# Reachable Distance Function for KNN Classification

arXiv: https://arxiv.org/abs/2103.09704 · HTML: https://mlsanity.com/paper/2103.09704/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 54 references that are in the map.
- First posted on arXiv 17 Mar 2021.

## Builds on (most cited first, 7 of 7)

- [Survey on Deep Multi-modal Data Analytics: Collaboration, Rivalry and Fusion](https://mlsanity.com/paper/2006.08159/) (2020)
- [Kernelized Multiview Subspace Analysis by Self-weighted Learning](https://mlsanity.com/paper/1911.10357/) (2019)
- [KNN Classification with One-step Computation](https://mlsanity.com/paper/2012.06047/) (2020)
- [BrePartition: Optimized High-Dimensional kNN Search with Bregman Distances](https://mlsanity.com/paper/2006.00227/) (2020)
- [Enhancing Factorization Machines with Generalized Metric Learning](https://mlsanity.com/paper/2006.11600/) (2020)
- [Acceleration of Large Margin Metric Learning for Nearest Neighbor Classification Using Triplet Mining and Stratified Sampling](https://mlsanity.com/paper/2009.14244/) (2020)
- [A Weighted Mutual k-Nearest Neighbour for Classification Mining](https://mlsanity.com/paper/2005.08640/) (2020)

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

- [Anomaly Detection in Dynamic Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2406.00134/) (2024)
- [Robust Graph Meta-learning for Weakly-supervised Few-shot Node Classification](https://mlsanity.com/paper/2106.06873/) (2021)
- [Unifying Token and Span Level Supervisions for Few-Shot Sequence Labeling](https://mlsanity.com/paper/2307.07946/) (2023)
- [Trustworthiness-Driven Graph Convolutional Networks for Signed Network Embedding](https://mlsanity.com/paper/2309.00816/) (2023)
- [Adaptive kNN graph model](https://mlsanity.com/paper/2601.16509/) (2026)

## Abstract (arXiv)

Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the affinity between data points. This paper proposes a reachable distance function for KNN classification. The reachable distance function is not a geometric direct-line distance between two data points. It gives a consideration to the class attribute of a training dataset when measuring the affinity between data points. Concretely speaking, the reachable distance between data points includes their class center distance and real distance. Its shape looks like "Z", and we also call it a Z distance function. In this way, the affinity between data points in the same class is always stronger than that in different classes. Or, the intraclass data points are always closer than those interclass data points. We evaluated the reachable distance with experiments, and demonstrated that the proposed distance function achieved better performance in KNN classification.