Geometric Algorithms for $k$-NN Poisoning

TL;DR

This paper introduces a novel algorithm for label poisoning attacks on $k$-nearest neighbor classifiers in geometric data, utilizing multi-scale random partitions to approximate optimal poisoning strategies efficiently.

Contribution

It presents the first algorithm to approximate optimal label poisoning for $k$-NN in geometric data using multi-scale random partitions.

Findings

Algorithm computes an $oldsymbol{ extstyle rac{ ext{approximation factor}}{ ext{time complexity}}}$ for poisoning.

Achieves $oldsymbol{ extstyle ext{approximate poisoning}}$ with provable guarantees.

Demonstrates effectiveness on high-dimensional geometric datasets.

Abstract

We propose a label poisoning attack on geometric data sets against $k$-nearest neighbor classification. We provide an algorithm that can compute an $\varepsilon n$-additive approximation of the optimal poisoning in $n\cdot 2^{2^{O(d+k/\varepsilon)}}$ time for a given data set $X \in \mathbb{R}^d$, where $|X| = n$. Our algorithm achieves its objectives through the application of multi-scale random partitions.