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TensorFlow實(shí)戰(zhàn):SoftMax手寫體MNIST識別(Python完整源碼)

 LibraryPKU 2018-10-09

之前的文章 TensorFlow的安裝與初步了解,從TensorFlow的安裝到基本的模塊單元進(jìn)行了初步的講解。今天這篇文章我們使用TensorFlow針對于手寫體識別數(shù)據(jù)集MNIST搭建一個softmax的多分類模型。


本文的程序主要分為兩大模塊,一個是對MNIST數(shù)據(jù)集的下載、解壓、重構(gòu)以及數(shù)據(jù)集的構(gòu)建;另一個是構(gòu)建softmax圖及訓(xùn)練圖。本程序主要是想去理解包含在這些代碼里面的設(shè)計思想:TensorFlow工作流程和機(jī)器學(xué)習(xí)的基本概念。本文所使用的數(shù)據(jù)集和Python源代碼都已經(jīng)上傳到我的GitHub(https://github.com/ml365/softmax_mnist),點(diǎn)擊文末閱讀原文直接跳轉(zhuǎn)下載頁面。


MNIST數(shù)據(jù)集的下載與重構(gòu)

MNIST是一個入門級的計算機(jī)視覺數(shù)據(jù)集,它包含各種手寫數(shù)字圖片:

它也包含每一張圖片對應(yīng)的標(biāo)簽,告訴我們這個是數(shù)字幾。比如,上面這四張圖片的標(biāo)簽分別是5,0,4,1。


下載下來的數(shù)據(jù)集被分成兩部分:60000行的訓(xùn)練數(shù)據(jù)集(mnist.train)和10000行的測試數(shù)據(jù)集(mnist.test)。正如前面提到的一樣,每一個MNIST數(shù)據(jù)單元有兩部分組成:一張包含手寫數(shù)字的圖片和一個對應(yīng)的標(biāo)簽。我們把這些圖片設(shè)為“xs”,把這些標(biāo)簽設(shè)為“ys”。訓(xùn)練數(shù)據(jù)集和測試數(shù)據(jù)集都包含xs和ys,比如訓(xùn)練數(shù)據(jù)集的圖片是 mnist.train.images ,訓(xùn)練數(shù)據(jù)集的標(biāo)簽是 mnist.train.labels。將上述的圖像按行展開,因此,在MNIST訓(xùn)練數(shù)據(jù)集中,mnist.train.images 是一個形狀為 [60000, 784] 的張量,第一個維度數(shù)字用來索引圖片,第二個維度數(shù)字用來索引每張圖片中的像素點(diǎn)。在此張量里的每一個元素,都表示某張圖片里的某個像素的強(qiáng)度值,值介于0和1之間。如圖所示

數(shù)據(jù)處理的代碼如下所示


'''Functions for downloading and reading MNIST data.'''


from __future__ import absolute_import

from __future__ import division

from __future__ import print_function

import os

import gzip

import collections

import numpy

from six.moves import xrange


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

Datasets = collections.namedtuple('Datasets', ['train', 'validation', 'test'])


def _read32(bytestream):

  dt = numpy.dtype(numpy.uint32).newbyteorder('>')

  return numpy.frombuffer(bytestream.read(4), dtype=dt)[0]



def extract_images(f):

  '''Extract the images into a 4D uint8 numpy array [index, y, x, depth].

  

  Args:

    f: A file object that can be passed into a gzip reader.


  Returns:

    data: A 4D uint8 numpy array [index, y, x, depth].


  Raises:

    ValueError: If the bytestream does not start with 2051.


  '''

  print('Extracting', f.name)

  with gzip.GzipFile(fileobj=f) as bytestream:

    magic = _read32(bytestream)

    if magic != 2051:

      raise ValueError('Invalid magic number %d in MNIST image file: %s' %

                       (magic, f.name))

    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):

  '''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(f, one_hot=False, num_classes=10):

  '''Extract the labels into a 1D uint8 numpy array [index].


  Args:

    f: A file object that can be passed into a gzip reader.

    one_hot: Does one hot encoding for the result.

    num_classes: Number of classes for the one hot encoding.


  Returns:

    labels: a 1D uint8 numpy array.


  Raises:

    ValueError: If the bystream doesn't start with 2049.

  '''

  print('Extracting', f.name)

  with gzip.GzipFile(fileobj=f) as bytestream:

    magic = _read32(bytestream)

    if magic != 2049:

      raise ValueError('Invalid magic number %d in MNIST label file: %s' %

                       (magic, f.name))

    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, num_classes)

    return labels



class DataSet(object):


  def __init__(self,

               images,

               labels,

               fake_data=False,

               one_hot=False,

               dtype=numpy.float32,

               reshape=True):

    '''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 = dtypes.as_dtype(dtype).base_dtype

    if dtype not in (numpy.uint8, numpy.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)

      if reshape:

        assert images.shape[3] == 1

        images = images.reshape(images.shape[0],

                                images.shape[1] * images.shape[2])

      if dtype == numpy.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 <=>

    end = self._index_in_epoch

    return self._images[start:end], self._labels[start:end]


def maybe_download(filename, work_directory, source_url):

  '''Download the data from source url, unless it's already here.


  Args:

      filename: string, name of the file in the directory.

      work_directory: string, path to working directory.

      source_url: url to download from if file doesn't exist.


  Returns:

      Path to resulting file.

  '''

  filepath = os.path.join(work_directory, filename)

  print('filepath:%s' % filepath)

  return filepath


def read_data_sets(train_dir,

                   fake_data=False,

                   one_hot=False,

                   dtype=numpy.float32,

                   reshape=True,

                   validation_size=5000):

  if fake_data:


    def fake():

      return DataSet([], [], fake_data=True, one_hot=one_hot, dtype=dtype)


    train = fake()

    validation = fake()

    test = fake()

    return Datasets(train=train, validation=validation, test=test)


  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'


  local_file = maybe_download(TRAIN_IMAGES, train_dir,

                                   SOURCE_URL + TRAIN_IMAGES)

  with open(local_file, 'rb') as f:

    train_images = extract_images(f)


  local_file = maybe_download(TRAIN_LABELS, train_dir,

                                   SOURCE_URL + TRAIN_LABELS)

  with open(local_file, 'rb') as f:

    train_labels = extract_labels(f, one_hot=one_hot)


  local_file = maybe_download(TEST_IMAGES, train_dir,

                                   SOURCE_URL + TEST_IMAGES)

  with open(local_file, 'rb') as f:

    test_images = extract_images(f)


  local_file = maybe_download(TEST_LABELS, train_dir,

                                   SOURCE_URL + TEST_LABELS)

  with open(local_file, 'rb') as f:

    test_labels = extract_labels(f, one_hot=one_hot)


  if not 0 <= validation_size=""><=>

    raise ValueError(

        'Validation size should be between 0 and {}. Received: {}.'

        .format(len(train_images), validation_size))


  validation_images = train_images[:validation_size]

  validation_labels = train_labels[:validation_size]

  train_images = train_images[validation_size:]

  train_labels = train_labels[validation_size:]


  train = DataSet(train_images, train_labels, dtype=dtype, reshape=reshape)

  validation = DataSet(validation_images,

                       validation_labels,

                       dtype=dtype,

                       reshape=reshape)

  test = DataSet(test_images, test_labels, dtype=dtype, reshape=reshape)


  return Datasets(train=train, validation=validation, test=test)



def load_mnist(train_dir='MNIST-data'):

  return read_data_sets(train_dir)



softmax多分類算法簡述

softmax模型可以用來給不同的對象分配概率。即使在卷積勝境網(wǎng)絡(luò)中,最后一步也需要用softmax來分配概率。softmax回歸(softmax regression)分兩步:


為了得到一張給定圖片屬于某個特定數(shù)字類的證據(jù)(evidence),我們對圖片像素值進(jìn)行加權(quán)求和。如果這個像素具有很強(qiáng)的證據(jù)說明這張圖片不屬于該類,那么相應(yīng)的權(quán)值為負(fù)數(shù),相反如果這個像素?fù)碛杏欣淖C據(jù)支持這張圖片屬于這個類,那么權(quán)值是正數(shù)。因此對于給定的輸入圖片 x 它代表的是數(shù)字 i 的證據(jù)可以表示為

其中 Wi,j 代表權(quán)重, bi 代表數(shù)字 i 類的偏置量,j 代表給定圖片 x 的像素索引用于像素求和。然后用softmax函數(shù)可以把這些證據(jù)轉(zhuǎn)換成概率 y:

為了訓(xùn)練我們的模型,我們首先需要定義一個指標(biāo)來評估這個模型是好的。一個非常常見的,非常漂亮的成本函數(shù)是“交叉熵”(cross-entropy)。交叉熵產(chǎn)生于信息論里面的信息壓縮編碼技術(shù),但是它后來演變成為從博弈論到機(jī)器學(xué)習(xí)等其他領(lǐng)域里的重要技術(shù)手段。它的定義如下:


softmax構(gòu)建與測試程序如下


# -*- coding: utf-8 -*-

import tensorflow as tf

from mnist import read_data_sets


input_data = read_data_sets('/home/gdw/PycharmProjects/projectOne/data', one_hot=True)


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


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

b = tf.Variable(tf.zeros([10]))


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


y_ = tf.placeholder(tf.float32, [None, 10])


cross_entropy = tf.reduce_mean(-tf.reduce_sum(y_ *tf.log(y), reduction_indices=[1]))


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


init = tf.initialize_all_variables()


sess = tf.Session()

sess.run(init)


for i in range(10000):

    batch_xs, batch_ys = input_data.train.next_batch(100)

    sess.run(train_step, feed_dict={x:batch_xs, y_:batch_ys})


correct_prediction = tf.equal(tf.argmax(y,1), tf.argmax(y_,1))

accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))

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




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