今天这篇文章我们使用TensorFlow针对于手写体识别数据集MNIST搭建一个softmax的多分类模型。
本文的程序主要分为两大模块，一个是对MNIST数据集的下载、解压、重构以及数据集的构建；另一个是构建softmax图及训练图。本程序主要是想去理解包含在这些代码里面的设计思想：TensorFlow工作流程和机器学习的基本概念。本文所使用的数据集和Python源代码都已经上传到我的GitHub（https://github.com/ml365/softmax_mnist），点击文末阅读原文直接跳转下载页面。
MNIST数据集的下载与重构
MNIST是一个入门级的计算机视觉数据集，它包含各种手写数字图片：
它也包含每一张图片对应的标签，告诉我们这个是数字几。比如，上面这四张图片的标签分别是5，0，4，1。
下载下来的数据集被分成两部分：60000行的训练数据集（mnist.train）和10000行的测试数据集（mnist.test）。正如前面提到的一样，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。将上述的图像按行展开，因此，在MNIST训练数据集中，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。如图所示
数据处理的代码如下所示
"""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.lecun.com/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 <= self._num_examples
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 <= len(train_images):
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多分类算法简述
softmax模型可以用来给不同的对象分配概率。即使在卷积胜境网络中，最后一步也需要用softmax来分配概率。softmax回归（softmax regression）分两步：
为了得到一张给定图片属于某个特定数字类的证据（evidence），我们对图片像素值进行加权求和。如果这个像素具有很强的证据说明这张图片不属于该类，那么相应的权值为负数，相反如果这个像素拥有有利的证据支持这张图片属于这个类，那么权值是正数。因此对于给定的输入图片 x 它代表的是数字 i 的证据可以表示为
其中 Wi,j 代表权重， bi 代表数字 i 类的偏置量，j 代表给定图片 x 的像素索引用于像素求和。然后用softmax函数可以把这些证据转换成概率 y：
为了训练我们的模型，我们首先需要定义一个指标来评估这个模型是好的。一个非常常见的，非常漂亮的成本函数是“交叉熵”（cross-entropy）。交叉熵产生于信息论里面的信息压缩编码技术，但是它后来演变成为从博弈论到机器学习等其他领域里的重要技术手段。它的定义如下：
softmax构建与测试程序如下
# -*- 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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