The effects of topological features on convolutional neural networks—an explanatory analysis via Grad-CAM

Topological data analysis (TDA) characterizes the global structure of data based on topological invariants such as persistent homology, whereas convolutional neural networks (CNNs) are capable of characterizing local features in the global structure of the data. In contrast, a combined model of TDA and CNN, a family of multimodal networks, simultaneously takes the image and the corresponding topological features as the input to the network for classification, thereby significantly improving the performance of a single CNN. This innovative approach has been recently successful in various applications. However, there is a lack of explanation regarding how and why topological signatures, when combined with a CNN, improve discriminative power. In this paper, we use persistent homology to compute topological features and subsequently demonstrate both qualitatively and quantitatively the effects of topological signatures on a CNN model, for which the Grad-CAM analysis of multimodal networks and topological inverse image map are proposed and appropriately utilized. For experimental validation, we utilize two famous datasets: the transient versus bogus image dataset and the HAM10000 dataset. Using Grad-CAM analysis of multimodal networks, we demonstrate that topological features enforce the image network of a CNN to focus more on significant and meaningful regions across images rather than task-irrelevant artifacts such as background noise and texture.