基于TensorFlow解决手写数字识别的Softmax方法、多层卷积网络方法和前馈神经网络方法

一.基于TensorFlow的softmax回归模型解决手写字母识别问题

详细步骤如下：

1.加载MNIST数据： input_data.read_data_sets('MNIST_data',one_hot=true)

2.运行TensorFlow的InterractiveSession: sess = tf.InteractiveSession()

3.构建Softmax回归模型: 占位符tf.placeholder 变量tf.Variable 类别预测与损失函数 tf.nn.softmax  tf.refuce_sum 训练模型 tf.train.GradientDescentOptimizer 评估模型

结果：在测试集上有91%正确率

二.构建多层卷积网络

详细步骤如下：

1.权重初始化函数

2.卷积和池化函数

3.第一层卷积

4.第二层卷积

5.密集连接层

6.输出层

7.训练和评估模型

代码：（DeepMnist.py）

 from tensorflow.examples.tutorials.mnist import input_data
 mnist = input_data.read_data_sets('MNIST_data', one_hot=True)

 import tensorflow as tf
 sess = tf.InteractiveSession()

 x = tf.placeholder(tf.float32, shape=[None, 784])
 y_ = tf.placeholder(tf.float32, shape=[None, 10])

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

 sess.run(tf.global_variables_initializer())

 y = tf.matmul(x ,w) + b

 cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels = y_, logits=y))

 train_step = tf.train.GradientDescentOptimizer(0.5).minimize(cross_entropy)

 for _ in range(1000):
     batch = mnist.train.next_batch(100)
     train_step.run(feed_dict={x:batch[0],y_:batch[1]})

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

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

 print(accuracy.eval(feed_dict={x:mnist.test.images,y_:mnist.test.labels}))

 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)

 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')

 w_conv1 = weight_variable([5,5,1,32])
 b_conv1 = bias_variable([32])

 x_image = tf.reshape(x, [-1,28,28,1])

 h_conv1 = tf.nn.relu(conv2d(x_image, w_conv1) + b_conv1)
 h_pool1 = max_pool_2x2(h_conv1)

 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)

 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)

 keep_prob = tf.placeholder(tf.float32)
 h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

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

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

 cross_entropy = tf.reduce_mean(
     tf.nn.softmax_cross_entropy_with_logits(labels=y_, logits=y_conv))
 train_step = tf.train.AdamOptimizer(1e-4).minimize(cross_entropy)
 correct_prediction = tf.equal(tf.argmax(y_conv,1), tf.argmax(y_,1))
 accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
 sess.run(tf.global_variables_initializer())
 for i in range(1000):
   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}))

输出：

训练1000次，测试准确率96.34%；20000次准确率达到99%以上；

三.简易前馈神经网络

代码如下：

 # Copyright 2015 The TensorFlow Authors. 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.
 # ==============================================================================

 """Builds the MNIST network.
 Implements the inference/loss/training pattern for model building.
 1. inference() - Builds the model as far as is required for running the network
 forward to make predictions.
 2. loss() - Adds to the inference model the layers required to generate loss.
 3. training() - Adds to the loss model the Ops required to generate and
 apply gradients.
 This file is used by the various "fully_connected_*.py" files and not meant to
 be run.
 """
 from __future__ import absolute_import
 from __future__ import division
 from __future__ import print_function

 import math

 import tensorflow as tf

 # The MNIST dataset has 10 classes, representing the digits 0 through 9.
 NUM_CLASSES = 10

 # The MNIST images are always 28x28 pixels.
 IMAGE_SIZE = 28
 IMAGE_PIXELS = IMAGE_SIZE * IMAGE_SIZE

 def inference(images, hidden1_units, hidden2_units):
   """Build the MNIST model up to where it may be used for inference.
   Args:
     images: Images placeholder, from inputs().
     hidden1_units: Size of the first hidden layer.
     hidden2_units: Size of the second hidden layer.
   Returns:
     softmax_linear: Output tensor with the computed logits.
   """
   # Hidden 1
   with tf.name_scope('hidden1'):
     weights = tf.Variable(
         tf.truncated_normal([IMAGE_PIXELS, hidden1_units],
                             stddev=1.0 / math.sqrt(float(IMAGE_PIXELS))),
         name='weights')
     biases = tf.Variable(tf.zeros([hidden1_units]),
                          name='biases')
     hidden1 = tf.nn.relu(tf.matmul(images, weights) + biases)
   # Hidden 2
   with tf.name_scope('hidden2'):
     weights = tf.Variable(
         tf.truncated_normal([hidden1_units, hidden2_units],
                             stddev=1.0 / math.sqrt(float(hidden1_units))),
         name='weights')
     biases = tf.Variable(tf.zeros([hidden2_units]),
                          name='biases')
     hidden2 = tf.nn.relu(tf.matmul(hidden1, weights) + biases)
   # Linear
   with tf.name_scope('softmax_linear'):
     weights = tf.Variable(
         tf.truncated_normal([hidden2_units, NUM_CLASSES],
                             stddev=1.0 / math.sqrt(float(hidden2_units))),
         name='weights')
     biases = tf.Variable(tf.zeros([NUM_CLASSES]),
                          name='biases')
     logits = tf.matmul(hidden2, weights) + biases
   return logits

 def loss(logits, labels):
   """Calculates the loss from the logits and the labels.
   Args:
     logits: Logits tensor, float - [batch_size, NUM_CLASSES].
     labels: Labels tensor, int32 - [batch_size].
   Returns:
     loss: Loss tensor of type float.
   """
   labels = tf.to_int64(labels)
   cross_entropy = tf.nn.sparse_softmax_cross_entropy_with_logits(
       labels=labels, logits=logits, name='xentropy')
   return tf.reduce_mean(cross_entropy, name='xentropy_mean')

 def training(loss, learning_rate):
   """Sets up the training Ops.
   Creates a summarizer to track the loss over time in TensorBoard.
   Creates an optimizer and applies the gradients to all trainable variables.
   The Op returned by this function is what must be passed to the
   `sess.run()` call to cause the model to train.
   Args:
     loss: Loss tensor, from loss().
     learning_rate: The learning rate to use for gradient descent.
   Returns:
     train_op: The Op for training.
   """
   # Add a scalar summary for the snapshot loss.
   tf.summary.scalar('loss', loss)
   # Create the gradient descent optimizer with the given learning rate.
   optimizer = tf.train.GradientDescentOptimizer(learning_rate)
   # Create a variable to track the global step.
   global_step = tf.Variable(0, name='global_step', trainable=False)
   # Use the optimizer to apply the gradients that minimize the loss
   # (and also increment the global step counter) as a single training step.
   train_op = optimizer.minimize(loss, global_step=global_step)
   return train_op

 def evaluation(logits, labels):
   """Evaluate the quality of the logits at predicting the label.
   Args:
     logits: Logits tensor, float - [batch_size, NUM_CLASSES].
     labels: Labels tensor, int32 - [batch_size], with values in the
       range [0, NUM_CLASSES).
   Returns:
     A scalar int32 tensor with the number of examples (out of batch_size)
     that were predicted correctly.
   """
   # For a classifier model, we can use the in_top_k Op.
   # It returns a bool tensor with shape [batch_size] that is true for
   # the examples where the label is in the top k (here k=1)
   # of all logits for that example.
   correct = tf.nn.in_top_k(logits, labels, 1)
   # Return the number of true entries.
   return tf.reduce_sum(tf.cast(correct, tf.int32))

mnist.py

 # Copyright 2015 The TensorFlow Authors. 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.
 # ==============================================================================

 """Trains and Evaluates the MNIST network using a feed dictionary."""
 from __future__ import absolute_import
 from __future__ import division
 from __future__ import print_function

 # pylint: disable=missing-docstring
 import argparse
 import os.path
 import sys
 import time

 from six.moves import xrange  # pylint: disable=redefined-builtin
 import tensorflow as tf

 from tensorflow.examples.tutorials.mnist import input_data
 from tensorflow.examples.tutorials.mnist import mnist

 # Basic model parameters as external flags.
 FLAGS = None

 def placeholder_inputs(batch_size):
   """Generate placeholder variables to represent the input tensors.
   These placeholders are used as inputs by the rest of the model building
   code and will be fed from the downloaded data in the .run() loop, below.
   Args:
     batch_size: The batch size will be baked into both placeholders.
   Returns:
     images_placeholder: Images placeholder.
     labels_placeholder: Labels placeholder.
   """
   # Note that the shapes of the placeholders match the shapes of the full
   # image and label tensors, except the first dimension is now batch_size
   # rather than the full size of the train or test data sets.
   images_placeholder = tf.placeholder(tf.float32, shape=(batch_size,
                                                          mnist.IMAGE_PIXELS))
   labels_placeholder = tf.placeholder(tf.int32, shape=(batch_size))
   return images_placeholder, labels_placeholder

 def fill_feed_dict(data_set, images_pl, labels_pl):
   """Fills the feed_dict for training the given step.
   A feed_dict takes the form of:
   feed_dict = {
       <placeholder>: <tensor of values to be passed for placeholder>,
       ....
   }
   Args:
     data_set: The set of images and labels, from input_data.read_data_sets()
     images_pl: The images placeholder, from placeholder_inputs().
     labels_pl: The labels placeholder, from placeholder_inputs().
   Returns:
     feed_dict: The feed dictionary mapping from placeholders to values.
   """
   # Create the feed_dict for the placeholders filled with the next
   # `batch size` examples.
   images_feed, labels_feed = data_set.next_batch(FLAGS.batch_size,
                                                  FLAGS.fake_data)
   feed_dict = {
       images_pl: images_feed,
       labels_pl: labels_feed,
   }
   return feed_dict

 def do_eval(sess,
             eval_correct,
             images_placeholder,
             labels_placeholder,
             data_set):
   """Runs one evaluation against the full epoch of data.
   Args:
     sess: The session in which the model has been trained.
     eval_correct: The Tensor that returns the number of correct predictions.
     images_placeholder: The images placeholder.
     labels_placeholder: The labels placeholder.
     data_set: The set of images and labels to evaluate, from
       input_data.read_data_sets().
   """
   # And run one epoch of eval.
   true_count = 0  # Counts the number of correct predictions.
   steps_per_epoch = data_set.num_examples // FLAGS.batch_size
   num_examples = steps_per_epoch * FLAGS.batch_size
   for step in xrange(steps_per_epoch):
     feed_dict = fill_feed_dict(data_set,
                                images_placeholder,
                                labels_placeholder)
     true_count += sess.run(eval_correct, feed_dict=feed_dict)
   precision = float(true_count) / num_examples
   print('  Num examples: %d  Num correct: %d  Precision @ 1: %0.04f' %
         (num_examples, true_count, precision))

 def run_training():
   """Train MNIST for a number of steps."""
   # Get the sets of images and labels for training, validation, and
   # test on MNIST.
   data_sets = input_data.read_data_sets(FLAGS.input_data_dir, FLAGS.fake_data)

   # Tell TensorFlow that the model will be built into the default Graph.
   with tf.Graph().as_default():
     # Generate placeholders for the images and labels.
     images_placeholder, labels_placeholder = placeholder_inputs(
         FLAGS.batch_size)

     # Build a Graph that computes predictions from the inference model.
     logits = mnist.inference(images_placeholder,
                              FLAGS.hidden1,
                              FLAGS.hidden2)

     # Add to the Graph the Ops for loss calculation.
     loss = mnist.loss(logits, labels_placeholder)

     # Add to the Graph the Ops that calculate and apply gradients.
     train_op = mnist.training(loss, FLAGS.learning_rate)

     # Add the Op to compare the logits to the labels during evaluation.
     eval_correct = mnist.evaluation(logits, labels_placeholder)

     # Build the summary Tensor based on the TF collection of Summaries.
     summary = tf.summary.merge_all()

     # Add the variable initializer Op.
     init = tf.global_variables_initializer()

     # Create a saver for writing training checkpoints.
     saver = tf.train.Saver()

     # Create a session for running Ops on the Graph.
     sess = tf.Session()

     # Instantiate a SummaryWriter to output summaries and the Graph.
     summary_writer = tf.summary.FileWriter(FLAGS.log_dir, sess.graph)

     # And then after everything is built:

     # Run the Op to initialize the variables.
     sess.run(init)

     # Start the training loop.
     for step in xrange(FLAGS.max_steps):
       start_time = time.time()

       # Fill a feed dictionary with the actual set of images and labels
       # for this particular training step.
       feed_dict = fill_feed_dict(data_sets.train,
                                  images_placeholder,
                                  labels_placeholder)

       # Run one step of the model.  The return values are the activations
       # from the `train_op` (which is discarded) and the `loss` Op.  To
       # inspect the values of your Ops or variables, you may include them
       # in the list passed to sess.run() and the value tensors will be
       # returned in the tuple from the call.
       _, loss_value = sess.run([train_op, loss],
                                feed_dict=feed_dict)

       duration = time.time() - start_time

       # Write the summaries and print an overview fairly often.
       if step % 100 == 0:
         # Print status to stdout.
         print('Step %d: loss = %.2f (%.3f sec)' % (step, loss_value, duration))
         # Update the events file.
         summary_str = sess.run(summary, feed_dict=feed_dict)
         summary_writer.add_summary(summary_str, step)
         summary_writer.flush()

       # Save a checkpoint and evaluate the model periodically.
       if (step + 1) % 1000 == 0 or (step + 1) == FLAGS.max_steps:
         checkpoint_file = os.path.join(FLAGS.log_dir, 'model.ckpt')
         saver.save(sess, checkpoint_file, global_step=step)
         # Evaluate against the training set.
         print('Training Data Eval:')
         do_eval(sess,
                 eval_correct,
                 images_placeholder,
                 labels_placeholder,
                 data_sets.train)
         # Evaluate against the validation set.
         print('Validation Data Eval:')
         do_eval(sess,
                 eval_correct,
                 images_placeholder,
                 labels_placeholder,
                 data_sets.validation)
         # Evaluate against the test set.
         print('Test Data Eval:')
         do_eval(sess,
                 eval_correct,
                 images_placeholder,
                 labels_placeholder,
                 data_sets.test)

 def main(_):
   if tf.gfile.Exists(FLAGS.log_dir):
     tf.gfile.DeleteRecursively(FLAGS.log_dir)
   tf.gfile.MakeDirs(FLAGS.log_dir)
   run_training()

 if __name__ == '__main__':
   parser = argparse.ArgumentParser()
   parser.add_argument(
       '--learning_rate',
       type=float,
       default=0.01,
       help='Initial learning rate.'
   )
   parser.add_argument(
       '--max_steps',
       type=int,
       default=2000,
       help='Number of steps to run trainer.'
   )
   parser.add_argument(
       '--hidden1',
       type=int,
       default=128,
       help='Number of units in hidden layer 1.'
   )
   parser.add_argument(
       '--hidden2',
       type=int,
       default=32,
       help='Number of units in hidden layer 2.'
   )
   parser.add_argument(
       '--batch_size',
       type=int,
       default=100,
       help='Batch size.  Must divide evenly into the dataset sizes.'
   )
   parser.add_argument(
       '--input_data_dir',
       type=str,
       default='/tmp/tensorflow/mnist/input_data',
       help='Directory to put the input data.'
   )
   parser.add_argument(
       '--log_dir',
       type=str,
       default='/tmp/tensorflow/mnist/logs/fully_connected_feed',
       help='Directory to put the log data.'
   )
   parser.add_argument(
       '--fake_data',
       default=False,
       help='If true, uses fake data for unit testing.',
       action='store_true'
   )

   FLAGS, unparsed = parser.parse_known_args()
   tf.app.run(main=main, argv=[sys.argv[0]] + unparsed)

full_connected_feed

full_connected_feed.py中main函数为入口点，调用run_training函数，函数体内调用了其他的函数。

输出：

 

小结：

1.多查TensorFlow官方帮助文档（不熟悉函数意思）；

2.上述例子参照官网例程编写；

3.尽量使用GPU版TensorFlow，卷积网络20000次训练时，需要时间很长，而且本机的CPU占用率几近100%（intel i7-4720k）；

4.安装python3.5时，注意添加路径到系统环境变量path中；

参考文献：1.https://www.tensorflow.org/get_started/mnist/pros

2.https://www.tensorflow.org/get_started/mnist/mechanics