# Inferring Underlying Manifold of Low Density Data using Adaptive Interpolation

### Noritaka Yamada, Takeshi Shibuya

#### Abstract

Inferring the topological shape of an underlying manifold of data is efficient for point cloud data analysis. This is accomplished by estimating the Betti numbers of the underlying manifold in each dimension from point cloud data. Futagami et al. proposed a method to automatically estimate the Betti numbers of the underlying manifold using persistent homology. However, this method estimates 2nd the Betti numbers of the underlying manifold less accurately as data density decreases. The low accuracy of estimating 2nd the Betti numbers is caused by the difficulty of detecting 2-dimensional holes. In this study, we propose a method to estimate 2nd the Betti number of the underlying manifold of low density data accurately. Concretely, we increase the density of data using interpolation that adds temporary points close to the underlying manifold. Then, we calculate persistent homology of data whose density has been increased and estimate 2nd Betti numbers from the calculation results. We confirm that our proposed method is effective to estimate 2nd the Betti numbers of the underlying manifold.

Download#### Paper Citation

#### in Harvard Style

Yamada N. and Shibuya T. (2020). **Inferring Underlying Manifold of Low Density Data using Adaptive Interpolation**.In *Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-395-7, pages 395-402. DOI: 10.5220/0008915803950402

#### in Bibtex Style

@conference{icaart20,

author={Noritaka Yamada and Takeshi Shibuya},

title={Inferring Underlying Manifold of Low Density Data using Adaptive Interpolation},

booktitle={Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2020},

pages={395-402},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0008915803950402},

isbn={978-989-758-395-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - Inferring Underlying Manifold of Low Density Data using Adaptive Interpolation

SN - 978-989-758-395-7

AU - Yamada N.

AU - Shibuya T.

PY - 2020

SP - 395

EP - 402

DO - 10.5220/0008915803950402