Clustering in stationary and nonstationary settings, where data distributions remain static or evolve over time, requires models that can adapt to distributional shifts while preserving previously learned cluster structures. This paper proposes an Adaptive Resonance Theory (ART)-based topological clustering algorithm that autonomously adjusts its recalculation interval and vigilance threshold through a diversity-driven adaptation mechanism. This mechanism enables hyperparameter-free learning that maintains cluster stability and continuity in dynamic environments. Experiments on 24 real-world datasets demonstrate that the proposed algorithm outperforms state-of-the-art methods in both clustering performance and continual learning capability. These results highlight the effectiveness of the proposed parameter adaptation in mitigating catastrophic forgetting and maintaining consistent clustering in evolving data streams. Source code is available at https://github.com/Masuyama-lab/IDAT

Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k means and its wide family of variants are still widely used, all of them require the number of clusters (k) to be supplied as input and many are notably sensitive to initialization. Convex clustering provides a more stable alternative by formulating the clustering task as a convex optimization problem, ensuring a unique global solution. However, it faces challenges in handling high-dimensional data, especially in the presence of noise and outliers. Additionally, strong fusion regularization, controlled by the tuning parameter, can hinder effective cluster formation within a convex clustering framework. To overcome these challenges, we introduce a robust approach that integrates convex clustering with the Median of Means (MoM) estimator, thus developing an outlier-resistant and efficient clustering framework that does not necessitate a prior knowledge of the number of clusters. By leveraging the robustness of MoM alongside the stability of convex clustering, our method enhances both performance and efficiency, especially on large-scale datasets. Theoretical analysis demonstrates weak consistency under specific conditions, while experiments on synthetic and real-world datasets validate the method's superior performance compared to existing approaches. Clustering is a fundamental task in unsupervised learning, aiming to organize unlabeled data into coherent groups for better interpretation and downstream applications.