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[译] TensorFlow 教程 #03 - PrettyTensor

题图来自: github

本文主要介绍了PrettyTensor,用来快速构建神经网络。
当然,原文写于16年,现在有更方便的API,后续会介绍。
本文有大段前篇教程的文字及代码,如果看过上一篇的朋友可以快速翻到下文PrettyTensor实现的那一部分去。

01 - 简单线性模型 / 02 - 卷积神经网络

by Magnus Erik Hvass Pedersen / GitHub / Videos on YouTube
中文翻译 thrillerist / Github

如有转载,请附上本文链接。


介绍

之前的教程演示了如何在TensorFlow中实现一个卷积神经网络,这需要了解一些TensorFlow工作的底层原理。它有点复杂,实现起来还容易犯错。

这篇教程为我们说明了如何使用TensorFlow的一个附加包PrettyTensor,它也是Google开发的。PrettyTensor提供了在TensorFlow中创建神经网络的更简单的方法,让我们可以关注自己想要实现的想法,而不用过多担心底层的实现细节。这也让代码更短、更容易阅读和修改。

除了用PrettyTensor构造图之外,这篇教程的大部分代码和教程 #02 中的一样,当然还有一些细微的变化。

这篇教程是基于教程 #02 之上的,如果你是TensorFlow新手的话,推荐先学完上一份教程。你需要熟悉基本的线性代数、Python和Jupyter Notebook编辑器。

流程图

下面的图表直接展示了之后实现的卷积神经网络中数据的传递。关于卷积的详细描述请看上一篇教程。

from IPython.display import Image
Image('images/02_network_flowchart.png')复制代码

输入图像在第一层卷基层中用权重过滤器处理。结果在16张新图里,每个代表了卷积层里一个过滤器(的处理结果)。图像也经过降采样,因此图像分辨率从28x28减少到14x14。

这16张小图在第二个卷积层中处理。这16个通道都需要一个权重过滤,这层的输出的每个通道也各需要一个权重过滤。总共有36个输出,所以在第二个卷积层有16 x 36 = 576个滤波器。输出图再一次降采样到7x7个像素。

第二个卷积层的输出是36张7x7像素的图像。它们被压到一个长为7 x 7 x 36 = 1764的向量中去,它作为一个有128个神经元(或元素)的全连接网络的输入。这些又输入到另一个有10个神经元的全连接层中,每个神经元代表一个类别,用来确定图像的类别,也即图像上的数字。

卷积滤波一开始是随机挑选的,因此分类也是随机完成的。根据交叉熵(cross-entropy)来测量输入图预测值和真实类别间的错误。然后优化器用链式法则自动地将这个误差传在卷积网络中传递,更新滤波权重来提升分类质量。这个过程迭代了几千次,直到分类误差足够低。

这些特定的滤波权重和中间图像是一个优化的结果,和你执行这些代码所看到的可能会有所不同。

注意,这些在TensorFlow上的计算是在一部分图像上执行,而非单独的一张图,这使得计算更有效。也意味着在TensorFlow上实现时,这个流程图实际上会有更多的数据维度。

导入

%matplotlib inline
import matplotlib.pyplot as plt
import tensorflow as tf
import numpy as np
from sklearn.metrics import confusion_matrix
import time
from datetime import timedelta
import math

# We also need PrettyTensor.
import prettytensor as pt复制代码

使用Python3.5.2(Anaconda)开发,TensorFlow版本是:

tf.__version__复制代码

'0.12.0-rc0'

PrettyTensor 版本:

pt.__version__复制代码

'0.7.1'

载入数据

MNIST数据集大约12MB,如果没在给定路径中找到就会自动下载。

from tensorflow.examples.tutorials.mnist import input_data
data = input_data.read_data_sets('data/MNIST/', one_hot=True)复制代码

Extracting data/MNIST/train-images-idx3-ubyte.gz
Extracting data/MNIST/train-labels-idx1-ubyte.gz
Extracting data/MNIST/t10k-images-idx3-ubyte.gz
Extracting data/MNIST/t10k-labels-idx1-ubyte.gz

现在已经载入了MNIST数据集,它由70,000张图像和对应的标签(比如图像的类别)组成。数据集分成三份互相独立的子集。我们在教程中只用训练集和测试集。

print("Size of:")
print("- Training-set:\t\t{}".format(len(data.train.labels)))
print("- Test-set:\t\t{}".format(len(data.test.labels)))
print("- Validation-set:\t{}".format(len(data.validation.labels)))复制代码

Size of:
-Training-set: 55000
-Test-set: 10000
-Validation-set: 5000

类型标签使用One-Hot编码,这意外每个标签是长为10的向量,除了一个元素之外,其他的都为零。这个元素的索引就是类别的数字,即相应图片中画的数字。我们也需要测试数据集类别数字的整型值,用下面的方法来计算。

data.test.cls = np.argmax(data.test.labels, axis=1)复制代码

数据维度

在下面的源码中,有很多地方用到了数据维度。它们只在一个地方定义,因此我们可以在代码中使用这些数字而不是直接写数字。

# We know that MNIST images are 28 pixels in each dimension.
img_size = 28

# Images are stored in one-dimensional arrays of this length.
img_size_flat = img_size * img_size

# Tuple with height and width of images used to reshape arrays.
img_shape = (img_size, img_size)

# Number of colour channels for the images: 1 channel for gray-scale.
num_channels = 1

# Number of classes, one class for each of 10 digits.
num_classes = 10复制代码

用来绘制图片的帮助函数

这个函数用来在3x3的栅格中画9张图像,然后在每张图像下面写出真实类别和预测类别。

def plot_images(images, cls_true, cls_pred=None):
    assert len(images) == len(cls_true) == 9

    # Create figure with 3x3 sub-plots.
    fig, axes = plt.subplots(3, 3)
    fig.subplots_adjust(hspace=0.3, wspace=0.3)

    for i, ax in enumerate(axes.flat):
        # Plot image.
        ax.imshow(images[i].reshape(img_shape), cmap='binary')

        # Show true and predicted classes.
        if cls_pred is None:
            xlabel = "True: {0}".format(cls_true[i])
        else:
            xlabel = "True: {0}, Pred: {1}".format(cls_true[i], cls_pred[i])

        # Show the classes as the label on the x-axis.
        ax.set_xlabel(xlabel)

        # Remove ticks from the plot.
        ax.set_xticks([])
        ax.set_yticks([])

    # Ensure the plot is shown correctly with multiple plots
    # in a single Notebook cell.
    plt.show()复制代码

绘制几张图像来看看数据是否正确

# Get the first images from the test-set.
images = data.test.images[0:9]

# Get the true classes for those images.
cls_true = data.test.cls[0:9]

# Plot the images and labels using our helper-function above.
plot_images(images=images, cls_true=cls_true)复制代码

TensorFlow图

TensorFlow的全部目的就是使用一个称之为计算图(computational graph)的东西,它会比直接在Python中进行相同计算量要高效得多。TensorFlow比Numpy更高效,因为TensorFlow了解整个需要运行的计算图,然而Numpy只知道某个时间点上唯一的数学运算。

TensorFlow也能够自动地计算需要优化的变量的梯度,使得模型有更好的表现。这是由于图是简单数学表达式的结合,因此整个图的梯度可以用链式法则推导出来。

TensorFlow还能利用多核CPU和GPU,Google也为TensorFlow制造了称为TPUs(Tensor Processing Units)的特殊芯片,它比GPU更快。

一个TensorFlow图由下面几个部分组成,后面会详细描述:

  • 占位符变量(Placeholder)用来改变图的输入。
  • 模型变量(Model)将会被优化,使得模型表现得更好。
  • 模型本质上就是一些数学函数,它根据Placeholder和模型的输入变量来计算一些输出。
  • 一个cost度量用来指导变量的优化。
  • 一个优化策略会更新模型的变量。

另外,TensorFlow图也包含了一些调试状态,比如用TensorBoard打印log数据,本教程不涉及这些。

占位符 (Placeholder)变量

Placeholder是作为图的输入,我们每次运行图的时候都可能改变它们。将这个过程称为feeding placeholder变量,后面将会描述这个。

首先我们为输入图像定义placeholder变量。这让我们可以改变输入到TensorFlow图中的图像。这也是一个张量(tensor),代表一个多维向量或矩阵。数据类型设置为float32,形状设为[None, img_size_flat]None代表tensor可能保存着任意数量的图像,每张图象是一个长度为img_size_flat的向量。

x = tf.placeholder(tf.float32, shape=[None, img_size_flat], name='x')复制代码

卷积层希望x被编码为4维张量,因此我们需要将它的形状转换至[num_images, img_height, img_width, num_channels]。注意img_height == img_width == img_size,如果第一维的大小设为-1,num_images的大小也会被自动推导出来。转换运算如下:

x_image = tf.reshape(x, [-1, img_size, img_size, num_channels])复制代码

接下来我们为输入变量x中的图像所对应的真实标签定义placeholder变量。变量的形状是[None, num_classes],这代表着它保存了任意数量的标签,每个标签是长度为num_classes的向量,本例中长度为10。

y_true = tf.placeholder(tf.float32, shape=[None, 10], name='y_true')复制代码

我们也可以为class-number提供一个placeholder,但这里用argmax来计算它。这里只是TensorFlow中的一些操作,没有执行什么运算。

y_true_cls = tf.argmax(y_true, dimension=1)复制代码

TensorFlow 实现

这一节显示了教程 #02 中直接用TensorFlow实现卷积神经网络的源代码。这份Notebook中并没有直接用到这些代码,只是为了方便和下面PrettyTensor的实现进行比较。

这里要注意的是有多少代码量以及TensorFlow保存数据、进行运算的底层细节。即使在很小的神经网络中也容易犯错。

帮助函数

在直接用TensorFlow实现时,我们创建一些在构造图时常用到的帮助函数。

这两个函数在TensorFlow图中创建新的变量并用随机值初始化。

def new_weights(shape):
    return tf.Variable(tf.truncated_normal(shape, stddev=0.05))复制代码
def new_biases(length):
    return tf.Variable(tf.constant(0.05, shape=[length]))复制代码

下面的帮助函数创建一个新的卷积网络。输入和输出是4维的张量(4-rank tensors)。注意TensorFlow API的底层细节,比如权重变量的大小。这里很容易犯错,可能会导致奇怪的错误信息,并且很难调试。

def new_conv_layer(input,              # The previous layer.
                   num_input_channels, # Num. channels in prev. layer.
                   filter_size,        # Width and height of filters.
                   num_filters,        # Number of filters.
                   use_pooling=True):  # Use 2x2 max-pooling.

    # Shape of the filter-weights for the convolution.
    # This format is determined by the TensorFlow API.
    shape = [filter_size, filter_size, num_input_channels, num_filters]

    # Create new weights aka. filters with the given shape.
    weights = new_weights(shape=shape)

    # Create new biases, one for each filter.
    biases = new_biases(length=num_filters)

    # Create the TensorFlow operation for convolution.
    # Note the strides are set to 1 in all dimensions.
    # The first and last stride must always be 1,
    # because the first is for the image-number and
    # the last is for the input-channel.
    # But e.g. strides=[1, 2, 2, 1] would mean that the filter
    # is moved 2 pixels across the x- and y-axis of the image.
    # The padding is set to 'SAME' which means the input image
    # is padded with zeroes so the size of the output is the same.
    layer = tf.nn.conv2d(input=input,
                         filter=weights,
                         strides=[1, 1, 1, 1],
                         padding='SAME')

    # Add the biases to the results of the convolution.
    # A bias-value is added to each filter-channel.
    layer += biases

    # Use pooling to down-sample the image resolution?
    if use_pooling:
        # This is 2x2 max-pooling, which means that we
        # consider 2x2 windows and select the largest value
        # in each window. Then we move 2 pixels to the next window.
        layer = tf.nn.max_pool(value=layer,
                               ksize=[1, 2, 2, 1],
                               strides=[1, 2, 2, 1],
                               padding='SAME')

    # Rectified Linear Unit (ReLU).
    # It calculates max(x, 0) for each input pixel x.
    # This adds some non-linearity to the formula and allows us
    # to learn more complicated functions.
    layer = tf.nn.relu(layer)

    # Note that ReLU is normally executed before the pooling,
    # but since relu(max_pool(x)) == max_pool(relu(x)) we can
    # save 75% of the relu-operations by max-pooling first.

    # We return both the resulting layer and the filter-weights
    # because we will plot the weights later.
    return layer, weights复制代码

下面的帮助函数将一个4维张量转换到2维,因此我们可以在卷积层之后添加一个全连接层。

def flatten_layer(layer):
    # Get the shape of the input layer.
    layer_shape = layer.get_shape()

    # The shape of the input layer is assumed to be:
    # layer_shape == [num_images, img_height, img_width, num_channels]

    # The number of features is: img_height * img_width * num_channels
    # We can use a function from TensorFlow to calculate this.
    num_features = layer_shape[1:4].num_elements()

    # Reshape the layer to [num_images, num_features].
    # Note that we just set the size of the second dimension
    # to num_features and the size of the first dimension to -1
    # which means the size in that dimension is calculated
    # so the total size of the tensor is unchanged from the reshaping.
    layer_flat = tf.reshape(layer, [-1, num_features])

    # The shape of the flattened layer is now:
    # [num_images, img_height * img_width * num_channels]

    # Return both the flattened layer and the number of features.
    return layer_flat, num_features复制代码

接下来的帮助函数创建一个全连接层。

def new_fc_layer(input,          # The previous layer.
                 num_inputs,     # Num. inputs from prev. layer.
                 num_outputs,    # Num. outputs.
                 use_relu=True): # Use Rectified Linear Unit (ReLU)?

    # Create new weights and biases.
    weights = new_weights(shape=[num_inputs, num_outputs])
    biases = new_biases(length=num_outputs)

    # Calculate the layer as the matrix multiplication of
    # the input and weights, and then add the bias-values.
    layer = tf.matmul(input, weights) + biases

    # Use ReLU?
    if use_relu:
        layer = tf.nn.relu(layer)

    return layer复制代码

构造图(Graph)

现在将会用上面的帮助函数来创建卷积神经网络。如果没有这些函数的话,代码将会又长又难以理解。

注意,我们并不会运行下面的代码。写在这里只是为了与PrettyTensor的代码进行比较。

之前的教程使用定义好的常量,因此很容易改变(变量)。比如,我们没有将 filter_size=5 当作 new_conv_layer()的参数,而是令filter_size=filter_size1,然后在其他地方定义filter_size1=5。这样子就很容易改变所有的常量。

if False:  # Don't execute this! Just show it for easy comparison.
    # First convolutional layer.
    layer_conv1, weights_conv1 = \
        new_conv_layer(input=x_image,
                       num_input_channels=num_channels,
                       filter_size=5,
                       num_filters=16,
                       use_pooling=True)

    # Second convolutional layer.
    layer_conv2, weights_conv2 = \
        new_conv_layer(input=layer_conv1,
                       num_input_channels=16,
                       filter_size=5,
                       num_filters=36,
                       use_pooling=True)

    # Flatten layer.
    layer_flat, num_features = flatten_layer(layer_conv2)

    # First fully-connected layer.
    layer_fc1 = new_fc_layer(input=layer_flat,
                             num_inputs=num_features,
                             num_outputs=128,
                             use_relu=True)

    # Second fully-connected layer.
    layer_fc2 = new_fc_layer(input=layer_fc1,
                             num_inputs=128,
                             num_outputs=num_classes,
                             use_relu=False)

    # Predicted class-label.
    y_pred = tf.nn.softmax(layer_fc2)

    # Cross-entropy for the classification of each image.
    cross_entropy = \
        tf.nn.softmax_cross_entropy_with_logits(logits=layer_fc2,
                                                labels=y_true)

    # Loss aka. cost-measure.
    # This is the scalar value that must be minimized.
    loss = tf.reduce_mean(cross_entropy)复制代码

PrettyTensor实现

这一节演示如何用PrettyTensor来实现一个相同的卷积神经网络。

基本思想就是用一个PrettyTensor object封装输入张量x_image,它有一个添加新卷积层的帮助函数,以此来创建整个神经网络。这有点像我们之前实现的那些帮助函数,但它更简单一些,因为PrettyTensor记录每一层的输入和输出维度等等。

x_pretty = pt.wrap(x_image)复制代码

现在我们已经将输入图像装到一个PrettyTensor的object中,再用几行代码就可以添加卷积层和全连接层。

注意,在with代码块中,pt.defaults_scope(activation_fn=tf.nn.relu)activation_fn=tf.nn.relu当作每个的层参数,因此这些层都用到了 Rectified Linear Units (ReLU) 。defaults_scope使我们能更方便地修改所有层的参数。

with pt.defaults_scope(activation_fn=tf.nn.relu):
    y_pred, loss = x_pretty.\
        conv2d(kernel=5, depth=16, name='layer_conv1').\
        max_pool(kernel=2, stride=2).\
        conv2d(kernel=5, depth=36, name='layer_conv2').\
        max_pool(kernel=2, stride=2).\
        flatten().\
        fully_connected(size=128, name='layer_fc1').\
        softmax_classifier(num_classes=num_classes, labels=y_true)复制代码

就是这样!现在我们用几行代码就创建了一个完全一样的卷积神经网络,如果直接用TensorFlow实现的话需要一大段非常复杂的代码。

用PrettyTensor来代替TensorFlow,我们可以清楚地看到网络的构造以及数据如何在网络中流通。这让我们可以专注于神经网络的关键思想而不是底层的实现细节。它十分简单优雅!

获取权重

不幸的是,使用PrettyTensor时并非所有的事都那么优雅。

下面,我们想要绘制出卷积层的权重。在用TensorFlow实现时,我们自己创建了变量,所以可以直接访问它们。但使用PrettyTensor构造网络时,所有的变量都是间接地由PrettyTensor创建。因此我们不得不从TensorFlow中找回变量。

我们用layer_conv1layer_conv2代表两个卷积层。这也叫变量作用域(不要与上面描述的defaults_scope混淆了)。PrettyTensor会自动给它为每个层创建的变量命名,因此我们可以通过层的作用域名称和变量名来取得某一层的权重。

函数实现有点笨拙,因为我们不得不用TensorFlow函数get_variable(),它是设计给其他用途的,创建新的变量或重用现有变量。创建下面的帮助函数很简单。

def get_weights_variable(layer_name):
    # Retrieve an existing variable named 'weights' in the scope
    # with the given layer_name.
    # This is awkward because the TensorFlow function was
    # really intended for another purpose.

    with tf.variable_scope(layer_name, reuse=True):
        variable = tf.get_variable('weights')

    return variable复制代码

借助这个帮助函数我们可以获取变量。这些是TensorFlow的objects。你需要类似的操作来获取变量的内容: contents = session.run(weights_conv1) ,下面会提到这个。

weights_conv1 = get_weights_variable(layer_name='layer_conv1')
weights_conv2 = get_weights_variable(layer_name='layer_conv2')复制代码

优化方法

PrettyTensor给我们提供了预测类型标签(y_pred)以及一个需要最小化的损失度量,用来提升神经网络分类图片的能力。

PrettyTensor的文档并没有说明它的损失度量是用cross-entropy还是其他的。但现在我们用AdamOptimizer来最小化损失。

优化过程并不是在这里执行。实际上,还没计算任何东西,我们只是往TensorFlow图中添加了优化器,以便后续操作。

optimizer = tf.train.AdamOptimizer(learning_rate=1e-4).minimize(loss)复制代码

性能度量

我们需要另外一些性能度量,来向用户展示这个过程。

首先我们从神经网络输出的y_pred中计算出预测的类别,它是一个包含10个元素的向量。类别数字是最大元素的索引。

y_pred_cls = tf.argmax(y_pred, dimension=1)复制代码

然后创建一个布尔向量,用来告诉我们每张图片的真实类别是否与预测类别相同。

correct_prediction = tf.equal(y_pred_cls, y_true_cls)复制代码

上面的计算先将布尔值向量类型转换成浮点型向量,这样子False就变成0,True变成1,然后计算这些值的平均数,以此来计算分类的准确度。

accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))复制代码

运行TensorFlow

创建TensorFlow会话(session)

一旦创建了TensorFlow图,我们需要创建一个TensorFlow会话,用来运行图。

session = tf.Session()复制代码

初始化变量

我们需要在开始优化weightsbiases变量之前对它们进行初始化。

session.run(tf.global_variables_initializer())复制代码

用来优化迭代的帮助函数

在训练集中有50,000张图。用这些图像计算模型的梯度会花很多时间。因此我们利用随机梯度下降的方法,它在优化器的每次迭代里只用到了一小部分的图像。
如果内存耗尽导致电脑死机或变得很慢,你应该试着减少这些数量,但同时可能还需要更优化的迭代。

train_batch_size = 64复制代码

函数执行了多次的优化迭代来逐步地提升网络层的变量。在每次迭代中,从训练集中选择一批新的数据,然后TensorFlow用这些训练样本来执行优化器。每100次迭代会打印出相关信息。

# Counter for total number of iterations performed so far.
total_iterations = 0

def optimize(num_iterations):
    # Ensure we update the global variable rather than a local copy.
    global total_iterations

    # Start-time used for printing time-usage below.
    start_time = time.time()

    for i in range(total_iterations,
                   total_iterations + num_iterations):

        # Get a batch of training examples.
        # x_batch now holds a batch of images and
        # y_true_batch are the true labels for those images.
        x_batch, y_true_batch = data.train.next_batch(train_batch_size)

        # Put the batch into a dict with the proper names
        # for placeholder variables in the TensorFlow graph.
        feed_dict_train = {x: x_batch,
                           y_true: y_true_batch}

        # Run the optimizer using this batch of training data.
        # TensorFlow assigns the variables in feed_dict_train
        # to the placeholder variables and then runs the optimizer.
        session.run(optimizer, feed_dict=feed_dict_train)

        # Print status every 100 iterations.
        if i % 100 == 0:
            # Calculate the accuracy on the training-set.
            acc = session.run(accuracy, feed_dict=feed_dict_train)

            # Message for printing.
            msg = "Optimization Iteration: {0:>6}, Training Accuracy: {1:>6.1%}"

            # Print it.
            print(msg.format(i + 1, acc))

    # Update the total number of iterations performed.
    total_iterations += num_iterations

    # Ending time.
    end_time = time.time()

    # Difference between start and end-times.
    time_dif = end_time - start_time

    # Print the time-usage.
    print("Time usage: " + str(timedelta(seconds=int(round(time_dif)))))复制代码

用来绘制错误样本的帮助函数

函数用来绘制测试集中被误分类的样本。

def plot_example_errors(cls_pred, correct):
    # This function is called from print_test_accuracy() below.

    # cls_pred is an array of the predicted class-number for
    # all images in the test-set.

    # correct is a boolean array whether the predicted class
    # is equal to the true class for each image in the test-set.

    # Negate the boolean array.
    incorrect = (correct == False)

    # Get the images from the test-set that have been
    # incorrectly classified.
    images = data.test.images[incorrect]

    # Get the predicted classes for those images.
    cls_pred = cls_pred[incorrect]

    # Get the true classes for those images.
    cls_true = data.test.cls[incorrect]

    # Plot the first 9 images.
    plot_images(images=images[0:9],
                cls_true=cls_true[0:9],
                cls_pred=cls_pred[0:9])复制代码

绘制混淆(confusion)矩阵的帮助函数

def plot_confusion_matrix(cls_pred):
    # This is called from print_test_accuracy() below.

    # cls_pred is an array of the predicted class-number for
    # all images in the test-set.

    # Get the true classifications for the test-set.
    cls_true = data.test.cls

    # Get the confusion matrix using sklearn.
    cm = confusion_matrix(y_true=cls_true,
                          y_pred=cls_pred)

    # Print the confusion matrix as text.
    print(cm)

    # Plot the confusion matrix as an image.
    plt.matshow(cm)

    # Make various adjustments to the plot.
    plt.colorbar()
    tick_marks = np.arange(num_classes)
    plt.xticks(tick_marks, range(num_classes))
    plt.yticks(tick_marks, range(num_classes))
    plt.xlabel('Predicted')
    plt.ylabel('True')

    # Ensure the plot is shown correctly with multiple plots
    # in a single Notebook cell.
    plt.show()复制代码

展示性能的帮助函数

函数用来打印测试集上的分类准确度。

为测试集上的所有图片计算分类会花费一段时间,因此我们直接用这个函数来调用上面的结果,这样就不用每次都重新计算了。

这个函数可能会占用很多电脑内存,这也是为什么将测试集分成更小的几个部分。如果你的电脑内存比较小或死机了,就要试着降低batch-size。

# Split the test-set into smaller batches of this size.
test_batch_size = 256

def print_test_accuracy(show_example_errors=False,
                        show_confusion_matrix=False):

    # Number of images in the test-set.
    num_test = len(data.test.images)

    # Allocate an array for the predicted classes which
    # will be calculated in batches and filled into this array.
    cls_pred = np.zeros(shape=num_test, dtype=np.int)

    # Now calculate the predicted classes for the batches.
    # We will just iterate through all the batches.
    # There might be a more clever and Pythonic way of doing this.

    # The starting index for the next batch is denoted i.
    i = 0

    while i < num_test:
        # The ending index for the next batch is denoted j.
        j = min(i + test_batch_size, num_test)

        # Get the images from the test-set between index i and j.
        images = data.test.images[i:j, :]

        # Get the associated labels.
        labels = data.test.labels[i:j, :]

        # Create a feed-dict with these images and labels.
        feed_dict = {x: images,
                     y_true: labels}

        # Calculate the predicted class using TensorFlow.
        cls_pred[i:j] = session.run(y_pred_cls, feed_dict=feed_dict)

        # Set the start-index for the next batch to the
        # end-index of the current batch.
        i = j

    # Convenience variable for the true class-numbers of the test-set.
    cls_true = data.test.cls

    # Create a boolean array whether each image is correctly classified.
    correct = (cls_true == cls_pred)

    # Calculate the number of correctly classified images.
    # When summing a boolean array, False means 0 and True means 1.
    correct_sum = correct.sum()

    # Classification accuracy is the number of correctly classified
    # images divided by the total number of images in the test-set.
    acc = float(correct_sum) / num_test

    # Print the accuracy.
    msg = "Accuracy on Test-Set: {0:.1%} ({1} / {2})"
    print(msg.format(acc, correct_sum, num_test))

    # Plot some examples of mis-classifications, if desired.
    if show_example_errors:
        print("Example errors:")
        plot_example_errors(cls_pred=cls_pred, correct=correct)

    # Plot the confusion matrix, if desired.
    if show_confusion_matrix:
        print("Confusion Matrix:")
        plot_confusion_matrix(cls_pred=cls_pred)复制代码

优化之前的性能

测试集上的准确度很低,这是由于模型只做了初始化,并没做任何优化,所以它只是对图像做随机分类。

print_test_accuracy()复制代码
Accuracy on Test-Set: 9.1% (909 / 10000)复制代码

1次迭代后的性能

做了一次优化后,此时优化器的学习率很低,性能其实并没有多大提升。

optimize(num_iterations=1)复制代码

Optimization Iteration: 1, Training Accuracy: 6.2%
Time usage: 0:00:00

print_test_accuracy()复制代码

Accuracy on Test-Set: 8.9% (892 / 10000)

100次迭代优化后的性能

100次优化迭代之后,模型显著地提升了分类的准确度。

optimize(num_iterations=99) # We already performed 1 iteration above.复制代码

Time usage: 0:00:00

print_test_accuracy(show_example_errors=True)复制代码

Accuracy on Test-Set: 83.9% (8393 / 10000)
Example errors:

1000次优化迭代后的性能

1000次优化迭代之后,模型在测试集上的准确度超过了90%。

optimize(num_iterations=900) # We performed 100 iterations above.复制代码

Optimization Iteration: 101, Training Accuracy: 93.8%
Optimization Iteration: 201, Training Accuracy: 89.1%
Optimization Iteration: 301, Training Accuracy: 85.9%
Optimization Iteration: 401, Training Accuracy: 87.5%
Optimization Iteration: 501, Training Accuracy: 92.2%
Optimization Iteration: 601, Training Accuracy: 95.3%
Optimization Iteration: 701, Training Accuracy: 95.3%
Optimization Iteration: 801, Training Accuracy: 90.6%
Optimization Iteration: 901, Training Accuracy: 98.4%
Time usage: 0:00:03

print_test_accuracy(show_example_errors=True)复制代码

Accuracy on Test-Set: 96.3% (9634 / 10000)
Example errors:

10,000次优化迭代后的性能

经过10,000次优化迭代后,测试集上的分类准确率高达99%。

optimize(num_iterations=9000) # We performed 1000 iterations above.复制代码

Optimization Iteration: 1001, Training Accuracy: 98.4%
Optimization Iteration: 1101, Training Accuracy: 95.3%
Optimization Iteration: 1201, Training Accuracy: 98.4%
Optimization Iteration: 1301, Training Accuracy: 96.9%
Optimization Iteration: 1401, Training Accuracy: 100.0%
Optimization Iteration: 1501, Training Accuracy: 95.3%
Optimization Iteration: 1601, Training Accuracy: 96.9%
Optimization Iteration: 1701, Training Accuracy: 96.9%
Optimization Iteration: 1801, Training Accuracy: 98.4%
Optimization Iteration: 1901, Training Accuracy: 96.9%
Optimization Iteration: 2001, Training Accuracy: 98.4%
Optimization Iteration: 2101, Training Accuracy: 95.3%
Optimization Iteration: 2201, Training Accuracy: 98.4%
Optimization Iteration: 2301, Training Accuracy: 98.4%
Optimization Iteration: 2401, Training Accuracy: 98.4%
Optimization Iteration: 2501, Training Accuracy: 93.8%
Optimization Iteration: 2601, Training Accuracy: 98.4%
Optimization Iteration: 2701, Training Accuracy: 98.4%
Optimization Iteration: 2801, Training Accuracy: 95.3%
Optimization Iteration: 2901, Training Accuracy: 98.4%
Optimization Iteration: 3001, Training Accuracy: 98.4%
Optimization Iteration: 3101, Training Accuracy: 100.0%
Optimization Iteration: 3201, Training Accuracy: 96.9%
Optimization Iteration: 3301, Training Accuracy: 100.0%
Optimization Iteration: 3401, Training Accuracy: 98.4%
Optimization Iteration: 3501, Training Accuracy: 96.9%
Optimization Iteration: 3601, Training Accuracy: 98.4%
Optimization Iteration: 3701, Training Accuracy: 96.9%
Optimization Iteration: 3801, Training Accuracy: 100.0%
Optimization Iteration: 3901, Training Accuracy: 98.4%
Optimization Iteration: 4001, Training Accuracy: 96.9%
Optimization Iteration: 4101, Training Accuracy: 98.4%
Optimization Iteration: 4201, Training Accuracy: 100.0%
Optimization Iteration: 4301, Training Accuracy: 100.0%
Optimization Iteration: 4401, Training Accuracy: 100.0%
Optimization Iteration: 4501, Training Accuracy: 100.0%
Optimization Iteration: 4601, Training Accuracy: 98.4%
Optimization Iteration: 4701, Training Accuracy: 96.9%
Optimization Iteration: 4801, Training Accuracy: 95.3%
Optimization Iteration: 4901, Training Accuracy: 100.0%
Optimization Iteration: 5001, Training Accuracy: 96.9%
Optimization Iteration: 5101, Training Accuracy: 100.0%
Optimization Iteration: 5201, Training Accuracy: 98.4%
Optimization Iteration: 5301, Training Accuracy: 98.4%
Optimization Iteration: 5401, Training Accuracy: 100.0%
Optimization Iteration: 5501, Training Accuracy: 98.4%
Optimization Iteration: 5601, Training Accuracy: 96.9%
Optimization Iteration: 5701, Training Accuracy: 100.0%
Optimization Iteration: 5801, Training Accuracy: 96.9%
Optimization Iteration: 5901, Training Accuracy: 100.0%
Optimization Iteration: 6001, Training Accuracy: 98.4%
Optimization Iteration: 6101, Training Accuracy: 98.4%
Optimization Iteration: 6201, Training Accuracy: 98.4%
Optimization Iteration: 6301, Training Accuracy: 98.4%
Optimization Iteration: 6401, Training Accuracy: 100.0%
Optimization Iteration: 6501, Training Accuracy: 100.0%
Optimization Iteration: 6601, Training Accuracy: 100.0%
Optimization Iteration: 6701, Training Accuracy: 100.0%
Optimization Iteration: 6801, Training Accuracy: 96.9%
Optimization Iteration: 6901, Training Accuracy: 100.0%
Optimization Iteration: 7001, Training Accuracy: 100.0%
Optimization Iteration: 7101, Training Accuracy: 100.0%
Optimization Iteration: 7201, Training Accuracy: 100.0%
Optimization Iteration: 7301, Training Accuracy: 96.9%
Optimization Iteration: 7401, Training Accuracy: 100.0%
Optimization Iteration: 7501, Training Accuracy: 100.0%
Optimization Iteration: 7601, Training Accuracy: 96.9%
Optimization Iteration: 7701, Training Accuracy: 100.0%
Optimization Iteration: 7801, Training Accuracy: 100.0%
Optimization Iteration: 7901, Training Accuracy: 100.0%
Optimization Iteration: 8001, Training Accuracy: 98.4%
Optimization Iteration: 8101, Training Accuracy: 100.0%
Optimization Iteration: 8201, Training Accuracy: 100.0%
Optimization Iteration: 8301, Training Accuracy: 100.0%
Optimization Iteration: 8401, Training Accuracy: 100.0%
Optimization Iteration: 8501, Training Accuracy: 98.4%
Optimization Iteration: 8601, Training Accuracy: 100.0%
Optimization Iteration: 8701, Training Accuracy: 100.0%
Optimization Iteration: 8801, Training Accuracy: 100.0%
Optimization Iteration: 8901, Training Accuracy: 100.0%
Optimization Iteration: 9001, Training Accuracy: 98.4%
Optimization Iteration: 9101, Training Accuracy: 98.4%
Optimization Iteration: 9201, Training Accuracy: 100.0%
Optimization Iteration: 9301, Training Accuracy: 100.0%
Optimization Iteration: 9401, Training Accuracy: 98.4%
Optimization Iteration: 9501, Training Accuracy: 100.0%
Optimization Iteration: 9601, Training Accuracy: 100.0%
Optimization Iteration: 9701, Training Accuracy: 100.0%
Optimization Iteration: 9801, Training Accuracy: 98.4%
Optimization Iteration: 9901, Training Accuracy: 100.0%
Time usage: 0:00:27

print_test_accuracy(show_example_errors=True,
                    show_confusion_matrix=True)复制代码

Accuracy on Test-Set: 98.8% (9881 / 10000)
Example errors:

Confusion Matrix:
[[ 975 0 0 0 0 0 1 1 3 0]
[ 0 1127 2 0 0 0 1 2 3 0]
[ 2 2 1019 1 1 0 1 2 4 0]
[ 0 0 0 1005 0 1 0 1 3 0]
[ 0 0 0 0 977 0 1 0 1 3]
[ 2 0 0 13 0 870 1 0 6 0]
[ 5 2 0 0 1 3 943 0 4 0]
[ 0 2 8 2 1 0 0 1007 1 7]
[ 2 0 2 3 1 1 0 0 964 1]
[ 0 2 0 4 5 1 0 1 2 994]]

权重和层的可视化

当我们直接用TensorFlow来实现卷积神经网络时,可以很容易地画出卷积权重和不同层的输出图像。当使用PrettyTensor的时候,我们也可以通过上面提到过的方法取得权重,但我们无法简单得到卷积层的输出(图像)。因此下面只绘制了权重。

绘制卷积权重的帮助函数

def plot_conv_weights(weights, input_channel=0):
    # Assume weights are TensorFlow ops for 4-dim variables
    # e.g. weights_conv1 or weights_conv2.

    # Retrieve the values of the weight-variables from TensorFlow.
    # A feed-dict is not necessary because nothing is calculated.
    w = session.run(weights)

    # Get the lowest and highest values for the weights.
    # This is used to correct the colour intensity across
    # the images so they can be compared with each other.
    w_min = np.min(w)
    w_max = np.max(w)

    # Number of filters used in the conv. layer.
    num_filters = w.shape[3]

    # Number of grids to plot.
    # Rounded-up, square-root of the number of filters.
    num_grids = math.ceil(math.sqrt(num_filters))

    # Create figure with a grid of sub-plots.
    fig, axes = plt.subplots(num_grids, num_grids)

    # Plot all the filter-weights.
    for i, ax in enumerate(axes.flat):
        # Only plot the valid filter-weights.
        if i<num_filters:
            # Get the weights for the i'th filter of the input channel.
            # See new_conv_layer() for details on the format
            # of this 4-dim tensor.
            img = w[:, :, input_channel, i]

            # Plot image.
            ax.imshow(img, vmin=w_min, vmax=w_max,
                      interpolation='nearest', cmap='seismic')

        # Remove ticks from the plot.
        ax.set_xticks([])
        ax.set_yticks([])

    # Ensure the plot is shown correctly with multiple plots
    # in a single Notebook cell.
    plt.show()复制代码

卷积层 1

现在绘制第一个卷积层的滤波权重。

其中正值权重是红色的,负值为蓝色。

plot_conv_weights(weights=weights_conv1)复制代码

卷积层 2

现在绘制第二个卷积层的滤波权重。

第一个卷积层有16个输出通道,代表着第二个卷基层有16个输入。第二个卷积层的每个输入通道也有一些权重滤波。我们先绘制第一个通道的权重滤波。

同样的,正值是红色,负值是蓝色。

plot_conv_weights(weights=weights_conv2, input_channel=0)复制代码

第二个卷积层共有16个输入通道,我们可以同样地画出15张其他滤波权重图像。这里我们再画一下第二个通道的图像。

plot_conv_weights(weights=weights_conv2, input_channel=1)复制代码

关闭TensorFlow会话

现在我们已经用TensorFlow完成了任务,关闭session,释放资源。

# This has been commented out in case you want to modify and experiment
# with the Notebook without having to restart it.
# session.close()复制代码

总结

相比直接使用TensorFlow,PrettyTensor可以用更简单的代码来实现神经网络。这使你能够专注于自己的想法而不是底层的实现细节。它让代码更易于理解,也减少犯错的可能。

然而,PrettyTensor中有一些矛盾和笨拙的设计,它的文档简短而又令人疑惑,也不易于学习。希望未来会有所改进(本文写于2016七月)。

还有一些PrettyTensor的替代品,包括TFLearnKeras

练习

下面使一些可能会让你提升TensorFlow技能的一些建议练习。为了学习如何更合适地使用TensorFlow,实践经验是很重要的。

在你对这个Notebook进行修改之前,可能需要先备份一下。

  • 将所有层的激活函数改成sigmod。
  • 在一些层中使用sigmod,一些层中使用relu。这里能用defaults_scope吗?
  • 在所有层里使用12loss。然后试着只在某些层里使用这个。
  • 用PrettyTensor的reshape函数代替TensorFlow的。其中某一个会更好吗?
  • 在全连接层后面添加一个dropout-layer。如果你在训练和测试的时候想要一个不同的keep_prob,就需要在feed-dict中设置一个placeholder变量。
  • 用stride=2来代替 2x2 max-pooling层。分类准确率会有所不同么?你多次优化它们之后呢?差异是随机的,你如何度量是否真实存在差异呢?在卷积层中使用max-pooling和stride的优缺点是什么?
  • 改变层的参数,比如kernel、depth、size等等。耗费的时间以及分类准确率有什么差别?
  • 添加或删除某些卷积层和全连接层。
  • 你设计的表现良好的最简网络是什么?
  • 取回卷积层的bias-values并打印出来。参考一下get_weights_variable()的实现。
  • 不看源码,自己重写程序。
  • 向朋友解释程序如何工作。