Bump hunting by topological data analysis | Zendy

Sommerfeld Max | Zendy; Heo Giseon | Zendy; Kim Peter | Zendy; Rush Stephen T. | Zendy; Marron J. S. | Zendy

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Bump hunting by topological data analysis

Author(s) -

Sommerfeld Max,

Heo Giseon,

Kim Peter,

Rush Stephen T.,

Marron J. S.

Publication year - 2017

Publication title -

stat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.61

H-Index - 18

ISSN - 2049-1573

DOI - 10.1002/sta4.167

Subject(s) - statistical inference , persistent homology , topological data analysis , inference , kernel density estimation , computer science , kernel (algebra) , data set , statistical hypothesis testing , statistical analysis , algorithm , mathematics , data mining , topology (electrical circuits) , statistics , discrete mathematics , artificial intelligence , combinatorics , estimator

A topological data analysis approach is taken to the challenging problem of finding and validating the statistical significance of local modes in a data set. As with the SIgnificance of the ZERo (SiZer) approach to this problem, statistical inference is performed in a multi‐scale way, that is, across bandwidths. The key contribution is a two‐parameter approach to the persistent homology representation. For each kernel bandwidth, a sub‐level set filtration of the resulting kernel density estimate is computed. Inference based on the resulting persistence diagram indicates statistical significance of modes. It is seen through a simulated example, and by analysis of the famous Hidalgo stamps data, that the new method has more statistical power for finding bumps than SiZer. Copyright © 2017 John Wiley & Sons, Ltd.

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