Improve Adversarial Robustness of MNIST Classification via Topological Data Analysis

Current defense methods for machine learning classification tasks against adversarial samples mostly focus on the propagation process of networks rather than leveraging the shape characteristics of target objects, as humans perform object recognition. We propose a novel approach named Topological Random Forest (TPRF) that captures the position and shape information of digits using topological features extracted via Topological Data Analysis (TDA) and combines it with a neural network trained with CROWN-IBP to improve the adversarial robustness of the classification on the MNIST dataset. We illustrate the process of topological feature extraction and explain the classification principle, which is compatible with the human recognition process. Experimental results show that TPRF achieves comparable clean and robust accuracies to state-of-the-art (SOTA) CNNs. We also conduct an analysis of misclassification cases, which offers insights valuable for further exploration of object recognition models that rely on shape bias.