High-dimensional manifold modeling increases the precision and performance of cortical morphometry analysisby densely sampling on the grey matters. But this also brings redundant information and increased computationalburden. Gaussian process regression has been used to tackle this problem by learning a mapping to alow-dimensional subspace. However, current methods may not take relevant morphometric properties, usuallymeasured by geometric features, into account, and as a result, may generate morphometrically insignificant selections.In this paper, we propose a morphometric Gaussian process (M-GP) as a novel Bayesian model on thegray matter tetrahedral meshes. We also implement an M-GP regression landmarking algorithm as a manifoldlearning method for non-linear dimensionality reduction. The definition of M-GP involves a scale-invariant wavekernel signature distance map measuring the local similarities of geometric features, and a heat ow entropywhich implicitly embeds the global curvature ow. With such a design, the prior knowledge fully encodes thegeometric information so that a posterior predictive inference is morphometrically significant. In experiments,we use 518 grey matter tetrahedral meshes generated from structural magnetic resonance images of a publiclyavailable Alzheimer's disease imaging cohort to empirically and numerically evaluate our method. The resultsverify that our method is theoretically and experimentally valid in selecting a representative subset from theoriginal massive data. Our work may benefit any studies involving large-scale or iterative computations onextensive manifold-valued data, including morphometry analyses and general medical data processing.
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