Abstract
Inferring underlying manifold of data is one of the important issues for point cloud data analysis. This is accomplished by inferring the topological shape of the underlying manifold. This is done by estimating the number of holes in the underlying manifold in each dimension.
Persistent homology is one of the means of estimating the number of holes in the underlying manifold. Calculating the persistent homology of data determines the size, number, and dimensions of holes produced from data points. However, the number of holes represented through persistent homology is far greater than that in underlying manifold. This problem is caused by noises in a result of calculating persistent homology. Therefore, reducing noises that result from calculating persistent homology is necessary to estimate the number of holes in the underlying manifold.
Conventional methods cannot reduce noises adequately when data are of low density and thus cannot estimate the number of holes in the underlying manifold without manual analysis by experts.
In this study, we propose a new method to estimate automatically the number of holes in the underlying manifolds. We also compare the proposed and conventional methods and show the effectiveness of the former.
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Futagami, R., Yamada, N., Shibuya, T. (2019). Inferring Underlying Manifold of Data by the Use of Persistent Homology Analysis. In: Marfil, R., Calderón, M., Díaz del Río, F., Real, P., Bandera, A. (eds) Computational Topology in Image Context. CTIC 2019. Lecture Notes in Computer Science(), vol 11382. Springer, Cham. https://doi.org/10.1007/978-3-030-10828-1_4
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DOI: https://doi.org/10.1007/978-3-030-10828-1_4
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