Persistent Cohomology and Circular Coordinates
@article{Silva2011PersistentCA, title={Persistent Cohomology and Circular Coordinates}, author={V. D. Silva and D. Morozov and Mikael Vejdemo-Johansson}, journal={Discrete & Computational Geometry}, year={2011}, volume={45}, pages={737-759} }
Nonlinear dimensionality reduction (NLDR) algorithms such as Isomap, LLE, and Laplacian Eigenmaps address the problem of representing high-dimensional nonlinear data in terms of low-dimensional coordinates which represent the intrinsic structure of the data. This paradigm incorporates the assumption that real-valued coordinates provide a rich enough class of functions to represent the data faithfully and efficiently. On the other hand, there are simple structures which challenge this assumption… CONTINUE READING
Topics from this paper
35 Citations
Persistent Cohomology for Data With Multicomponent Heterogeneous Information
- Computer Science, Biology
- SIAM J. Math. Data Sci.
- 2020
- 3
- PDF
Sparse Circular Coordinates via Principal $\mathbb{Z}$-Bundles.
- Mathematics, Computer Science
- 2018
- 2
- Highly Influenced
- PDF
Sparse Circular Coordinates via Principal ℤ-Bundles
- Computer Science, Physics
- ArXiv
- 2018
- 4
- Highly Influenced
- PDF
Spectral Simplicial Theory for Feature Selection and Applications to Genomics
- Mathematics, Computer Science
- ArXiv
- 2018
- 2
- PDF
Computing persistent homology with various coefficient fields in a single pass
- Mathematics, Computer Science
- J. Appl. Comput. Topol.
- 2019
- 4
- PDF