This repo contains the implementation code for the article "Nonparametric Regression for 3D Point Cloud Learning."
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Simulation Main Functions: main_eg1_SP.m: main file for simulation study in Section 6.1 with domain Omega_1. main_eg1_HS.m: main file for simulation study in Section 6.1 with domain Omega_2.
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Data Generator: dataGeneratorRandomSP.m: generating simulated data (random design) for simulation study in Section 6.1 with domain Omega_1. dataGeneratorRandomHS.m: generating simulated data (random design) for simulation study in Section 6.1 with domain Omega_2. popGeneratorSP.m: generating true data over a set of grid points (Omega_1). popGeneratorHS.m: generating true data over a set of grid points (Omega_2).
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Trivariate Penalized Spline over Triangulation (TPST) estimation: TPST_est.m: Model fitting via TPST. (GCV is used to choose the best tuning parameter.)
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Functions for constructing TPST basis, penalty function, and smoothness constraints: basis.p: generating spline basis. energyM3D.p: generating energy/penalty function. smoothness.p: generating H matrix for smoothness conditions.
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Other functions that helped to construct TPST estimator include: bary.p, build.p, choose.p, dtri.p, HQbary.p, HQblkdiag.p, indices.p, indices3d.p, insideVT.p, loop3.p, qrH.p, and volume.p.