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Deep learning has become the leading approach to assisted target recognition. While these methods typically require large amounts of labeled training data, domain adaptation (DA) or transfer learning (TL) enables these algorithms to transfer knowledge from a labelled (source) data set to an unlabelled but related (target) data set of interest. DA enables networks to overcome the distribution mismatch between the source and target that leads to poor generalization in the target domain. DA techniques align these distributions by minimizing a divergence measurement between source and target, making the transfer of knowledge from source to target possible. While these algorithms have advanced significantly in recent years, most do not explicitly leverage global data manifold structure in aligning the source and target. We propose to leverage global data structure by applying a topological data analysis (TDA) technique called persistent homology to TL. In this paper, we examine the use of persistent homology in a domain adversarial (DAd) convolutional neural network (CNN) architecture. The experiments show that aligning persistence alone is insufficient for transfer, but must be considered along with the lifetimes of the topological singularities. In addition, we found that longer lifetimes indicate robust discriminative features and more favorable structure in data. We found that existing divergence minimization based approaches to DA improve the topological structure, as indicated over a baseline without these regularization techniques. We hope these experiments highlight how topological structure can be leveraged to boost performance in TL tasks.
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