This paper proposes an early detection method for cluster structural changes. Cluster structure refers to discrete structural characteristics, such as the number of clusters, when data are represented using finite mixture models, such as Gaussian mixture models. We focused on scenarios in which the cluster structure gradually changed over time. For finite mixture models, the concept of mixture complexity (MC) measures the continuous cluster size by considering the cluster proportion bias and overlap between clusters. In this paper, we propose MC fusion as an extension of MC to handle situations in which multiple mixture numbers are possible in a finite mixture model. By incorporating the fusion of multiple models, our approach accurately captured the cluster structure during transitional periods of gradual change. Moreover, we introduce a method for detecting changes in the cluster structure by examining the transition of MC fusion. We demonstrate the effectiveness of our method through empirical analysis using both artificial and real-world datasets.

翻译：本文提出了一种用于聚类结构变化的早期检测方法。聚类结构是指当数据采用有限混合模型（例如高斯混合模型）表示时，所呈现的离散结构特征，如聚类数量。我们重点研究了聚类结构随时间逐渐演变的场景。对于有限混合模型，混合复杂度（MC）这一概念通过考虑聚类比例偏差和聚类间重叠来衡量连续的聚类大小。本文提出了MC融合作为MC的扩展，以处理有限混合模型中可能存在多个混合数量的情况。通过融合多个模型，我们的方法在渐变过渡时期准确捕捉了聚类结构。此外，我们引入了一种通过检测MC融合的变迁来识别聚类结构变化的方法。通过使用人工数据集和真实世界数据集进行实证分析，我们证明了该方法的有效性。