论文总字数：24503字

摘 要

深度自编码器构成了深度学习的“构建基块”，其通过重构原始输入来进行特征学习，以实现降维的目的。随着信息时代的到来，对于信息处理的要求越来越高，随着维度的增加信息处理的成本呈指数型上升，对数据进行降维有利于处理高维海量的大数据。近年来，深度自编码器在计算机视觉、语音识别、自然语言处理等领域均得到广泛应用。本文专注于研究深度自编码器的降维能力，并在MNIST数据集上进行实验探讨其降维性能。

本文在MNIST数据集上利用深度自编码器进行数据特征降维算法的测试。具体研究内容如下：

第一，深度自编码器作为无监督学习方式，通过逐步调整节点之间连接的权值与偏差，达到信息处理、模拟输入输出之间关系的目的。在深度自编码器训练的微调阶段，本文采用梯度下降法以及误差反向传播算法进行权值与偏差的迭代更新。实验结果表明，随着迭代次数的加深，深度自编器的权值与偏差逐渐逼近收敛，逐渐减小的重构误差使得数据降维性能越来越好。

第二，隐藏层的层数决定了深度自编码器的深度，在合理设置范围内层数越多越能学习到更为复杂的数据特征。在隐藏层层数不变的情况下，本文通过修改隐藏层节点的数量研究深度自编码器的性能变化。实验结表明，隐藏层节点设置越多，重构误差越小，数据降维性能越好。

第三，主成分分析法作为线性降维的代表，被广泛应用于数据特征降维。本文分别使用主成分分析法与深度自编码器对MNIST手写字符集进行数据特征降维，实验结果表明深度自编码器的降维能力优于主成分分析法。

关键词：手写字识别，深度学习，深度自编码器，数据特征降维

Data Feature Reduction Algorithm Test Based on Deep Auto-Encoder

Abstract

The deep auto-encoder constitutes the ‘building block’ of deep learning, which carries out feature learning by reconstructing the original input, so as to achieve the goal of dimensionality reduction. With the advent of the information age, the requirements for information processing are getting higher and higher. The cost of information processing increases exponentially with the increase of dimensions. The dimensionality reduction of data is conducive to the processing of massive big data with high dimensions. In recent years, deep auto-encoders have been widely used in computer vision, speech recognition, natural language processing and other fields. This paper focuses on the research of the dimensionality reduction ability of the deep encoder, and performs experiments based on the MNIST data set in order to discuss the performance of dimensionality reduction.

In this paper, the deep auto-encoder is used to test the data feature dimensionality reduction algorithm based on MNIST data set. The specific research contents are discussed as follows:

First, as an unsupervised learning method, the deep auto-encoder achieves the purpose of processing information and simulating the relationship between input and output by gradually adjusting the weight and deviation of the connection between nodes. In the fine-tuning phase of deep self-encoder training, the gradient descent method and error back propagation algorithm are used to update the weights and deviations iteratively. The experimental results show that, the weight value and deviation of the deep auto-encoder gradually approach convergence with the deepening of the iteration times, and the gradually reduced reconstruction error makes the performance of data dimensionality reduction better and better.

Second, the number of hidden layers determines the depth of the deep auto-encoder. The more layers are within the reasonable setting range, the more features of complex data can be learned. In this paper, the performance of the deep auto-encoder is studied by modifying the number of hidden layer nodes when the number of hidden layer remains unchanged. The experimental results show that the more nodes in the hidden layer are set, the smaller the reconstruction error is and the better the performance of data dimensionality reduction is.

Third, as the representative of linear dimensionality reduces, the principal component analysis is widely used in data dimensionality reduction. In this paper, the principal component analysis and the deep auto-encoder were used to conduct data dimensionality reduction for the MNIST handwritten character set. The experimental results showed that the deep auto-encoder was superior to the principal component analysis in dimensionality reduction.

Key words: handwritten word recognition, deep learning, deep auto-encoder, dimensionality reduction

目录

摘要 I

第一章 绪论 1

1.1 课题研究的背景 1

1.2 深度自编码器的研究现状 2

1.3 课题研究内容 3

1.4 论文组织结构 4

第二章 深度自编码器概述 5

2.1 引言 5

2.2人工神经网络 5

2.2.1 MP神经元模型 5

2.2.2 感知器模型 5

2.2.3 误差反向传播 6

2.3 自编码器 9

2.4 深度自编码器 10

2.5 Softmax分类器 11

2.6 MNIST数据集简介 12

2.7 本章小结 13

第三章 基于深度自编码器的数据特征降维算法测试 14

3.1 前言 14

3.2 MNIST数据集 14

3.3 基于深度自编码器的数据特征降维算法 15

3.3.1 深度自编码器的训练 15

3.4 仿真实验及结果分析 17

3.4.1 MNIST数据特征降维 17

3.4.2 MNIST识别 21

3.5 本章小结 22

第四章 总结与展望 23

4.1 本文工作总结 23

4.2 未来工作展望 23

参考文献 24

致谢 27

第一章 绪论

1.1 课题研究的背景

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