我们首先导入已经清洗好的数据。
这个清洗过程在之前的博文实战(1)。
# These are all the modules we'll be using later. Make sure you can import them
# before proceeding further.
from __future__ import print_function
import numpy as np
import tensorflow as tf
from six.moves import cPickle as pickle
from six.moves import range
pickle_file = 'notMNIST.pickle'
with open(pickle_file, 'rb') as f:
save = pickle.load(f)
train_dataset = save['train_dataset']
train_labels = save['train_labels']
valid_dataset = save['valid_dataset']
valid_labels = save['valid_labels']
test_dataset = save['test_dataset']
test_labels = save['test_labels']
del save # hint to help gc free up memory
print('Training set', train_dataset.shape, train_labels.shape)
print('Validation set', valid_dataset.shape, valid_labels.shape)
print('Test set', test_dataset.shape, test_labels.shape)卷积神经网络需要的图片矩阵是三维的，这一点需要做一下改变。(利用np.reshape)
其次，所有的label都是one-shot的。
image_size = 28
num_labels = 10
num_channels = 1 # grayscale
# it is a picture in gray scale originally we only need add a dimention
def reformat(dataset, labels):
dataset = dataset.reshape((-1, image_size, image_size, num_channels)).astype(np.float32)
labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)
return dataset, labels
train_dataset, train_labels = reformat(train_dataset, train_labels)
valid_dataset, valid_labels = reformat(valid_dataset, valid_labels)
test_dataset, test_labels = reformat(test_dataset, test_labels)
print('Training set', train_dataset.shape, train_labels.shape)
print('Validation set', valid_dataset.shape, valid_labels.shape)
print('Test set', test_dataset.shape, test_labels.shape)
def accuracy(predictions, labels):
return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1)) / predictions.shape[0])Training set (200000, 28, 28, 1) (200000, 10) Validation set (10000, 28, 28, 1) (10000, 10) Test set (10000, 28, 28, 1) (10000, 10)
1.简单卷积神经网络
tensorflow提供了卷积函数nn.conv2d。
我们来看一下这个函数的文档，学习下如何使用。
Signature: tf.nn.conv2d(input, filter, strides, padding, use_cudnn_on_gpu=None, data_format=None, name=None)Docstring:Computes a 2-D convolution given 4-Dinput and filter tensors.
Given an input tensor of shape [batch, in_height, in_width, in_channels]and a filter / kernel tensor of shape[filter_height, filter_width, in_channels, out_channels], this opperforms the following:
Flattens the filter to a 2-D matrix with shape[filter_height * filter_width * in_channels, output_channels].
Extracts image patches from the input tensor to form avirtual tensor of shape [batch, out_height, out_width, filter_height * filter_width * in_channels].
For each patch, right-multiplies the filter matrix and the image patchvector.
In detail, with the default NHWC format,
output[b, i, j, k] =
sum_{di, dj, q} input[b, strides[1] * i + di, strides[2] * j + dj, q] *
filter[di, dj, q, k]
Must have strides[0] = strides[3] = 1. For the most common case of the samehorizontal and vertices strides,strides = [1, stride, stride, 1].
Args:
input:
A Tensor. Must be one of the following types:half, float32, float64.
filter: A Tensor. Must have the same type asinput.
strides: A list of ints. 1-D of length 4. The stride of the sliding window for each dimension ofinput. Must be in the same order as the dimension specified with format.
padding: A string from:"SAME", "VALID". The type of padding algorithm to use.
use_cudnn_on_gpu: An optionalbool. Defaults to True.
data_format: An optional string from: "NHWC", "NCHW". Defaults to "NHWC". Specify the data format of the input and output data. With the default format "NHWC", the data is stored in the order of: [batch, in_height, in_width, in_channels]. Alternatively, the format could be "NCHW", the data storage order of: [batch, in_channels, in_height, in_width]. name: A name for the operation (optional).
Returns: A Tensor. Has the same type asinput.Type: function输入input就是我们的一组图片数据，这里是4维的。
filter：过滤器，也叫权重矩阵，要与input的类型一样。
stride：步长，含有四个整数的列表，一般第一个和第四个都应该为1，中间两个分别代表像素扫描的间隔。
padding：输入分割的方式，valid和same
最为重要的使理解conv2d对我们的输入参数都做了什么变化，这样我们才能知道如何设置好输入参数，满足conv2d的需要。
在conv2d中，
假设inpute的四个维度是[batch, in_height, in_width, in_channels]，
filter的四个维度是[filter_height, filter_width, in_channels, out_channels]。
进入conv2d函数后，filter被拉伸为2维数组.
新的二维数组A的维度是[filter_height＊filter_width＊in_channels, out_channels].
其次，input数组依然为4维数组，但是维度发生了变化。
input产生新的4维数组B的维度是[batch, out_height, out_width, filter_height * filter_width * in_channels]。
最后进行乘法B＊A。
所以在设置filter时应注意filter的维度以及input的维度的设置，否则conv2d无法进行运算。
领会了其中的缘由就可以设置好自己的卷积神经网络。
batch_size = 128
patch_size = 5 # padding image pixels by 5*5
depth = 16 # depth
num_hidden = 64 # num of node in hidden layer
graph = tf.Graph()
with graph.as_default():
# Input data.
tf_train_dataset = tf.placeholder(tf.float32, shape=(batch_size, image_size, image_size, num_channels)) # num_channels=1 grayscale
tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
tf_valid_dataset = tf.constant(valid_dataset)
tf_test_dataset = tf.constant(test_dataset)
# Variables.
layer1_weights = tf.Variable(tf.truncated_normal([patch_size, patch_size, num_channels, depth], stddev=0.1))
layer1_biases = tf.Variable(tf.zeros([depth]))
layer2_weights = tf.Variable(tf.truncated_normal( [patch_size, patch_size, depth, depth], stddev=0.1))
layer2_biases = tf.Variable(tf.constant(1.0, shape=[depth]))
layer3_weights = tf.Variable(tf.truncated_normal([image_size // 4 * image_size // 4 * depth, num_hidden], stddev=0.1))
layer3_biases = tf.Variable(tf.constant(1.0, shape=[num_hidden]))
layer4_weights = tf.Variable(tf.truncated_normal([num_hidden, num_labels], stddev=0.1))
layer4_biases = tf.Variable(tf.constant(1.0, shape=[num_labels]))
# Model.
def model(data):
# data (batch, 28, 28, 1)
# weights reshaped to (patch_size*patch_size*num_channels, depth)
# data reshaped to (batch, 14, 14, patch_size*patch_size*num_channels)
# conv shape (batch, 14, 14, depth)
conv = tf.nn.conv2d(data, layer1_weights, [1, 2, 2, 1], padding='SAME') # convolution
hidden = tf.nn.relu(conv + layer1_biases)
# weights shape (patch_size, patch_size, depth, depth)
# weights reshaped into (patch_size*patch_size* depth, depth)
# hidden reshaped into (batch, 7, 7, patch_size*patch_size* depth)
# conv shape (batch, 7, 7, depth)
conv = tf.nn.conv2d(hidden, layer2_weights, [1, 2, 2, 1], padding='SAME') # convolution
hidden = tf.nn.relu(conv + layer2_biases)
# hidden shape (batch, 7, 7, depth)
shape = hidden.get_shape().as_list()
reshape = tf.reshape(hidden, [shape[0], shape[1] * shape[2] * shape[3]])
# reshape (batch, 7*7*depth)
# weights shape( 28//4 * 28//4*depth, num_hidden)
# hidden shape(batch, num_hidden)
hidden = tf.nn.relu(tf.matmul(reshape, layer3_weights) + layer3_biases)
# return tensor (batch, num_labels)
return tf.matmul(hidden, layer4_weights) + layer4_biases
# Training computation.
logits = model(tf_train_dataset)
loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(0.01).minimize(loss)
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(logits)
valid_prediction = tf.nn.softmax(model(tf_valid_dataset))
test_prediction = tf.nn.softmax(model(tf_test_dataset))num_steps = 1001
with tf.Session(graph=graph) as session:
tf.initialize_all_variables().run()
print('Initialized')
for step in range(num_steps):
offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
batch_data = train_dataset[offset:(offset + batch_size), :, :, :]
batch_labels = train_labels[offset:(offset + batch_size), :]
feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
_, l, predictions = session.run(
[optimizer, loss, train_prediction], feed_dict=feed_dict)
if (step % 50 == 0):
print('Minibatch loss at step %d: %f' % (step, l))
print('Minibatch accuracy: %.1f%%' % accuracy(predictions, batch_labels))
print('Validation accuracy: %.1f%%' % accuracy(
valid_prediction.eval(), valid_labels))
print('Test accuracy: %.1f%%' % accuracy(test_prediction.eval(), test_labels))2. 池化 pooling
2. 池化 poolingpooling会充分利用输入的信息，减少信息流失，但同样增加了计算量。
tensorflow提供了max pooling 以及 average pooling函数，计算基本类似，只不过将求最大值改为了求平均值。
nn.max_pool函数的文档如下：
Signature: tf.nn.max_pool(value, ksize, strides, padding, data_format='NHWC', name=None)Docstring:Performs the max pooling on the input.
Args: value: A 4-D Tensor with shape[batch, height, width, channels] and type tf.float32.
ksize: A list of ints that has length >= 4. The size of the window for each dimension of the input tensor.
strides: A list of ints that has length >= 4. The stride of the sliding window for each dimension of the input tensor.
padding: A string, either 'VALID' or'SAME'. The padding algorithm. See the comment here
data_format: A string. 'NHWC' and 'NCHW' are supported.
name: Optional name for the operation.
Returns: A Tensor with type tf.float32. The max pooled output tensor. Type: functionstride与conv2d中的定义一样，理解为扫描步长。它的存在，定义了，max_pool函数返回的tensor的维度。
在写卷积神经网络时，最好先定义好模型函数(如上文的model函数)，这样再在前面补充权重矩阵的维度。没有写普通神经网络那么简洁(定义权重矩阵的时候,模型就定好了)。
# 87.5%
batch_size = 128
patch_size = 5 # padding image pixels by 5*5
depth = 16 # depth
num_hidden = 64 # num of node in hidden layer
graph = tf.Graph()
with graph.as_default():
# Input data.
tf_train_dataset = tf.placeholder(tf.float32, shape=(batch_size, image_size, image_size, num_channels)) # num_channels=1 grayscale
tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
tf_valid_dataset = tf.constant(valid_dataset)
tf_test_dataset = tf.constant(test_dataset)
# Variables.
layer1_weights = tf.Variable(tf.truncated_normal([patch_size, patch_size, num_channels, depth], stddev=0.1))
layer1_biases = tf.Variable(tf.zeros([depth]))
layer2_weights = tf.Variable(tf.truncated_normal( [patch_size, patch_size, depth, depth], stddev=0.1))
layer2_biases = tf.Variable(tf.constant(1.0, shape=[depth]))
layer3_weights = tf.Variable(tf.truncated_normal([28//7 * 28//7 * depth, num_hidden], stddev=0.1))
layer3_biases = tf.Variable(tf.constant(1.0, shape=[num_hidden]))
layer4_weights = tf.Variable(tf.truncated_normal([num_hidden, num_labels], stddev=0.1))
layer4_biases = tf.Variable(tf.constant(1.0, shape=[num_labels]))
# Model.
def model(data):
# data (batch, 28, 28, 1)
# weights reshaped to (patch_size*patch_size*num_channels, depth)
# data reshaped to (batch, 14, 14, patch_size*patch_size*num_channels)
# conv shape (batch, 14, 14, depth)
conv = tf.nn.conv2d(data, layer1_weights, [1, 2, 2, 1], padding='SAME') # convolution
hidden = tf.nn.relu(conv + layer1_biases)
# weights shape (patch_size, patch_size, depth, depth)
# weights reshaped into (patch_size*patch_size* depth, depth)
# hidden reshaped into (batch, 7, 7, patch_size*patch_size* depth)
# conv shape (batch, 7, 7, depth)
conv = tf.nn.conv2d(hidden, layer2_weights, [1, 2, 2, 1], padding='SAME') # convolution
# conv shape (batch, 7, 7, depth)
#print('conv1 shape', conv.get_shape().as_list())
conv = tf.nn.max_pool(conv, [1,2,2,1], [1,2,2,1], padding='SAME') # strides change dimensions
#print('conv2 shape', conv.get_shape().as_list())
hidden = tf.nn.relu(conv + layer2_biases)
# hidden shape (batch, 4, 4, depth)
shape = hidden.get_shape().as_list()
reshape = tf.reshape(hidden, [shape[0], shape[1] * shape[2] * shape[3]])
# reshape (batch,4*4*depth)
# weights shape( 4 * 4*depth, num_hidden)
# hidden shape(batch, num_hidden)
#print('reshape shape', reshape.get_shape().as_list())
#print('layer3_weights', layer3_weights.get_shape().as_list())
hidden = tf.nn.relu(tf.matmul(reshape, layer3_weights) + layer3_biases)
# return tensor (batch, num_labels)
return tf.matmul(hidden, layer4_weights) + layer4_biases
# Training computation.
logits = model(tf_train_dataset)
loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(0.01).minimize(loss)
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(logits)
valid_prediction = tf.nn.softmax(model(tf_valid_dataset))
test_prediction = tf.nn.softmax(model(tf_test_dataset))
num_steps = 1001
with tf.Session(graph=graph) as session:
tf.initialize_all_variables().run()
print('Initialized')
for step in range(num_steps):
offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
batch_data = train_dataset[offset:(offset + batch_size), :, :, :]
batch_labels = train_labels[offset:(offset + batch_size), :]
feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
_, l, predictions = session.run(
[optimizer, loss, train_prediction], feed_dict=feed_dict)
if (step % 50 == 0):
print('Minibatch loss at step %d: %f' % (step, l))
print('Minibatch accuracy: %.1f%%' % accuracy(predictions, batch_labels))
print('Validation accuracy: %.1f%%' % accuracy(valid_prediction.eval(), valid_labels))
print('Test accuracy: %.1f%%' % accuracy(test_prediction.eval(), test_labels))这还没有普通的神经网络好。
所以神经网络的架构很重要。
如果没有好的架构，再深的神经网络也许没有简单的逻辑回归的效果好，还浪费了大量资源，真是吃力不讨好。
这里可以用学习速率衰减来提高一下测试集的准确度。准确度在，92.6%左右。
# only add learning rate decay
# 92.6%
batch_size = 128
patch_size = 5 # padding image pixels by 5*5
depth = 16 # depth
num_hidden = 64 # num of node in hidden layer
graph = tf.Graph()
with graph.as_default():
# Input data.
tf_train_dataset = tf.placeholder(tf.float32, shape=(batch_size, image_size, image_size, num_channels)) # num_channels=1 grayscale
tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
tf_valid_dataset = tf.constant(valid_dataset)
tf_test_dataset = tf.constant(test_dataset)
# Variables.
global_step = tf.Variable(0)
learning_rate = tf.train.exponential_decay(0.1, global_step, 300, 0.7)
layer1_weights = tf.Variable(tf.truncated_normal([patch_size, patch_size, num_channels, depth], stddev=0.1))
layer1_biases = tf.Variable(tf.zeros([depth]))
layer2_weights = tf.Variable(tf.truncated_normal( [patch_size, patch_size, depth, depth], stddev=0.1))
layer2_biases = tf.Variable(tf.constant(1.0, shape=[depth]))
layer3_weights = tf.Variable(tf.truncated_normal([28//7 * 28//7 * depth, num_hidden], stddev=0.1))
layer3_biases = tf.Variable(tf.constant(1.0, shape=[num_hidden]))
layer4_weights = tf.Variable(tf.truncated_normal([num_hidden, num_labels], stddev=0.1))
layer4_biases = tf.Variable(tf.constant(1.0, shape=[num_labels]))
# Model.
def model(data):
# data (batch, 28, 28, 1)
# weights reshaped to (patch_size*patch_size*num_channels, depth)
# data reshaped to (batch, 14, 14, patch_size*patch_size*num_channels)
# conv shape (batch, 14, 14, depth)
conv = tf.nn.conv2d(data, layer1_weights, [1, 2, 2, 1], padding='SAME') # convolution
hidden = tf.nn.relu(conv + layer1_biases)
# weights shape (patch_size, patch_size, depth, depth)
# weights reshaped into (patch_size*patch_size* depth, depth)
# hidden reshaped into (batch, 7, 7, patch_size*patch_size* depth)
# conv shape (batch, 7, 7, depth)
conv = tf.nn.conv2d(hidden, layer2_weights, [1, 2, 2, 1], padding='SAME') # convolution
# conv shape (batch, 7, 7, depth)
#print('conv1 shape', conv.get_shape().as_list())
conv = tf.nn.max_pool(conv, [1,2,2,1], [1,2,2,1], padding='SAME') # strides change dimensions
#print('conv2 shape', conv.get_shape().as_list())
hidden = tf.nn.relu(conv + layer2_biases)
# hidden shape (batch, 4, 4, depth)
shape = hidden.get_shape().as_list()
reshape = tf.reshape(hidden, [shape[0], shape[1] * shape[2] * shape[3]])
# reshape (batch,4*4*depth)
# weights shape( 4 * 4*depth, num_hidden)
# hidden shape(batch, num_hidden)
# print('reshape shape', reshape.get_shape().as_list())
# print('layer3_weights', layer3_weights.get_shape().as_list())
hidden = tf.nn.relu(tf.matmul(reshape, layer3_weights) + layer3_biases)
# return tensor (batch, num_labels)
return tf.matmul(hidden, layer4_weights) + layer4_biases
# Training computation.
logits = model(tf_train_dataset)
loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))
# Optimizer.
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)
# Predictions for the training, validation, and test data.
train_prediction = tf.nn.softmax(logits)
valid_prediction = tf.nn.softmax(model(tf_valid_dataset))
test_prediction = tf.nn.softmax(model(tf_test_dataset))
num_steps = 20001
with tf.Session(graph=graph) as session:
tf.initialize_all_variables().run()
print('Initialized')
for step in range(num_steps):
offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
batch_data = train_dataset[offset:(offset + batch_size), :, :, :]
batch_labels = train_labels[offset:(offset + batch_size), :]
feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
_, l, predictions = session.run(
[optimizer, loss, train_prediction], feed_dict=feed_dict)
if (step % 300 == 0):
print('current Learning rate', learning_rate.eval())
print('Minibatch loss at step %d: %f' % (step, l))
print('Minibatch accuracy: %.1f%%' % accuracy(predictions, batch_labels))
print('Validation accuracy: %.1f%%' % accuracy(valid_prediction.eval(), valid_labels))
print('Test accuracy: %.1f%%' % accuracy(test_prediction.eval(), test_labels))
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