A1 Refereed original research article in a scientific journal
Kurtosis-based projection pursuit for matrix-valued data
Authors: Radojičić, Una; Nordhausen, Klaus; Virta, Joni
Publisher: Institute of Mathematical Statistics
Publication year: 2025
Journal: Annals of Statistics
Volume: 53
Issue: 6
First page : 2563
Last page: 2591
ISSN: 0090-5364
eISSN: 2168-8966
DOI: https://doi.org/10.1214/25-AOS2555
Publication's open availability at the time of reporting: No Open Access
Publication channel's open availability : No Open Access publication channel
Web address : https://doi.org/10.1214/25-aos2555
Preprint address: https://arxiv.org/abs/2109.04167
We develop projection pursuit for data that admit a natural representation in matrix form. For projection indices, we propose extensions of the classical kurtosis and Mardia’s multivariate kurtosis. The first index estimates projections for both sides of the matrices simultaneously, while the second index finds the two projections separately. Both indices are shown to recover the optimally separating projection for two-group Gaussian mixtures in the absence of any label information. We further establish the strong consistency of the corresponding sample estimators, as well as the asymptotic normality and high-dimensional consistency for the first estimator. Simulations and real data examples on hand-written postal codes and video data are used to demonstrate the method.
Funding information in the publication:
The work of UR was supported in whole by the Austrian Science Fund (FWF) [10.55776/I5799].
The work of KN and JV was supported by the Research Council of Finland (grants 335077, 347501, 353769 and 363261).
KN acknowledges prior affiliation with University of Jyväskylä, which supported the early stages of this work.
