Abstract:

Convolutional Neural Network （CNN） is sensitive to the local features of data due to the complex classification boundaries and too many parameters. As a result， the accuracy of CNN model will decrease significantly when it is attacked by adversarial attacks. However， the Topological Data Analysis （TDA） method pays more attention to the macro features of data， which naturally can resist noise and gradient attacks. Therefore， an image classification algorithm named MCN （Mapper-Combined neural Network） combining topological data analysis and CNN was proposed. Firstly， the Mapper algorithm was used to obtain the Mapper map that described the macro features of the dataset. Each sample point was represented by a new feature using a multi-view Mapper map， and the new feature was represented as a binary vector. Then， the hidden layer feature was enhanced by combining the new feature with the hidden layer feature extracted by the CNN. Finally， the feature-enhanced sample data was used to train the fully connected classification network to complete the image classification task. Comparing MCN with pure convolutional network and single Mapper feature classification algorithm on MNIST and FashionMNIST data sets， the initial classification accuracy of the MCN with PCA （Principal Component Analysis） dimension reduction is improved by 4.65% and 8.05%， the initial classification accuracy of the MCN with LDA （Linear Discriminant Analysis） dimensionality reduction is improved by 8.21% and 5.70%. Experimental results show that MCN has higher classification accuracy and stronger anti-attack capability.

Key words: Convolutional Neural Network (CNN), adversarial attack, Topological Data Analysis (TDA), feature enhancement, multi-view

摘要：

卷积神经网络（CNN）参数众多、分类边界复杂，对数据的局部特征较敏感，导致当CNN模型受到对抗攻击时，精度明显下降；而拓扑数据分析（TDA）方法更关注数据的宏观特征，天然具有对抗噪声和梯度攻击的能力。为此，提出一种耦合拓扑数据分析和CNN的图像分类算法MCN（Mapper-Combined neural Network）。首先，利用Mapper算法得到刻画数据集宏观特征的Mapper图，通过多视图的Mapper图对每一个样本点进行新的特征表示，并将新特征表示成二值向量；其次，结合新特征和CNN提取的隐藏层特征，增强隐藏层特征；最后，使用特征增强后的样本数据训练全连接的分类网络，完成图像分类任务。在MNIST和FashionMNIST数据集上，将MCN与纯卷积网络、单一Mapper特征分类算法进行对比，采用主成分分析（PCA）降维的MCN的初始分类精度提升了4.65%和8.05%；采用线性判别分析（LDA）降维的MCN的初始分类精度提高了8.21%和5.70%。实验结果表明，MCN分类精度更高，并且对抗攻击能力更强。

关键词: 卷积神经网络, 对抗攻击, 拓扑数据分析, 特征增强, 多视图