# Generalized partitioned local depth

arXiv: https://arxiv.org/abs/2303.10167 · HTML: https://mlsanity.com/paper/2303.10167/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 22 references that are in the map.
- First posted on arXiv 17 Mar 2023.

## Builds on (most cited first, 5 of 5)

- [Topological Data Analysis](https://mlsanity.com/paper/1609.08227/) (2016)
- [Benchmarking distance-based partitioning methods for mixed-type data](https://mlsanity.com/paper/2203.16287/) (2022)
- [Lens depth function and k-relative neighborhood graph: versatile tools for ordinal data analysis](https://mlsanity.com/paper/1602.07194/) (2016)
- [Crowdsourced correlation clustering with relative distance comparisons](https://mlsanity.com/paper/1709.08459/) (2017)
- [Partitioned K-nearest neighbor local depth for scalable comparison-based learning](https://mlsanity.com/paper/2108.08864/) (2021)

## Built on by (most cited first, 1 of 1)

- [Online Partitioned Local Depth for semi-supervised applications](https://mlsanity.com/paper/2512.15436/) (2025)

## Abstract (arXiv)

In this paper we provide a generalization of the concept of cohesion as introduced recently by Berenhaut, Moore and Melvin [Proceedings of the National Academy of Sciences, 119 (4) (2022)]. The formulation presented builds on the technique of partitioned local depth by distilling two key probabilistic concepts: local relevance and support division. Earlier results are extended within the new context, and examples of applications to revealing communities in data with uncertainty are included. The work sheds light on the foundations of partitioned local depth, and extends the original ideas to enable probabilistic consideration of uncertain, variable and potentially conflicting information.