TY - GEN
T1 - Perturbation robust representations of topological persistence diagrams
AU - Som, Anirudh
AU - Thopalli, Kowshik
AU - Ramamurthy, Karthikeyan Natesan
AU - Venkataraman, Vinay
AU - Shukla, Ankita
AU - Turaga, Pavan
N1 - Funding Information:
Acknowledgments. This work was supported in part by ARO grant W911NF-17-1-0293 and NSF CAREER award 1452163.
Publisher Copyright:
© Springer Nature Switzerland AG 2018.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Grassmann manifold
KW - Invariance learning
KW - Persistence diagrams
KW - Perturbed topological signature
KW - Topological data analysis
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U2 - 10.1007/978-3-030-01234-2_38
DO - 10.1007/978-3-030-01234-2_38
M3 - Conference contribution
AN - SCOPUS:85055087009
SN - 9783030012335
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 638
EP - 659
BT - Computer Vision – ECCV 2018 - 15th European Conference, 2018, Proceedings
A2 - Ferrari, Vittorio
A2 - Sminchisescu, Cristian
A2 - Hebert, Martial
A2 - Weiss, Yair
PB - Springer Verlag
T2 - 15th European Conference on Computer Vision, ECCV 2018
Y2 - 8 September 2018 through 14 September 2018
ER -