  Persistence diagrams have been widely used to quantify the underlying
features of filtered topological spaces in data visualization. In many
applications, computing distances between diagrams is essential; however,
computing these distances has been challenging due to the computational cost.
In this paper, we propose a persistence diagram hashing framework that learns a
binary code representation of persistence diagrams, which allows for fast
computation of distances. This framework is built upon a generative adversarial
network (GAN) with a diagram distance loss function to steer the learning
process. Instead of using standard representations, we hash diagrams into
binary codes, which have natural advantages in large-scale tasks. The training
of this model is domain-oblivious in that it can be computed purely from
synthetic, randomly created diagrams. As a consequence, our proposed method is
directly applicable to various datasets without the need for retraining the
model. These binary codes, when compared using fast Hamming distance, better
maintain topological similarity properties between datasets than other
vectorized representations. To evaluate this method, we apply our framework to
the problem of diagram clustering and we compare the quality and performance of
our approach to the state-of-the-art. In addition, we show the scalability of
our approach on a dataset with 10k persistence diagrams, which is not possible
with current techniques. Moreover, our experimental results demonstrate that
our method is significantly faster with the potential of less memory usage,
while retaining comparable or better quality comparisons.
