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New Clustering Algorithm Unifies Nominal and Ordinal Data Distances.

Yiqun Zhang, Yiu-ming Cheung· July 8, 2026 View original

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Summary

This paper proposes a novel clustering algorithm that unifies the measurement of intra-attribute distances for both nominal and ordinal categorical attributes, preserving ordinal relationships. It simultaneously learns these intra-attribute distance weights and data partitions within a single paradigm, outperforming existing methods.

Categorical data clustering heavily relies on effective distance metrics to measure dissimilarity between objects. However, many existing methods fail to differentiate between nominal and ordinal categorical attributes, neglecting the inherent order information present in ordinal values. Furthermore, interdependencies among these attribute types are often overlooked, which could provide valuable insights into dissimilarity. This research introduces a novel distance metric designed to address these limitations. It measures intra-attribute distances for both nominal and ordinal attributes in a unified manner, crucially preserving the relative order for ordinal values. The approach views the intrinsic differences and connections between attribute values from a graph-like perspective. Building on this metric, the paper proposes a new clustering algorithm. This algorithm integrates the learning of intra-attribute distance weights with the partitioning of data objects into a single, cohesive learning paradigm. This integrated approach avoids suboptimal solutions that arise from separate, sequential steps, and experimental results demonstrate its superior efficacy compared to current state-of-the-art methods.

Why it matters

Data scientists and analysts working with complex categorical datasets can achieve more accurate and meaningful clustering results, leading to better insights for customer segmentation, market analysis, and anomaly detection.

How to implement this in your domain

  1. 1Evaluate the proposed clustering algorithm on your organization's categorical datasets, especially those with mixed nominal and ordinal attributes.
  2. 2Compare its performance against existing clustering methods using relevant internal metrics.
  3. 3Integrate the new distance metric and clustering approach into data analysis and machine learning pipelines.
  4. 4Train data science teams on the nuances of handling nominal and ordinal data for improved clustering.

Who benefits

MarketingRetailHealthcareFinanceSocial Sciences

Key takeaways

  • Existing categorical clustering methods often treat nominal and ordinal attributes similarly.
  • A new algorithm unifies intra-attribute distance measurement for both types, preserving ordinality.
  • It learns distance weights and data partitions simultaneously, avoiding suboptimal solutions.
  • This approach leads to more accurate and meaningful categorical data clustering.

Original post by Yiqun Zhang, Yiu-ming Cheung

"arXiv:2607.05464v1 Announce Type: new Abstract: The success of categorical data clustering generally much relies on the distance metric that measures the dissimilarity degree between two objects. However, most of the existing clustering methods treat the two categorical subtypes,…"

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Originally posted by Yiqun Zhang, Yiu-ming Cheung on X · view source

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