Kurtosis-based projection pursuit for matrix-valued data
Conference
65th ISI World Statistics Congress
Format: IPS Abstract - WSC 2025
Keywords: asymptotics, dimension-reduction, discriminant analysis
Session: IPS 914 - Recent Advances on High-Dimensional Statistics for Complex Data
Tuesday 7 October 10:50 a.m. - 12:30 p.m. (Europe/Amsterdam)
Abstract
We develop projection pursuit for data that admit a 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 full 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. A video data example is used to demonstrate the method.