Robust Local Scaling using Conditional Quantiles of Graph Similarities

TL;DR

This paper introduces a neural network-based method for estimating local scales in neighborhood graphs using conditional quantiles, enhancing robustness to noise and reducing parameter tuning in spectral clustering and label propagation.

Contribution

It presents a novel auto-encoding neural network approach for inferring conditional quantiles to improve local scale estimation in graph construction.

Findings

Outperforms existing locally scaled graph methods in spectral clustering

Demonstrates robustness to noise and outliers

Reduces need for extensive parameter tuning

Abstract

Spectral analysis of neighborhood graphs is one of the most widely used techniques for exploratory data analysis, with applications ranging from machine learning to social sciences. In such applications, it is typical to first encode relationships between the data samples using an appropriate similarity function. Popular neighborhood construction techniques such as k-nearest neighbor (k-NN) graphs are known to be very sensitive to the choice of parameters, and more importantly susceptible to noise and varying densities. In this paper, we propose the use of quantile analysis to obtain local scale estimates for neighborhood graph construction. To this end, we build an auto-encoding neural network approach for inferring conditional quantiles of a similarity function, which are subsequently used to obtain robust estimates of the local scales. In addition to being highly resilient to noise or outlying data, the proposed approach does not require extensive parameter tuning unlike several existing methods. Using applications in spectral clustering and single-example label propagation, we show that the proposed neighborhood graphs outperform existing locally scaled graph construction approaches.