Learning Nearest Neighbor Graphs from Noisy Distance Samples

TL;DR

This paper introduces an active algorithm for learning nearest neighbor graphs from noisy distance samples, applicable to general metrics and effective in practical crowdsourced preference data.

Contribution

It presents a novel, noise-tolerant method for graph learning that does not require Euclidean assumptions, with proven theoretical efficiency and empirical validation.

Findings

Requires O(n log n) queries in favorable conditions

Outperforms baseline methods in experiments

Effective on crowdsourced shoe similarity data

Abstract

We consider the problem of learning the nearest neighbor graph of a dataset of n items. The metric is unknown, but we can query an oracle to obtain a noisy estimate of the distance between any pair of items. This framework applies to problem domains where one wants to learn people's preferences from responses commonly modeled as noisy distance judgments. In this paper, we propose an active algorithm to find the graph with high probability and analyze its query complexity. In contrast to existing work that forces Euclidean structure, our method is valid for general metrics, assuming only symmetry and the triangle inequality. Furthermore, we demonstrate efficiency of our method empirically and theoretically, needing only O(n log(n)Delta^-2) queries in favorable settings, where Delta^-2 accounts for the effect of noise. Using crowd-sourced data collected for a subset of the UT Zappos50K dataset, we apply our algorithm to learn which shoes people believe are most similar and show that it beats both an active baseline and ordinal embedding.