Using the software FRUITS, we apply the discrete signature to a knotted protein dataset. We show that discrete signatures have high correlation with aminoacid sequence similarity and knot depth.

The discrete signature map is invariant under consecutive repetitions and translations of time-points. We show that actually it is injective up to these two relations. This makes the discrete landscape feature map more than descriptive than the (continuous) landscape feature map.

To a persistence landscape we associate the time-series of its critical points, of which we compute the discrete signature. We show that the resulting discrete feature map is uniformly continuous.

The resulting "feature map" is still stable, but loses injectivity because the Chen signature map is invariant under tree-like equivalence of paths. We address this by proposing a discrete alternative.

The landscape embedding associates a path to a barcode, and this map is stable and injective. Chevyrev, Nanda and Oberhauser compose it with the Chen signature map, which assigns to a path a sequence of tensors of increasing order.