# Ranking with Adaptive Neighbors

## TL;DR

This paper introduces an adaptive neighbor ranking algorithm that jointly learns data affinity and ranking scores, improving retrieval accuracy by dynamically adjusting neighborhood relationships based on local data structure.

## Contribution

It proposes a novel optimization framework that adaptively assigns neighbors and learns ranking scores simultaneously, outperforming fixed-graph methods.

## Key findings

- Outperforms existing ranking methods on synthetic and real datasets.
- Effectively captures local data geometry for improved ranking accuracy.
- Demonstrates robustness to variations in data affinity matrices.

## Abstract

Retrieving the most similar objects in a large-scale database for a given query is a fundamental building block in many application domains, ranging from web searches, visual, cross media, and document retrievals. State-of-the-art approaches have mainly focused on capturing the underlying geometry of the data manifolds. Graph-based approaches, in particular, define various diffusion processes on weighted data graphs. Despite success, these approaches rely on fixed-weight graphs, making ranking sensitive to the input affinity matrix. In this study, we propose a new ranking algorithm that simultaneously learns the data affinity matrix and the ranking scores. The proposed optimization formulation assigns adaptive neighbors to each point in the data based on the local connectivity, and the smoothness constraint assigns similar ranking scores to similar data points. We develop a novel and efficient algorithm to solve the optimization problem. Evaluations using synthetic and real datasets suggest that the proposed algorithm can outperform the existing methods.