基于MNIST数据的卷积神经网络CNN

• 基于tensorflow使用CNN识别MNIST

• 参数数量：第一个卷积层5x5x1x32=800个参数，第二个卷积层5x5x32x64=51200个参数，第三个全连接层7x7x64x1024=3211264个参数，第四个输出层1024x10=10240个参数，总量级为330万个参数，单机训练时间约为30分钟。

• 关于优化算法：随机梯度下降法的learning rate需要逐渐变小，因为随机抽取样本引入了噪音，使得我们在最小点处的随机梯度仍然不为0。对于batch gradient descent不存在这个问题，在最小点损失函数的梯度变为0，因此batch gradient descent可以使用固定的learning rate。为了让learning rate逐渐变小，有以下几种变种算法。

• Momentum algorithm accumulates an exponentially decaying moving average of past gradients and continues to move in their direction.
• AdaGrad adapts the learning rates of all model parameters by scaling them inversely proportional to the square root of the sum of all their historical squared values. But the accumulation of squared gradients from the beginning of training can result in a premature and excessive decrease in the effective learning rate.
• RMSProp： AdaGrad is designed to converge rapidly when applied to a convex function. When applied to a non-convex function to train a neural network, the learning trajectory may pass through many different structures and eventually arrive at a region that is a locally convex bowl. AdaGrad shrinks the learning rate according to the entire history of the squared gradient and may have made the learning rate too small before arriving at such a convex structure.RMSProp uses an exponentially decaying average to discard history from the extreme past so that it can converge rapidly after finding a convex bowl, as if it were an instance of the AdaGrad algorithm initialized within that bowl.
• Adam：The name “Adam” derives from the phrase “adaptive moments.” It is a variant on the combination of RMSProp and momentum with a few important distinctions. Adam is generally regarded as being fairly robust to the choice of hyperparameters, though the learning rate sometimes needs to be changed from the suggested default.
• 如果将MNIST数据集的AdamOptimizer换成GradientDescentOptimizer，测试集的准确率为0.9296.

官方demo

• https://github.com/tensorflow/tensorflow/blob/master/tensorflow/examples/tutorials/mnist/mnist_deep.py

"""A deep MNIST classifier using convolutional layers.
See extensive documentation at
https://www.tensorflow.org/get_started/mnist/pros
"""
# Disable linter warnings to maintain consistency with tutorial.
# pylint: disable=invalid-name
# pylint: disable=g-bad-import-order

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import argparse
import sys
import tempfile

from tensorflow.examples.tutorials.mnist import input_data

import tensorflow as tf

FLAGS = None


def deepnn(x):
  """deepnn builds the graph for a deep net for classifying digits.
  Args:
    x: an input tensor with the dimensions (N_examples, 784), where 784 is the
    number of pixels in a standard MNIST image.
  Returns:
    A tuple (y, keep_prob). y is a tensor of shape (N_examples, 10), with values
    equal to the logits of classifying the digit into one of 10 classes (the
    digits 0-9). keep_prob is a scalar placeholder for the probability of
    dropout.
  """
  # Reshape to use within a convolutional neural net.
  # Last dimension is for "features" - there is only one here, since images are
  # grayscale -- it would be 3 for an RGB image, 4 for RGBA, etc.
  with tf.name_scope('reshape'):
    x_image = tf.reshape(x, [-1, 28, 28, 1])

  # First convolutional layer - maps one grayscale image to 32 feature maps.
  with tf.name_scope('conv1'):
    W_conv1 = weight_variable([5, 5, 1, 32])
    b_conv1 = bias_variable([32])
    h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1)

  # Pooling layer - downsamples by 2X.
  with tf.name_scope('pool1'):
    h_pool1 = max_pool_2x2(h_conv1)

  # Second convolutional layer -- maps 32 feature maps to 64.
  with tf.name_scope('conv2'):
    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)

  # Second pooling layer.
  with tf.name_scope('pool2'):
    h_pool2 = max_pool_2x2(h_conv2)

  # Fully connected layer 1 -- after 2 round of downsampling, our 28x28 image
  # is down to 7x7x64 feature maps -- maps this to 1024 features.
  with tf.name_scope('fc1'):
    W_fc1 = weight_variable([7 * 7 * 64, 1024])
    b_fc1 = bias_variable([1024])

    h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*64])
    h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)

  # Dropout - controls the complexity of the model, prevents co-adaptation of
  # features.
  with tf.name_scope('dropout'):
    keep_prob = tf.placeholder(tf.float32)
    h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

  # Map the 1024 features to 10 classes, one for each digit
  with tf.name_scope('fc2'):
    W_fc2 = weight_variable([1024, 10])
    b_fc2 = bias_variable([10])

    y_conv = tf.matmul(h_fc1_drop, W_fc2) + b_fc2
  return y_conv, keep_prob


def conv2d(x, W):
  """conv2d returns a 2d convolution layer with full stride."""
  return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')


def max_pool_2x2(x):
  """max_pool_2x2 downsamples a feature map by 2X."""
  return tf.nn.max_pool(x, ksize=[1, 2, 2, 1],
                        strides=[1, 2, 2, 1], padding='SAME')


def weight_variable(shape):
  """weight_variable generates a weight variable of a given shape."""
  initial = tf.truncated_normal(shape, stddev=0.1)
  return tf.Variable(initial)


def bias_variable(shape):
  """bias_variable generates a bias variable of a given shape."""
  initial = tf.constant(0.1, shape=shape)
  return tf.Variable(initial)


def main(_):
  # Import data
  mnist = input_data.read_data_sets(FLAGS.data_dir, one_hot=True)

  # Create the model
  x = tf.placeholder(tf.float32, [None, 784])

  # Define loss and optimizer
  y_ = tf.placeholder(tf.float32, [None, 10])

  # Build the graph for the deep net
  y_conv, keep_prob = deepnn(x)

  with tf.name_scope('loss'):
    cross_entropy = tf.nn.softmax_cross_entropy_with_logits(labels=y_,
                                                            logits=y_conv)
  cross_entropy = tf.reduce_mean(cross_entropy)

  with tf.name_scope('adam_optimizer'):
    train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)

  with tf.name_scope('accuracy'):
    correct_prediction = tf.equal(tf.argmax(y_conv, 1), tf.argmax(y_, 1))
    correct_prediction = tf.cast(correct_prediction, tf.float32)
  accuracy = tf.reduce_mean(correct_prediction)

  graph_location = tempfile.mkdtemp()
  print('Saving graph to: %s' % graph_location)
  train_writer = tf.summary.FileWriter(graph_location)
  train_writer.add_graph(tf.get_default_graph())

  with tf.Session() as sess:
    sess.run(tf.global_variables_initializer())
    for i in range(20000):
      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})
        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}))

if __name__ == '__main__':
  parser = argparse.ArgumentParser()
  parser.add_argument('--data_dir', type=str,
                      default='/tmp/tensorflow/mnist/input_data',
                      help='Directory for storing input data')
  FLAGS, unparsed = parser.parse_known_args()
  tf.app.run(main=main, argv=[sys.argv[0]] + unparsed)

reuslt

"D:\Program Files\Anaconda3\python.exe" "D:\Program Files\JetBrains\PyCharm Community Edition 2017.2.2\helpers\pydev\pydevd.py" --multiproc --qt-support=auto --client 127.0.0.1 --port 1541 --file F:/RANJIEWEN/Deep_learning/TensorFlow/基于MNIST数据的卷积神经网络CNN.py
pydev debugger: process 3288 is connecting

Connected to pydev debugger (build 172.3757.67)
Start processing MNIST handwritten digits data...
Start evaluating CNN model by tensorflow...
WARNING:tensorflow:From D:\Program Files\Anaconda3\lib\site-packages\tensorflow\python\util\tf_should_use.py:175: initialize_all_variables (from tensorflow.python.ops.variables) is deprecated and will be removed after 2017-03-02.
Instructions for updating:
Use `tf.global_variables_initializer` instead.
2017-09-08 16:50:19.814600: W C:\tf_jenkins\home\workspace\rel-win\M\windows\PY\35\tensorflow\core\platform\cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use AVX instructions, but these are available on your machine and could speed up CPU computations.
2017-09-08 16:50:19.814600: W C:\tf_jenkins\home\workspace\rel-win\M\windows\PY\35\tensorflow\core\platform\cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use AVX2 instructions, but these are available on your machine and could speed up CPU computations.
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test accuracy 0.9923

Process finished with exit code 1

• 最后19900次迭代完成后，会消耗大量内存，8G都会卡死。。。

参考dmeo

# -*- coding: utf-8 -*-
"""
Created on Thu Sep  7 11:06:36 2017

@author: Administrator
"""

# @description: implement a CNN model upon MNIST handwritten digits
# @ref: http://yann.lecun.com/exdb/mnist/

import gzip
import struct
import numpy as np
from sklearn import preprocessing
import tensorflow as tf

# MNIST data is stored in binary format, 
# and we transform them into numpy ndarray objects by the following two utility functions
def read_image(file_name):
    with gzip.open(file_name, 'rb') as f:
        buf = f.read()
        index = 0
        magic, images, rows, columns = struct.unpack_from('>IIII' , buf , index)
        index += struct.calcsize('>IIII')

        image_size = '>' + str(images*rows*columns) + 'B'
        ims = struct.unpack_from(image_size, buf, index)
        
        im_array = np.array(ims).reshape(images, rows, columns)
        return im_array

def read_label(file_name):
    with gzip.open(file_name, 'rb') as f:
        buf = f.read()
        index = 0
        magic, labels = struct.unpack_from('>II', buf, index)
        index += struct.calcsize('>II')
        
        label_size = '>' + str(labels) + 'B'
        labels = struct.unpack_from(label_size, buf, index)

        label_array = np.array(labels)
        return label_array

print ("Start processing MNIST handwritten digits data...")
train_x_data = read_image("MNIST_data/train-images-idx3-ubyte.gz")  # shape: 60000x28x28
train_x_data = train_x_data.reshape(train_x_data.shape[0], train_x_data.shape[1], train_x_data.shape[2], 1).astype(np.float32)
train_y_data = read_label("MNIST_data/train-labels-idx1-ubyte.gz")  
test_x_data = read_image("MNIST_data/t10k-images-idx3-ubyte.gz")  # shape: 10000x28x28
test_x_data = test_x_data.reshape(test_x_data.shape[0], test_x_data.shape[1], test_x_data.shape[2], 1).astype(np.float32)
test_y_data = read_label("MNIST_data/t10k-labels-idx1-ubyte.gz")

train_x_minmax = train_x_data / 255.0
test_x_minmax = test_x_data / 255.0

# Of course you can also use the utility function to read in MNIST provided by tensorflow
# from tensorflow.examples.tutorials.mnist import input_data
# mnist = input_data.read_data_sets("MNIST_data/", one_hot=False)
# train_x_minmax = mnist.train.images
# train_y_data = mnist.train.labels
# test_x_minmax = mnist.test.images
# test_y_data = mnist.test.labels

# Reformat y into one-hot encoding style
lb = preprocessing.LabelBinarizer()
lb.fit(train_y_data)
train_y_data_trans = lb.transform(train_y_data)
test_y_data_trans = lb.transform(test_y_data)

print ("Start evaluating CNN model by tensorflow...")

# Model input
x = tf.placeholder(tf.float32, shape=[None, 28, 28, 1])
y_ = tf.placeholder(tf.float32, [None, 10])

# Weight initialization
def weight_variable(shape):
    initial = tf.truncated_normal(shape, stddev=0.1)
    return tf.Variable(initial)

def bias_variable(shape):
    initial = tf.constant(0.1, shape=shape)
    return tf.Variable(initial)

# Convolution and Pooling
def conv2d(x, W):
    # `tf.nn.conv2d()` computes a 2-D convolution given 4-D `input` and `filter` tensors
    # input tensor shape `[batch, in_height, in_width, in_channels]`, batch is number of observation 
    # filter tensor shape `[filter_height, filter_width, in_channels, out_channels]`
    # strides: the stride of the sliding window for each dimension of input.
    # padding: 'SAME' or 'VALID', determine the type of padding algorithm to use
    return tf.nn.conv2d(x, W, strides=[1, 1, 1, 1], padding='SAME')

def max_pool_2x2(x):
    # `tf.nn.max_pool` performs the max pooling on the input
    #  ksize: the size of the window for each dimension of the input tensor.
    return tf.nn.max_pool(x, ksize=[1, 2, 2, 1], strides=[1, 2, 2, 1], padding='SAME')


# First convolutional layer
# Convolution: compute 32 features for each 5x5 patch
# Max pooling: reduce image size to 14x14.
W_conv1 = weight_variable([5, 5, 1, 32])
b_conv1 = bias_variable([32])

h_conv1 = tf.nn.relu(conv2d(x,  W_conv1) + b_conv1)
h_pool1 = max_pool_2x2(h_conv1)

# Second convolutional layer
# Convolution: compute 64 features for each 5x5 patch
# Max pooling: reduce image size to 7x7
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)

# Densely connected layer
# Fully-conected layer with 1024 neurons
W_fc1 = weight_variable([7 * 7 * 64, 1024])
b_fc1 = bias_variable([1024])

h_pool2_flat = tf.reshape(h_pool2, [-1, 7*7*64])
h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)

# Dropout
# To reduce overfitting, we apply dropout before the readout layer.
keep_prob = tf.placeholder(tf.float32)
h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

# Readout layer
W_fc2 = weight_variable([1024, 10])
b_fc2 = bias_variable([10])

y_conv = tf.matmul(h_fc1_drop, W_fc2) + b_fc2

# Train and evaluate
loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=y_conv,labels= y_)) #
# y = tf.nn.softmax(y_conv)
# loss = tf.reduce_mean(-tf.reduce_sum(y_ * tf.log(y), reduction_indices=[1]))
optimizer = tf.train.AdamOptimizer(1e-4)
# optimizer = tf.train.GradientDescentOptimizer(1e-4)
train = optimizer.minimize(loss)

correct_prediction = tf.equal(tf.argmax(y_conv, 1), tf.argmax(y_, 1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))

init = tf.initialize_all_variables()
sess = tf.Session()
sess.run(init)

for step in range(20000):
    sample_index = np.random.choice(train_x_minmax.shape[0], 50)
    batch_xs = train_x_minmax[sample_index, :]
    batch_ys = train_y_data_trans[sample_index, :]
    if step % 100 == 0:
        train_accuracy = sess.run(accuracy, feed_dict={
            x: batch_xs, y_: batch_ys, keep_prob: 1.0})
        print ("step %d, training accuracy %g" % (step, train_accuracy))
    sess.run(train, feed_dict={x: batch_xs, y_: batch_ys, keep_prob: 0.5})

print ("test accuracy %g" % sess.run(accuracy, feed_dict={
    x: test_x_minmax, y_: test_y_data_trans, keep_prob: 1.0}))