Categorical attributes with qualitative values are ubiquitous in cluster analysis of real datasets. Unlike the Euclidean distance of numerical attributes, the categorical attributes lack well-defined relationships of their possible values (also called categories interchangeably), which hampers the exploration of compact categorical data clusters. Although most attempts are made for developing appropriate distance metrics, they typically assume a fixed topological relationship between categories when learning distance metrics, which limits their adaptability to varying cluster structures and often leads to suboptimal clustering performance. This paper, therefore, breaks the intrinsic relationship tie of attribute categories and learns customized distance metrics suitable for flexibly and accurately revealing various cluster distributions. As a result, the fitting ability of the clustering algorithm is significantly enhanced, benefiting from the learnable category relationships. Moreover, the learned category relationships are proved to be Euclidean distance metric-compatible, enabling a seamless extension to mixed datasets that include both numerical and categorical attributes. Comparative experiments on 12 real benchmark datasets with significance tests show the superior clustering accuracy of the proposed method with an average ranking of 1.25, which is significantly higher than the 5.21 ranking of the best-performing methods. Code and extended version with detailed proofs are provided online.

Understanding categorical data with vague qualitative values by forming clusters is crucial in many data-driven AI fields. Compared with numerical data with its quantitative values embedded in well-defined Euclidean distance space, distances of the qualitative values are naturally unknown and are specially defined for certain data types or tasks. This paper, therefore, proposes a distance metric space fusion framework, which learns to fuse multiple distance metrics to form a statistical information-complete and prior knowledge-comprehensive metric for robust and accurate cluster analysis of qualitative data. To better serve various clustering tasks, the metric fusion objective is incorporated into the clustering objective through iterative learning. It turns out that the proposed method stably demonstrates superiority on various challenging real benchmark datasets. Extensive experiments including significance tests, ablation studies, etc. validate its efficacy. Source code of the proposed method is available at https://github.com/Sen-Feng/ICASSP-MSF/tree/main/CODE.