# Query-augmented Active Metric Learning

arXiv: https://arxiv.org/abs/2111.04871 · HTML: https://mlsanity.com/paper/2111.04871/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 46 references that are in the map.
- First posted on arXiv 8 Nov 2021.

## Builds on (most cited first, 2 of 2)

- [COBRA: A Fast and Simple Method for Active Clustering with Pairwise Constraints](https://mlsanity.com/paper/1801.09955/) (2018)
- [Individualized Multi-directional Variable Selection](https://mlsanity.com/paper/1709.05062/) (2017)

## Built on by (most cited first, 4 of 4)

- [A3S: A General Active Clustering Method with Pairwise Constraints](https://mlsanity.com/paper/2407.10196/) (2024)
- [Efficient Human-in-the-Loop Active Learning: A Novel Framework for Data Labeling in AI Systems](https://mlsanity.com/paper/2501.00277/) (2024)
- [Random Normed k-Means: A Paradigm-Shift in Clustering within Probabilistic Metric Spaces](https://mlsanity.com/paper/2504.03928/) (2025)
- [Data Skeleton Learning: Scalable Active Clustering with Sparse Graph Structures](https://mlsanity.com/paper/2509.08530/) (2025)

## Abstract (arXiv)

In this paper we propose an active metric learning method for clustering with pairwise constraints. The proposed method actively queries the label of informative instance pairs, while estimating underlying metrics by incorporating unlabeled instance pairs, which leads to a more accurate and efficient clustering process. In particular, we augment the queried constraints by generating more pairwise labels to provide additional information in learning a metric to enhance clustering performance. Furthermore, we increase the robustness of metric learning by updating the learned metric sequentially and penalizing the irrelevant features adaptively. In addition, we propose a novel active query strategy that evaluates the information gain of instance pairs more accurately by incorporating the neighborhood structure, which improves clustering efficiency without extra labeling cost. In theory, we provide a tighter error bound of the proposed metric learning method utilizing augmented queries compared with methods using existing constraints only. Furthermore, we also investigate the improvement using the active query strategy instead of random selection. Numerical studies on simulation settings and real datasets indicate that the proposed method is especially advantageous when the signal-to-noise ratio between significant features and irrelevant features is low.