Abstract. Topological methods for data analysis present opportunities
for enforcing certain invariances of broad interest in computer vision,
including view-point in activity analysis, articulation in shape analysis,
and measurement invariance in non-linear dynamical modeling. The increasing success of these methods is attributed to the complementary
information that topology provides, as well as availability of tools for
computing topological summaries such as persistence diagrams. However, persistence diagrams are multi-sets of points and hence it is not
straightforward to fuse them with features used for contemporary machine learning tools like deep-nets. In this paper we present theoretically
well-grounded approaches to develop novel perturbation robust topological representations, with the long-term view of making them amenable
to fusion with contemporary learning architectures. We term the proposed representation as Perturbed Topological Signatures, which live
on a Grassmann manifold and hence can be efficiently used in machine
learning pipelines. We explore the use of the proposed descriptor on
three applications: 3D shape analysis, view-invariant activity analysis,
and non-linear dynamical modeling. We show favorable results in both
high-level recognition performance and time-complexity when compared
to other baseline methods