本文參考Yann LeCun的LeNet5經典架構，稍加ps得到下面適用於本手寫識別的cnn結構，構造一個兩層卷積神經網絡，神經網絡的結構如下圖所示：
輸入-卷積-pooling-卷積-pooling-全連接層-Dropout-Softmax輸出
第一層卷積利用5*5的patch，32個卷積核，可以計算出32個特征。然后進行maxpooling。第二層卷積利用5*5的patch，64個卷積核，可以計算出64個特征。然后進行max pooling。卷積核的個數是我們自己設定，可以增加卷積核數目提高分類精度，但是那樣會增加更大參數，提高計算成本。
這樣輸入是分辨率為28*28的圖片。利用5*5的patch進行卷積。我們的卷積使用1步長（stride size），0填充模塊（zero padded），這樣得到的輸出和輸入是同一個大小。經過第一層卷積之后，卷積特征大小為28*28。然后通過ReLU函數激活。我們的pooling用簡單傳統的2x2大小的模板做max pooling，這樣pooling后得到14*14大小的特征。經過第二層卷積后，卷積特征大小為14*14，然后通過ReLU函數激活，再經過pooling后得到特征大小為7*7。
現在，圖片尺寸減小到7x7，我們加入一個有1024個神經元的全連接層，用於處理整個圖片。我們把池化層輸出的張量展開成一些向量，乘上權重矩陣，加上偏置，然后對其使用ReLU。
為了避免過擬合，在全連接層輸出接上dropout層。Dropout層在訓練時屏蔽一半的神經元。
1、輸入數據
直接使用tensorflow中的模塊，導入輸入數據：
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文件下載mnist數據
2、啟動session
（1）交互方式啟動session
sess = tf.InteractiveSession()
（2）一般方式啟動session
sess = tf.Session()
ps: 使用交互方式不用提前構建計算圖，而使用一般方式必須提前構建好計算圖才能啟動session
3、權重和偏置初始化
權重初始化的原則：應該加入少量的噪聲來打破對稱性並且要避免0梯度（初始化為0）
權重初始化一般選擇均勻分布或是正態分布
定義權重初始化方法：
def weight_variable(shape):
#截尾正態分布,stddev是正態分布的標准偏差
initial = tf.truncated_normal(shape=shape, stddev=0.1)
return tf.Variable(initial)
定義偏置初始化方法：
def bias_variable(shape):
initial = tf.constant(0.1, shape=shape)
return tf.Variable(initial)
4、定義卷積和池化方法
TensorFlow在卷積和Pooling上有很強的靈活性。我們怎么處理邊界？步長應該設多大？在這個實例里，我們的卷積使用1步長（stride size），0填充模塊（zero padded），保證輸出和輸入是同一個大小。我們的pooling用簡單傳統的2x2大小的模板做maxpooling。為了代碼更簡潔，我們把這部分抽象成一個函數。
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、直接貼完整代碼
from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf
#加載數據集
mnist = input_data.read_data_sets('MNIST_data', one_hot=True)
#以交互式方式啟動session
#如果不使用交互式session，則在啟動session前必須
# 構建整個計算圖，才能啟動該計算圖
sess = tf.InteractiveSession()
"""構建計算圖"""
#通過占位符來為輸入圖像和目標輸出類別創建節點
#shape參數是可選的，有了它tensorflow可以自動捕獲維度不一致導致的錯誤
x = tf.placeholder("float", shape=[None, 784]) #原始輸入
y_ = tf.placeholder("float", shape=[None, 10]) #目標值
#為了不在建立模型的時候反復做初始化操作，
# 我們定義兩個函數用於初始化
def weight_variable(shape):
#截尾正態分布,stddev是正態分布的標准偏差
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)
#卷積核池化,步長為1,0邊距
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')
"""第一層卷積"""
#由一個卷積和一個最大池化組成。濾波器5x5中算出32個特征，是因為使用32個濾波器進行卷積
#卷積的權重張量形狀是[5, 5, 1, 32],1是輸入通道的個數，32是輸出通道個數
W_conv1 = weight_variable([5, 5, 1, 32])
#每一個輸出通道都有一個偏置量
b_conv1 = bias_variable([32])
#位了使用卷積，必須將輸入轉換成4維向量，2、3維表示圖片的寬、高
#最后一維表示圖片的顏色通道（因為是灰度圖像所以通道數維1，RGB圖像通道數為3）
x_image = tf.reshape(x, [-1, 28, 28, 1])
#第一層的卷積結果,使用Relu作為激活函數
h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1))
#第一層卷積后的池化結果
h_pool1 = max_pool_2x2(h_conv1)
"""第二層卷積"""
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)
"""全連接層"""
#圖片尺寸減小到7*7，加入一個有1024個神經元的全連接層
W_fc1 = weight_variable([7*7*64, 1024])
b_fc1 = bias_variable([1024])
#將最后的池化層輸出張量reshape成一維向量
h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*64])
#全連接層的輸出
h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)
"""使用Dropout減少過擬合"""
#使用placeholder占位符來表示神經元的輸出在dropout中保持不變的概率
#在訓練的過程中啟用dropout，在測試過程中關閉dropout
keep_prob = tf.placeholder("float")
h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)
"""輸出層"""
W_fc2 = weight_variable([1024, 10])
b_fc2 = bias_variable([10])
#模型預測輸出
y_conv = tf.nn.softmax(tf.matmul(h_fc1_drop, W_fc2) + b_fc2)
#交叉熵損失
cross_entropy = -tf.reduce_sum(y_ * tf.log(y_conv))
#模型訓練,使用AdamOptimizer來做梯度最速下降
train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)
#正確預測,得到True或False的List
correct_prediction = tf.equal(tf.argmax(y_, 1), tf.argmax(y_conv, 1))
#將布爾值轉化成浮點數，取平均值作為精確度
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
#在session中先初始化變量才能在session中調用
sess.run(tf.initialize_all_variables())
#迭代優化模型
for i in range(20000):
#每次取50個樣本進行訓練
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}) #模型中間不使用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中沒有xrange，其range與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