# Learning Local Metrics and Influential Regions for Classification

arXiv: https://arxiv.org/abs/1802.03452 · HTML: https://mlsanity.com/paper/1802.03452/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2018.

## Built on by (most cited first, 5 of 5)

- [Adaptive neighborhood Metric learning](https://mlsanity.com/paper/2201.08314/) (2022)
- [Projection-free Graph-based Classifier Learning using Gershgorin Disc Perfect Alignment](https://mlsanity.com/paper/2106.01642/) (2021)
- [Semi-supervised Learning with Deterministic Labeling and Large Margin Projection](https://mlsanity.com/paper/2208.08058/) (2022)
- [Unfolding Projection-free SDP Relaxation of Binary Graph Classifier via GDPA Linearization](https://mlsanity.com/paper/2109.04697/) (2021)
- [Global Ground Metric Learning with Applications to scRNA data](https://mlsanity.com/paper/2506.15383/) (2025)

## Abstract (arXiv)

The performance of distance-based classifiers heavily depends on the underlying distance metric, so it is valuable to learn a suitable metric from the data. To address the problem of multimodality, it is desirable to learn local metrics. In this short paper, we define a new intuitive distance with local metrics and influential regions, and subsequently propose a novel local metric learning method for distance-based classification. Our key intuition is to partition the metric space into influential regions and a background region, and then regulate the effectiveness of each local metric to be within the related influential regions. We learn local metrics and influential regions to reduce the empirical hinge loss, and regularize the parameters on the basis of a resultant learning bound. Encouraging experimental results are obtained from various public and popular data sets.