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.

Clustering is one of the most important data analysis techniques, as it extracts knowledge without requiring data labels, making it crucial in many unsupervised application scenarios. However, conventional k -clustering struggles to detect irregularly distributed clusters owing to its inherent preference for convex clusters, while density-based clustering often lacks the ability to customise an appropriate metric space for different clustering tasks owing to the lack of a task-oriented optimisation process. To simultaneously address these biases in cluster shape and metric space, this paper proposes an unbiased hybrid framework to perform density-based clustering in subspaces. These subspaces are constructed through a newly developed attribute-weighted k -clustering paradigm. To exploit the irregularly distributed clusters obtained via density-based clustering for subspace learning, a novel strategy is designed to subdivide the clusters into compact sub-clusters, which are more suitable for evaluating attribute importance through k -clustering. As a result, the proposed subspace density K -clustering algorithm inherits the shape flexibility of density-based clustering and the metric adaptiveness of k -clustering. Moreover, the learnable design enables mutual optimisation between density clusters and subspaces, yielding robust and superior clustering performance across various datasets. Comprehensive evaluations, including comparative clustering performance evaluation, ablation studies, significance tests, noise-robustness evaluation, and hyper-parameter sensitivity studies, are conducted. Among 10 compared methods, the proposed Subspace DENsity-K-clustering (SDENK) achieves an average rank of 1.75 on 12 datasets in terms of the clustering accuracy metric ARI. • The merits of density and k -clustering are integrated, serving as a hybrid general framework for unbiased clustering. • A novel re-clustering mechanism is proposed to subdivide the density clusters for more appropriately determining the subspace. • The proposed unbiased clustering algorithm is suitable for datasets with various cluster distributions.

Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space such as the Euclidean distance space of numerical data, the distribution of categorical data is usually under-represented, and thus valuable information can be easily twisted in clustering. This paper, therefore, introduces a novel order distance metric learning approach to intuitively represent categorical attribute values by learning their optimal order relationship and quantifying their distance in a line similar to that of the numerical attributes. Since subjectively created qualitative categorical values involve ambiguity and fuzziness, the order distance metric is learned in the context of clustering. Accordingly, a new joint learning paradigm is developed to alternatively perform clustering and order distance metric learning with low time complexity and a guarantee of convergence. Due to the clustering-friendly order learning mechanism and the homogeneous ordinal nature of the order distance and Euclidean distance, the proposed method achieves superior clustering accuracy on categorical and mixed datasets. More importantly, the learned order distance metric greatly reduces the difficulty of understanding and managing the non-intuitive categorical data. Experiments with ablation studies, significance tests, case studies, etc., have validated the efficacy of the proposed method. The source code is available at https://github.com/csmjzhao/OCL_Source_Code.

Unsupervised Outlier Detection (UOD) is crucial for the analysis of biomedical and health data with undesirable outliers. However, the complex distribution of real data often brings difficulties to UOD where the "masking effect", i.e., only a small number of densely distributed outliers (also called clustliers) can collectively mask themselves from being detected, is particularly challenging. Another difficulty derived from this is how to distinguish clustliers from small clusters. Therefore, we propose a novel Multi-Granular Outlier Detector (MGOD). It first partitions the dataset into subsets with natural neighbor topological relationships to circumvent the non-trivial neighbor range setting. Then it effectively detects both clustliers and isolated samples (also called scatliers) based on a newly designed anomaly score. The score comprehensively takes into account the density and connectivity of samples to reflect different extents and types of abnormality. It turns out that MGOD is accurate and highly interpretable. The performance of MGOD is also robust to the involved hyper-parameters, which are easy to set. Comprehensive evaluations have been conducted to compare seven counterparts on 15 datasets, most of which are biomedical datasets. The results of significance tests confirm the effectiveness and superiority of MGOD. The source code is opened at https://anonymous.4open.science/r/MGOD-C531.

Clustering is a fundamental approach to understanding data patterns, wherein the intuitive Euclidean distance space is commonly adopted. However, this is not the case for implicit cluster distributions reflected by qualitative attribute values, e.g., the nominal values of attributes like symptoms, marital status, etc. This paper, therefore, discovered a tree-like distance structure to flexibly represent the local order relationship among intra-attribute qualitative values. That is, treating a value as the vertex of the tree allows to capture rich order relationships among the vertex value and the others. To obtain the trees in a clustering-friendly form, a joint learning mechanism is proposed to iteratively obtain more appropriate tree structures and clusters. It turns out that the latent distance space of the whole dataset can be well-represented by a forest consisting of the learned trees. Extensive experiments demonstrate that the joint learning adapts the forest to the clustering task to yield accurate results. Comparisons of 10 counterparts on 12 real benchmark datasets with significance tests verify the superiority of the proposed method. Source code of the proposed method is available at [39].