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Kurtosis-based projection pursuit for matrix-valued data
Tekijät: Radojičić, Una; Nordhausen, Klaus; Virta, Joni
Kustantaja: Institute of Mathematical Statistics
Julkaisuvuosi: 2025
Lehti: Annals of Statistics
Vuosikerta: 53
Numero: 6
Aloitussivu: 2563
Lopetussivu: 2591
ISSN: 0090-5364
eISSN: 2168-8966
DOI: https://doi.org/10.1214/25-AOS2555
Julkaisun avoimuus kirjaamishetkellä: Ei avoimesti saatavilla
Julkaisukanavan avoimuus : Ei avoin julkaisukanava
Verkko-osoite: https://doi.org/10.1214/25-aos2555
Preprintin osoite: 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.
Julkaisussa olevat rahoitustiedot:
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.
