University of Oulu

Ville Vuollo, Lasse Holmström, A scale space approach for exploring structure in spherical data, Computational Statistics & Data Analysis, Volume 125, 2018, Pages 57-69, ISSN 0167-9473,

A scale space approach for exploring structure in spherical data

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Author: Vuollo, Ville1,2,3; Holmström, Lasse3
Organizations: 1Research Unit of Oral Health Sciences, Faculty of Medicine, University of Oulu, Oulu, Finland
2Medical Research Center, Oulu University Hospital, Oulu, Finland
3Research Unit of Mathematical Sciences, Faculty of Science, University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 2.6 MB)
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Language: English
Published: Elsevier, 2018
Publish Date: 2018-05-16


A novel scale space approach, SphereSiZer, is proposed for exploring structure in spherical data, that is, directional data on the unit sphere of the three-dimensional Euclidean space. The method finds statistically significant gradients of the smooths of the probability density function underlying the observed data. Bootstrap is used to establish significance and inference is summarized with planar maps of contour plots of smooths of the data, overlaid with arrows that indicate the directions and magnitudes of the significant gradients. An effective way to explore such maps is a movie where each frame corresponds to a fixed level of smoothing, that is, a particular spatial scale on the sphere. The SphereSiZer is demonstrated using simulated data as well as two real-data examples. The first example examines the distribution of infant head normal vector directions. The presence of local maxima in the normal vector distribution may indicate head deformity, such as severe flatness or asymmetry. The second example considers the distribution of earthquakes in the Northern Hemisphere.

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Series: Computational statistics & data analysis
ISSN: 0167-9473
ISSN-E: 1872-7352
ISSN-L: 0167-9473
Volume: 125
Pages: 57 - 69
DOI: 10.1016/j.csda.2018.03.014
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
112 Statistics and probability
Funding: The work of Ville Vuollo was supported by the Finnish Doctoral Program in Oral Sciences.
Dataset Reference: Earthquake data for this study were accessed through the Northern California Earthquake Data Center (NCEDC), doi: 10.7932/NCEDC.
Copyright information: © 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (