  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.
