Add to ORKGModern computer technology has facilitated the presence of high-dimensional data, whose graphical representations are curves, images or shapes. Because of the high-dimensionality, a dimension reduction such as functional principal component analysis or singular value decomposition is often employed. By using functional principal component analysis, a set of observed high-dimensional data can be decomposed into functional principal components and their uncorrelated principal component scores, that is, f t(χ i) = f̄(x i) + ∑ k=1 ∞ ξ t;κφ κ (χ i); t = 1; ⋯ ; n; i = 1; ⋯ ; p; where f̄(χ i) is the sample mean, ξ t;k is the κ th principal component score of observation t, and φκ(x i) is the κ th functional principal component observed at data poi...