A scale space approach for exploring structure in spherical data

Ville Vuollo and Lasse Holmström

Computational Statistics & Data Analysis, 2018, vol. 125, issue C, 57-69

Abstract: 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.

Keywords: 3D surface imaging; Directional statistics; Kernel density estimation; Scale space; SiZer; Spherical data (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:125:y:2018:i:c:p:57-69

DOI: 10.1016/j.csda.2018.03.014

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