Image Classification Using Deep Neural Networks and Persistent Homology

Persistent Homology (PH), a key tool in Topological Data Analysis (TDA), has gained significant traction in Machine Learning and Data Science applications in recent years. By combining techniques from algebraic topology, statistics, and computer science, PH captures the topological characteristics of datasets. This study aims to propose new classification models that integrate deep learning and Persistent Homology, exploring the impact of PH on model performance. Additionally, a transfer learning approach incorporating pre-trained networks and topological signatures is evaluated. Real-world datasets are used to assess the effectiveness of these models. The findings contribute to understanding the role of Persistent Homology in improving classification models, bridging the gap between deep learning, topological analysis, and practical data analysis. The performance of the models that include topological signatures showed better performance than the models that do not.