# Learning Unified Distance Metric for Heterogeneous Attribute Data Clustering

arXiv: https://arxiv.org/abs/2603.04458 · HTML: https://mlsanity.com/paper/2603.04458/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 50 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 3 of 3)

- [The Impact of Random Models on Clustering Similarity](https://mlsanity.com/paper/1701.06508/) (2017)
- [Unsupervised Heterogeneous Coupling Learning for Categorical Representation](https://mlsanity.com/paper/2007.10720/) (2020)
- [Significance-Based Categorical Data Clustering](https://mlsanity.com/paper/2211.03956/) (2022)

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

- [Hierarchical Reference Sets for Robust Unsupervised Detection of Scattered and Clustered Outliers](https://mlsanity.com/paper/2603.12847/) (2026)
- [Beyond Statistical Co-occurrence: Unlocking Intrinsic Semantics for Tabular Data Clustering](https://mlsanity.com/paper/2604.10865/) (2026)
- [Bridge the Gaps: Heterogeneous Attributed Graph Clustering via Quaternion Representation Learning](https://mlsanity.com/paper/2606.23199/) (2026)
- [GRACE: LLM-Grounded Semantic Metric Spaces for Scalable Mixed-Data Clustering](https://mlsanity.com/paper/2608.07881/) (2026)

## Abstract (arXiv)

Datasets composed of numerical and categorical attributes (also called mixed data hereinafter) are common in real clustering tasks. Differing from numerical attributes that indicate tendencies between two concepts (e.g., high and low temperature) with their values in well-defined Euclidean distance space, categorical attribute values are different concepts (e.g., different occupations) embedded in an implicit space. Simultaneously exploiting these two very different types of information is an unavoidable but challenging problem, and most advanced attempts either encode the heterogeneous numerical and categorical attributes into one type, or define a unified metric for them for mixed data clustering, leaving their inherent connection unrevealed. This paper, therefore, studies the connection among any-type of attributes and proposes a novel Heterogeneous Attribute Reconstruction and Representation (HARR) learning paradigm accordingly for cluster analysis. The paradigm transforms heterogeneous attributes into a homogeneous status for distance metric learning, and integrates the learning with clustering to automatically adapt the metric to different clustering tasks. Differing from most existing works that directly adopt defined distance metrics or learn attribute weights to search clusters in a subspace. We propose to project the values of each attribute into unified learnable multiple spaces to more finely represent and learn the distance metric for categorical data. HARR is parameter-free, convergence-guaranteed, and can more effectively self-adapt to different sought number of clusters k. Extensive experiments illustrate its superiority in terms of accuracy and efficiency.