Iterated geometric harmonics for data imputation and reconstruction of missing data

TL;DR

This paper introduces an iterated geometric harmonics method for data imputation that effectively reconstructs missing data in high-dimensional datasets and damaged images, converging quickly and with high accuracy.

Contribution

The paper adapts geometric harmonics to incomplete data using an iterative scheme, demonstrating fast convergence and high-quality data reconstruction in various datasets.

Findings

Converges within 4-6 iterations

Reconstructs damaged images with high accuracy

Operates efficiently on high-dimensional data

Abstract

The method of geometric harmonics is adapted to the situation of incomplete data by means of the iterated geometric harmonics (IGH) scheme. The method is tested on natural and synthetic data sets with 50--500 data points and dimensionality of 400--10,000. Experiments suggest that the algorithm converges to a near optimal solution within 4--6 iterations, at runtimes of less than 30 minutes on a medium-grade desktop computer. The imputation of missing data values is applied to collections of damaged images (suffering from data annihilation rates of up to 70\%) which are reconstructed with a surprising degree of accuracy.