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

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