# Similarity Function Tracking using Pairwise Comparisons

## TL;DR

This paper introduces OCELAD, an adaptive online learning framework for tracking optimal similarity metrics in nonstationary environments, demonstrated on synthetic and Twitter data with improved robustness.

## Contribution

The paper presents OCELAD, a novel adaptive online approach for dynamic metric learning that effectively handles nonstationary data distributions, outperforming existing methods.

## Key findings

- OCELAD effectively tracks changing metrics in nonstationary data.
- RICE-OCELAD outperforms previous batch and online metric learning algorithms.
- Significant robustness improvements demonstrated on synthetic and Twitter datasets.

## Abstract

Recent work in distance metric learning has focused on learning transformations of data that best align with specified pairwise similarity and dissimilarity constraints, often supplied by a human observer. The learned transformations lead to improved retrieval, classification, and clustering algorithms due to the better adapted distance or similarity measures. Here, we address the problem of learning these transformations when the underlying constraint generation process is nonstationary. This nonstationarity can be due to changes in either the ground-truth clustering used to generate constraints or changes in the feature subspaces in which the class structure is apparent. We propose Online Convex Ensemble StrongLy Adaptive Dynamic Learning (OCELAD), a general adaptive, online approach for learning and tracking optimal metrics as they change over time that is highly robust to a variety of nonstationary behaviors in the changing metric. We apply the OCELAD framework to an ensemble of online learners. Specifically, we create a retro-initialized composite objective mirror descent (COMID) ensemble (RICE) consisting of a set of parallel COMID learners with different learning rates, and demonstrate parameter-free RICE-OCELAD metric learning on both synthetic data and a highly nonstationary Twitter dataset. We show significant performance improvements and increased robustness to nonstationary effects relative to previously proposed batch and online distance metric learning algorithms.