# Guarantees on Nearest-Neighbor Condensation heuristics

## TL;DR

This paper introduces theoretical guarantees for nearest-neighbor condensation algorithms, proposing two new methods with proven bounds and comparing them to existing algorithms to understand their reduction capabilities.

## Contribution

It presents the first theoretical bounds for practical NN condensation algorithms and introduces two new algorithms, RSS and VSS, with provable size guarantees.

## Key findings

- RSS and VSS have provable upper bounds on selected subset size
- Comparison of MSS and FCNN with new algorithms reveals differences in reduction efficiency
- Theoretical analysis provides insights into the selection size of state-of-the-art algorithms

## Abstract

The problem of nearest-neighbor (NN) condensation aims to reduce the size of a training set of a nearest-neighbor classifier while maintaining its classification accuracy. Although many condensation techniques have been proposed, few bounds have been proved on the amount of reduction achieved. In this paper, we present one of the first theoretical results for practical NN condensation algorithms. We propose two condensation algorithms, called RSS and VSS, along with provable upper-bounds on the size of their selected subsets. Additionally, we shed light on the selection size of two other state-of-the-art algorithms, called MSS and FCNN, and compare them to the new algorithms.