PDE-Inspired Algorithms for Semi-Supervised Learning on Point Clouds

09/23/2019 ∙ by Oliver M. Crook, et al. ∙ 33

Given a data set and a subset of labels the problem of semi-supervised learning on point clouds is to extend the labels to the entire data set. In this paper we extend the labels by minimising the constrained discrete p-Dirichlet energy. Under suitable conditions the discrete problem can be connected, in the large data limit, with the minimiser of a weighted continuum p-Dirichlet energy with the same constraints. We take advantage of this connection by designing numerical schemes that first estimate the density of the data and then apply PDE methods, such as pseudo-spectral methods, to solve the corresponding Euler-Lagrange equation. We prove that our scheme is consistent in the large data limit for two methods of density estimation: kernel density estimation and spline kernel density estimation.



There are no comments yet.


page 19

page 20

page 26

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.