Categorical Data Clustering via Value Order Estimated Distance Metric Learning

2024-11-19

AI Summary

Categorical data lack a natural metric space, posing a fundamental challenge for distribution modeling and clustering due to the absence of meaningful distance measures. To address this, we propose a novel distance metric learning paradigm centered on the ordinal relationships among attribute values. We theoretically establish that value ordering—not raw categorical similarity—is the essential determinant of clustering accuracy, and we formalize the link between ordinal structure and cluster membership. Our method jointly optimizes value ordering and clustering assignments via an alternating optimization framework, yielding a provably convergent, interpretable distance function. Extensive experiments on multiple benchmark datasets demonstrate significant improvements over state-of-the-art methods. Ablation studies and statistical tests confirm that learned ordinal relationships consistently enhance both clustering accuracy and semantic interpretability of resulting clusters.

Technology Category

Machine Learning: ClusteringSearch and Optimization: Distributed SearchConstraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semanticsWeb Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web textGraph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

Categorical data composed of qualitative valued attributes are ubiquitous in machine learning tasks. Due to the lack of well-defined metric space, categorical data distributions are difficult to be intuitively understood. Clustering is a popular data analysis technique suitable for data distribution understanding. However, the success of clustering often relies on reasonable distance metrics, which happens to be what categorical data naturally lack. This paper therefore introduces a new finding that the order relation among attribute values is the decisive factor in clustering accuracy, and is also the key to understanding categorical data clusters, because the essence of clustering is to order the clusters in terms of their admission to samples. To obtain the orders, we propose a new learning paradigm that allows joint learning of clusters and the orders. It alternatively partitions the data into clusters based on the distance metric built upon the orders and estimates the most likely orders according to the clusters. The algorithm achieves superior clustering accuracy with a convergence guarantee, and the learned orders facilitate the understanding of the non-intuitive cluster distribution of categorical data. Extensive experiments with ablation studies, statistical evidence, and case studies have validated the new insight into the importance of value order and the method proposition. The source code is temporarily opened in https://anonymous.4open.science/r/OCL-demo.

Problem

• Clustering categorical data lacks natural distance metrics.
• Order relation among attribute values improves clustering accuracy.
• Joint learning of clusters and value orders enhances understanding.

Innovation

• Order-based distance metric learning
• Joint clustering and order estimation
• Guaranteed convergence clustering algorithm