# Inversion-Free Evaluation of Nearest Neighbors in Method of Moments

## TL;DR

This paper presents an inversion-free, scalable method for evaluating nearest neighbors in the method of moments, enhancing shape perturbation analysis and data mining applications.

## Contribution

It extends topology sensitivity in method of moments by incorporating degrees-of-freedom reconstruction, enabling efficient parallelizable nearest neighbor evaluation.

## Key findings

- Effective for small shape perturbation evaluation
- Suitable for parallel computation
- Useful for machine learning data mining

## Abstract

A recently introduced technique of topology sensitivity in method of moments is extended by the possibility of adding degrees-of-freedom (reconstruct) into underlying structure. The algebraic formulation is inversion-free, suitable for parallelization and scales favorably with the number of unknowns. The reconstruction completes the nearest neighbors procedure for an evaluation of the smallest shape perturbation. The performance of the method is studied with a greedy search over a Hamming graph representing the structure in which initial positions are chosen from a random set. The method is shown to be effective data mining tool for machine learning-related applications.