIST数据集下载

参考文档中使用的是input_data.py文件进行MNIST数据的下载，但这份源码在参照文档中的链接是googlesource，国内无法下载，只好把从其他地方下载源码。代码如下：
我使用的python3以上的版本，如果使用的是python2.7的版本请将下面两点
- urllib.request.urlretrieve修改成urllib.urlretrieve
- numpy.frombuffer(bytestream.read(4), dtype=dt)[0]修改成numpy.frombuffer(bytestream.read(4), dtype=dt)

"""Functions for downloading and reading MNIST data."""
from __future__ import print_function
import gzip
import os
import urllib.request
import numpy
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)
  print("filepath %s",filepath)
  if not os.path.exists(filepath):
    filepath, _ = urllib.request.urlretrieve(SOURCE_URL + filename, filepath)
    statinfo = os.stat(filepath)
    print('Succesfully downloaded', filename, statinfo.st_size, 'bytes.')

  print("There is source %s",filepath)
  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,"rb") 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):
    if fake_data:
      self._num_examples = 10000
    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])
      # 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 = [1.0 for _ in xrange(784)]
      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):
  class DataSets(object):
    pass
  data_sets = DataSets()
  if fake_data:
    data_sets.train = DataSet([], [], fake_data=True)
    data_sets.validation = DataSet([], [], fake_data=True)
    data_sets.test = DataSet([], [], fake_data=True)
    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)
  data_sets.validation = DataSet(validation_images, validation_labels)
  data_sets.test = DataSet(test_images, test_labels)
  return data_sets

Softmax回归简介

Softmax通俗来说是对一个集合的每一项是否是正确答案给出一个概率，总和是1.比如0~9的数字，结果的正确答案是9，那个9的概率比如是80%，其他0~8加起来的概率总和是20%。一般用于神经网络的最后一步计算出集合的概率分布。

简单的数学表达式

softmax = normalize(exp(evidence))

其中

evidencej=∑jWi,jxj+bi

W：权重（针对每个像素点的加权）
x ：输入（本次代表的是图片中的像素点）
b ：偏移量（去除输入带来的干扰项）

矩阵表达式

Tensorflow代码

使用TensorFlow之前先导入他

import tensorflow as tf

下载导入我们的数据

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

定义我们的输入变量

x = tf.placeholder("float", [None, 784])

目前为止x还没有实际的值，只是通过placeholder占了一个位置，在后面Tensorflow运行的时候赋值。其中的784是因为本次MNIST的数据集图片大小是28*28=784。None表示有很多张图片，具体数量没有定死。

定义之前说过的权重和偏移量

W = tf.Variable(tf.zeros([784,10]))
b = tf.Variable(tf.zeros([10]))

Variable代表这个变量是可变的，因为在后面的训练中会对W和b进行修改。784代表一张图片的大小，10代表最后我们的输出一共有10种，即0~9。这部分也可以使用placeholder来定义。

模型实现

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

tf.matmul代表矩阵乘法

定义与计算损失函数

损失函数是用来评估我们的模型好坏的。通俗来说就是比对预算的结果和真实结果的差距。一般采用交叉熵函数。

表达式：

Hy′(y)=−∑iyi′log(yi)

其中y 是我们预测的概率分布, y’ 是实际的分布

代码：

y_ = tf.placeholder("float", [None,10])
cross_entropy = -tf.reduce_sum(y_*tf.log(y))

y_是我们预测的结果，y是实际结果
reduce_sum是元素的总和

训练函数

采用梯度下降算法，以0.01的学习速率最小化交叉熵
如果要替换其他的学习方法替换这一行代码就可以了

代码：

train_step = tf.train.GradientDescentOptimizer(0.01).minimize(cross_entropy)

开始训练

初始化，并开始训练

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

前三行初始化，然后让模型训练1000次每次使用100张图片的数据
feed_dict中指定输入和实际结果，即最开始定义的placeholder和用来和我们预测结果进行比对的实际结果

评估我们的结果

用测试数据来评价我们的模型输入x变成了mnist.test.images而不是之前mnist.train.images

correct_prediction = tf.equal(tf.argmax(y,1), tf.argmax(y_,1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
print(sess.run(accuracy, feed_dict={x: mnist.test.images, y_: mnist.test.labels}))

工程整体代码:https://github.com/larry-kof/tensorflow_study1

参考：http://www.tensorfly.cn/tfdoc/tutorials/mnist_beginners.html