MNIST手写字体数据集解析

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本文详细介绍了MNIST手写数字数据集的结构、获取方法及数据读取过程，展示了如何使用TensorFlow读取MNIST数据，并通过图表形式直观展示数据集中的图像和标签。此外，还探讨了数据集在机器学习领域的应用，包括使用卷积神经网络和混淆矩阵进行错误率分析。

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1 MNIST数据集

1.0 简介

按国家标准修订技术数据集(Modified National Institute of Standards and Technology database, MNIST database)是大型的手写数字数据集,用于训练多样的图像处理系统,数据集广泛应用于机器学习领域的训练和测试,数据集通过对MNIST的原始数据集进行re-mixing而来,作者认为MNIST的训练数据集是来自美国人口调查局,而测试数据集来自高中生,所以该数据集并不能完全适用于机器学习的实验.该数据集中的NIST黑白图通过归一化处理,使其匹配到 $28\times 28$ 像素的边框中,并进行反锯齿处理.
MNIST数据集包含60000张训练图片和10000张测试图片,其中一半的训练数据和一半的测试数据取自MNIST的训练数据集,另外一半来自MNIST的测试数据集.有大量的科技论文在该数据集上试图达到最低错误率,其中一篇论文使用卷积神经网络的分层系统,在MNIST数据集上错误率为0.23%.数据集作者的文章中,使用支持向量机方法的错误率为0.8%,扩展的类似MNIST数据集成为EMNIST于2017年发布,该数据集包含240000训练数据,40000测试数据.

1.2 数据获取

github函数

2 数据读取

注:为方便参数查看,定义的变量直接给出解释.

import tensorflow as tf
tf.reset_default_graph()
from tensorflow.examples.tutorials.mnist import input_data
import matplotlib.pyplot as plt
import numpy as np

mnist = input_data.read_data_sets("../mnist_data", one_hot=True)
def mnist_train_datasets():
    '''Train image datasets.
        :params train_images: train images data list
        :params train_num: number of train images 
        :params train_labels: train images label list
        :params train_num: number of train images lable
    '''
    train_images = mnist.train.images
    train_labels = mnist.train.labels
    train_data_nums = mnist.train.num_examples 
    train_images_shape = train_images.shape
    train_images_value = train_images[0]
    train_images_value_shape = train_images_value.shape
    train_images_label = train_labels[0]
    train_images_label_shape = train_images_label.shape
    print("type or image value: {}".format(type(train_images_value)))
    print("Train images numbers: {}".format(train_data_nums))
    print("Train images shape: {}".format(train_images_shape))
#     print("train images value: {}".format(train_images_value))
    print("Train images label: {}".format(train_images_label))
    print("Train images value shape: {}".format(train_images_value_shape))
    print("Train images label shape: {}".format(train_images_label_shape))
    
def mnist_test_datasets():
    '''Test image datasets.
        :params test_images: test images data list
        :params test_num: number of test images 
        :params test_labels: test images label list
        :params test_num: number of test images lable
    '''
    test_images = mnist.test.images
    test_labels = mnist.test.labels
    test_data_nums = mnist.test.num_examples
    test_images_shape = test_images.shape
    test_images_value = test_images[0]
    test_images_label = test_labels[0]
    test_images_value_shape = test_images_value.shape
    test_images_label_shape = test_images_label.shape
    print("Test data numbers: {}".format(test_data_nums))
    print("Test images shape: {}".format(test_images_shape))
#     print("Test image value: {}".format(test_images_value))
    print("Test images label: {}".format(test_images_label))
    print("Test images value shape: {}".format(test_images_value_shape))
    print("Test images label shape: {}".format(test_images_label_shape))

mnist_train_datasets()
mnist_test_datasets()

Result

Extracting ../mnist_data/train-images-idx3-ubyte.gz
Extracting ../mnist_data/train-labels-idx1-ubyte.gz
Extracting ../mnist_data/t10k-images-idx3-ubyte.gz
Extracting ../mnist_data/t10k-labels-idx1-ubyte.gz
type or image value: <class 'numpy.ndarray'>
Train images numbers: 55000
Train images shape: (55000, 784)
Train images label: [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]
Train images value shape: (784,)
Train images label shape: (10,)
Test data numbers: 10000
Test images shape: (10000, 784)
Test images label: [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]
Test images value shape: (784,)
Test images label shape: (10,)

Analysis
(1) MNIST图像数据引入:from tensorflow.examples.tutorials.mnist import input_data
(2) MNIST数据读取:mnist = input_data.read_data_sets("../mnist_data", one_hot=True)
(3) 获取训练图像数据及标签:mnist.train.images,mnist.train.labels
(4) 获取测试图像数据及标签:mnist.test.images,mnist.test.labels
(5) MNIST数据集结构:图像数据和标签均为列向量.

3 数据显示

import tensorflow as tf
tf.reset_default_graph()
from tensorflow.examples.tutorials.mnist import input_data
import matplotlib.pyplot as plt
import numpy as np

mnist = input_data.read_data_sets("../mnist_data", one_hot=True)
def mnist_train_datasets():
    '''Train image datasets.
        :params train_images: train images data list
        :params train_num: number of train images 
        :params train_labels: train images label list
        :params train_num: number of train images lable
    '''
    train_images = mnist.train.images
    train_labels = mnist.train.labels
    train_data_nums = mnist.train.num_examples 
    train_images_shape = train_images.shape
    train_images_value = train_images[0]
    print("type or image value: {}".format(type(train_images_value)))
    train_value = train_images_value.reshape((28, 28, -1))
    plt.figure()
    plt.imshow(train_value[:,:,0], cmap="Greys_r")
    plt.show()
    train_images_label = train_labels[0]
    
def mnist_test_datasets():
    '''Test image datasets.
        :params test_images: test images data list
        :params test_num: number of test images 
        :params test_labels: test images label list
        :params test_num: number of test images lable
    '''
    test_images = mnist.test.images
    test_labels = mnist.test.labels
    test_data_nums = mnist.test.num_examples
    test_images_shape = test_images.shape
    test_images_value = test_images[0]
    test_images_label = test_labels[0]
    test_value = test_images_value.reshape((28, 28, -1))
    plt.figure()
    plt.imshow(test_value[:,:,0], cmap="Greys_r")
    plt.show()

mnist_train_datasets()
mnist_test_datasets()

Result

图1.0 训练数据图像

在这里插入图片描述

图1.2 测试数据图像

Analysis
(1) 由于MNIST数据集的图像数据单通道数据即(28,28,1)，在使用matplotlib绘制图像时需要采用提取通道数据的方法绘制，即[:,:,0];
(2) MNIST数据集的图像为黑白图，所以直接绘制时会出现图1.3的情况，需要设定显示参数cmap为Greys_r获取灰度图像；

在这里插入图片描述

图1.3 变色的数字

4 混淆矩阵

from sklearn.metrics import confusion_matrix
tf.reset_default_graph()
from tensorflow.examples.tutorials.mnist import input_data
import matplotlib.pyplot as plt
import numpy as np
def _bytes_feature(value):
    return tf.train.Feature(bytes_list=tf.train.BytesList(value=[value]))
def _int64_feature(value):
    return tf.train.Feature(int64_list=tf.train.Int64List(value=[value]))
mnist = input_data.read_data_sets("../mnist_data", one_hot=True)
def mnist_train_datasets():
    '''Train image datasets.
        :params train_images: train images data list
        :params train_num: number of train images 
        :params train_labels: train images label list
        :params train_num: number of train images lable
    '''
    train_images = mnist.train.images
    train_labels = mnist.train.labels
    train_data_nums = mnist.train.num_examples 
    train_images_shape = train_images.shape
    train_images_value = train_images[0]
    print("type or image value: {}".format(type(train_images_value)))
    train_value = train_images_value.reshape((28, 28, -1))
    plt.figure()
    plt.imshow(train_value[:,:,0], cmap="Greys_r")
    plt.show()
    train_images_label = train_labels[0]
    
def mnist_test_datasets():
    '''Test image datasets.
        :params test_images: test images data list
        :params test_num: number of test images 
        :params test_labels: test images label list
        :params test_num: number of test images lable
    '''
    test_images = mnist.test.images
    test_labels = mnist.test.labels
    test_data_nums = mnist.test.num_examples
    test_images_shape = test_images.shape
    test_images_value = test_images[0]
    test_images_label = test_labels[0]
    test_value = test_images_value.reshape((28, 28, -1))
    plt.figure()
    plt.imshow(test_value[:,:,0], cmap="Greys_r")
    plt.show()
  
train_label = mnist_train_datasets()
test_label = mnist_test_datasets()
conf_mx = confusion_matrix(train_label, test_label)
plt.figure()
plt.matshow(conf_mx, cmap=plt.cm.gray)
plt.savefig("./images/cofusion_image1.png", format="png")
plt.show()

Result

图1.3 两个图像标签的混淆矩阵

5 总结

(1) MINIST数据集包含训练集和测试,图像数据存储为[784,1]的列向量,标签为[10, 1]的列向量,图像原始尺寸为(28, 28, 1);
(2) MNIST图像数据引入:from tensorflow.examples.tutorials.mnist import input_data
(3) MNIST数据读取:mnist = input_data.read_data_sets("../mnist_data", one_hot=True)
(4) 数据结构: