G. Kusano, K. Fukumizu, and Y. Hiraoka. Kernel method for persistence diagrams via kernel embedding and weight factor. The Journal of Machine Learning Research, 18(1):6947-6987, 2017.
W. Liu, H. Guo, W. Zhang, Y. Zang, C. Wang, and J. Li. TopoSeg: Topology-aware segmentation for point clouds. In L. D. Raedt, editor, Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI-22, pages 1201-1208. International Joint Conferences on Artificial Intelligence Organization, 7 2022. doi: 10.24963/ijcai.2022/168. URL https://doi.org/10.24963/ijcai.2022/168. Main Track.
X. Ma, C. Qin, H. You, H. Ran, and Y. Fu. Rethinking network design and local geometry in point cloud: A simple residual mlp framework. In International Conference on Learning Representations, 2022.
Z. Meng, D. V. Anand, Y. Lu, J. Wu, and K. Xia. Weighted persistent homology for biomolecular data analysis. Scientific reports, 10(1):2079, 2020.
T. Nakamura, Y. Hiraoka, A. Hirata, E. G. Escolar, and Y. Nishiura. Persistent homology and many-body atomic structure for medium-range order in the glass. *Nanotechnology*, 26(30):304001, 2015.
I. Obayashi, T. Nakamura, and Y. Hiraoka. Persistent homology analysis for materials research and persistent homology software: HomCloud. Journal of the Physical Society of Japan, 91(9):091013, 2022.
N. Otter, M. A. Porter, U. Tillmann, P. Grindrod, and H. A. Harrington. A roadmap for the computation of persistent homology. EPJ Data Science, 6:1-38, 2017.
C. R. Qi, H. Su, K. Mo, and L. J. Guibas. PointNet: Deep learning on point sets for 3d classification and segmentation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 652-660, 2017a.
C. R. Qi, L. Yi, H. Su, and L. J. Guibas. PointNet++: Deep hierarchical feature learning on point sets in a metric space. Advances in Neural Information Processing Systems, 30, 2017b.
A. Som, H. Choi, K. N. Ramamurthy, M. P. Buman, and P. Turaga. Pi-Net: A deep learning approach to extract topological persistence images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pages 834–835, 2020.
A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin. Attention is all you need. Advances in Neural Information Processing Systems, 30, 2017.
D. Widdowson and V. Kurlin. Recognizing rigid patterns of unlabeled point clouds by complete and continuous isometry invariants with no false negatives and no false positives. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1275-1284, 2023.
Z. Wu, S. Song, A. Khosla, F. Yu, L. Zhang, X. Tang, and J. Xiao. 3D ShapeNets: A deep representation for volumetric shapes. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1912-1920, 2015.
J. Xu, X. Tang, Y. Zhu, J. Sun, and S. Pu. SGMNet: Learning rotation-invariant point cloud representations via sorted gram matrix. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 10468-10477, 2021.
Z. Yan, T. Ma, L. Gao, Z. Tang, Y. Wang, and C. Chen. Neural approximation of extended persistent homology on graphs. arXiv preprint arXiv:2201.12032, 2022.
M. Zaheer, S. Kottur, S. Ravanbakhsh, B. Poczos, R. R. Salakhutdinov, and A. J. Smola. Deep Sets. Advances in Neural Information Processing Systems, 30, 2017.
M. Zeppelinzauer, B. Zielinski, M. Juda, and M. Seidl. Topological descriptors for 3d surface analysis. In Computational Topology in Image Context: 6th International Workshop, CTIC 2016, Marseille, France, June 15-17, 2016, Proceedings 6, pages 77-87. Springer, 2016.