本文参考Yann LeCun的LeNet5经典架构，稍加ps得到下面适用于本手写识别的cnn结构，构造一个两层卷积神经网络，神经网络的结构如下图所示：
输入-卷积-pooling-卷积-pooling-全连接层-Dropout-Softmax输出
第一层卷积利用5*5的patch，32个卷积核，可以计算出32个特征。然后进行maxpooling。第二层卷积利用5*5的patch，64个卷积核，可以计算出64个特征。然后进行max pooling。卷积核的个数是我们自己设定，可以增加卷积核数目提高分类精度，但是那样会增加更大参数，提高计算成本。
这样输入是分辨率为28*28的图片。利用5*5的patch进行卷积。我们的卷积使用1步长（stride size），0填充模块（zero padded），这样得到的输出和输入是同一个大小。经过第一层卷积之后，卷积特征大小为28*28。然后通过ReLU函数激活。我们的pooling用简单传统的2x2大小的模板做max pooling，这样pooling后得到14*14大小的特征。经过第二层卷积后，卷积特征大小为14*14，然后通过ReLU函数激活，再经过pooling后得到特征大小为7*7。
现在，图片尺寸减小到7x7，我们加入一个有1024个神经元的全连接层，用于处理整个图片。我们把池化层输出的张量展开成一些向量，乘上权重矩阵，加上偏置，然后对其使用ReLU。
为了避免过拟合，在全连接层输出接上dropout层。Dropout层在训练时屏蔽一半的神经元。
1、输入数据
直接使用tensorflow中的模块，导入输入数据：
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets('MNIST_data', one_hot=True)
或者使用官方提供的input_data.py文件下载mnist数据
2、启动session
（1）交互方式启动session
sess = tf.InteractiveSession()
（2）一般方式启动session
sess = tf.Session()
ps: 使用交互方式不用提前构建计算图，而使用一般方式必须提前构建好计算图才能启动session
3、权重和偏置初始化
权重初始化的原则：应该加入少量的噪声来打破对称性并且要避免0梯度（初始化为0）
权重初始化一般选择均匀分布或是正态分布
定义权重初始化方法：
def weight_variable(shape):
#截尾正态分布,stddev是正态分布的标准偏差
initial = tf.truncated_normal(shape=shape, stddev=0.1)
return tf.Variable(initial)
定义偏置初始化方法：
def bias_variable(shape):
initial = tf.constant(0.1, shape=shape)
return tf.Variable(initial)
4、定义卷积和池化方法
TensorFlow在卷积和Pooling上有很强的灵活性。我们怎么处理边界？步长应该设多大？在这个实例里，我们的卷积使用1步长（stride size），0填充模块（zero padded），保证输出和输入是同一个大小。我们的pooling用简单传统的2x2大小的模板做maxpooling。为了代码更简洁，我们把这部分抽象成一个函数。
def conv2d(x, W):
return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')
def max_pool_2x2(x):
return tf.nn.max_pool(x, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')
5、直接贴完整代码
from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf
#加载数据集
mnist = input_data.read_data_sets('MNIST_data', one_hot=True) #以交互式方式启动session
#如果不使用交互式session，则在启动session前必须
# 构建整个计算图，才能启动该计算图
sess = tf.InteractiveSession() """构建计算图"""
#通过占位符来为输入图像和目标输出类别创建节点
#shape参数是可选的，有了它tensorflow可以自动捕获维度不一致导致的错误
x = tf.placeholder("float", shape=[None, 784]) #原始输入
y_ = tf.placeholder("float", shape=[None, 10]) #目标值 #为了不在建立模型的时候反复做初始化操作，
# 我们定义两个函数用于初始化
def weight_variable(shape):
#截尾正态分布,stddev是正态分布的标准偏差
initial = tf.truncated_normal(shape=shape, stddev=0.1)
return tf.Variable(initial)
def bias_variable(shape):
initial = tf.constant(0.1, shape=shape)
return tf.Variable(initial) #卷积核池化,步长为1,0边距
def conv2d(x, W):
return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')
def max_pool_2x2(x):
return tf.nn.max_pool(x, ksize=[1, 2, 2, 1],
strides=[1, 2, 2, 1], padding='SAME') """第一层卷积"""
#由一个卷积和一个最大池化组成。滤波器5x5中算出32个特征，是因为使用32个滤波器进行卷积
#卷积的权重张量形状是[5, 5, 1, 32],1是输入通道的个数，32是输出通道个数
W_conv1 = weight_variable([5, 5, 1, 32])
#每一个输出通道都有一个偏置量
b_conv1 = bias_variable([32]) #位了使用卷积，必须将输入转换成4维向量，2、3维表示图片的宽、高
#最后一维表示图片的颜色通道（因为是灰度图像所以通道数维1，RGB图像通道数为3）
x_image = tf.reshape(x, [-1, 28, 28, 1]) #第一层的卷积结果,使用Relu作为激活函数
h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1))
#第一层卷积后的池化结果
h_pool1 = max_pool_2x2(h_conv1) """第二层卷积"""
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) """全连接层"""
#图片尺寸减小到7*7，加入一个有1024个神经元的全连接层
W_fc1 = weight_variable([7*7*64, 1024])
b_fc1 = bias_variable([1024])
#将最后的池化层输出张量reshape成一维向量
h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*64])
#全连接层的输出
h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1) """使用Dropout减少过拟合"""
#使用placeholder占位符来表示神经元的输出在dropout中保持不变的概率
#在训练的过程中启用dropout，在测试过程中关闭dropout
keep_prob = tf.placeholder("float")
h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob) """输出层"""
W_fc2 = weight_variable([1024, 10])
b_fc2 = bias_variable([10])
#模型预测输出
y_conv = tf.nn.softmax(tf.matmul(h_fc1_drop, W_fc2) + b_fc2) #交叉熵损失
cross_entropy = -tf.reduce_sum(y_ * tf.log(y_conv)) #模型训练,使用AdamOptimizer来做梯度最速下降
train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy) #正确预测,得到True或False的List
correct_prediction = tf.equal(tf.argmax(y_, 1), tf.argmax(y_conv, 1))
#将布尔值转化成浮点数，取平均值作为精确度
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float")) #在session中先初始化变量才能在session中调用
sess.run(tf.initialize_all_variables()) #迭代优化模型
for i in range(20000):
#每次取50个样本进行训练
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}) #模型中间不使用dropout
print("step %d, training 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}))
6、input_data.py文件
注：python3中没有xrange，其range与python2中的xrange作用相同
#!/urs/bin/env python
# -*- coding:utf-8 -*-
# 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
import urllib
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 range(batch_size)], [
fake_label for _ in range(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