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Title: Non-linear two-dimensional PCA Authors:  Joni Virta - University of Turku (Finland) [presenting]
Andreas Artemiou - Cardiff University (United Kingdom)
Abstract: Non-linear principal component analysis for matrix-valued data is developed. Our approach is based on applying non-linear transformations separately to the left and right singular vectors of the observed matrices, guaranteeing that the estimated latent components enjoy the left-right structure typically expected in matrix dimension reduction. We treat both population and sample-level estimation and also establish the convergence rates of the estimators. The results are illustrated with numerical examples.