應用一般化袋形距離於深度局部中心分群之框架研究

Abstract

在群集分析中，對具備非凸幾何、嚴重密度異質性與非對稱結構的資料進行無監督劃分，始終是一項根本性的挑戰。本研究擴展深度局部中心分群(DLCC)演算法，以處理其在資料分派上的限制。為緩解由嚴重密度異質性引發的結構失衡，本方法基於嚴格的鄰域重疊準則保留稀疏中心，並限制過渡群集的初始擴張，從而防止稀疏觀測值遭到系統性誤派。針對未分派的觀測值，本程序相對於結構核心，評估連續的深度適應性袋形距離。此幾何適應性距離能有效捕捉局部非等向性特徵與非對稱結構。經數值實驗證實，本框架能維持非凸幾何中的結構連通性，並防止在嚴重密度異質性與結構非對稱下發生系統性分類錯誤。

The unsupervised partitioning of data characterized by non-convex geometries, severe density heterogeneity, and asymmetric structures remains a fundamental challenge in cluster analysis. This study extends the Depth-Based Local Center Clustering (DLCC) algorithm to address its allocation limitations. To mitigate the structural imbalance induced by severe density heterogeneity, the methodology retains sparse centers based on a strict neighborhood overlap criterion and constrains the initial expansion of interim clusters, thereby preventing the systematic misallocation of sparse observations. For unallocated observations, the procedure evaluates continuous depth-adapted bagdistance relative to the structural cores. This geometry-adaptive distance captures local anisotropic features and asymmetric structures. Numerical experiments demonstrate that the framework maintains structural connectivity in non-convex geometries and prevents systematic misclassifications under severe density heterogeneity and structural asymmetry.