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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳彥賓 | zh_TW |
| dc.contributor.advisor | Yan-Bin Chen | en |
| dc.contributor.author | 郭軒丞 | zh_TW |
| dc.contributor.author | Shiuan-Cheng Kuo | en |
| dc.date.accessioned | 2026-03-04T16:20:08Z | - |
| dc.date.available | 2026-03-28 | - |
| dc.date.copyright | 2026-03-04 | - |
| dc.date.issued | 2026 | - |
| dc.date.submitted | 2026-02-11 | - |
| dc.identifier.citation | [1] J. Albert-Smet, A. Torrente, and J. Romo. Band depth based initialization of K-means for functional data clustering. Advances in Data Analysis and Classification, 17:463–484, 2023.
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/101758 | - |
| dc.description.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。 | zh_TW |
| dc.description.abstract | 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. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2026-03-04T16:20:08Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2026-03-04T16:20:08Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員會審定書i
摘要ii Abstract iii Contents iv List of Figures vi List of Tables vii Chapter 1 Introduction 1 1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Contributions and Organization . . . . . . . . . . . . . . . . . . . 3 Chapter 2 Preliminaries 5 2.1 Statistical Depth Functions . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Mahalanobis Depth . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Spatial Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3 Skew-Adjusted Projection Depth . . . . . . . . . . . . . . . . . . 7 2.2 Bagdistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 DLCC Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Chapter 3 Methodology 13 3.1 Framework Overview . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2 Phase I: Local Structure Identification . . . . . . . . . . . . . . . 14 3.2.1 Similarity Matrix and Local Centers . . . . . . . . . . . . . . . . 16 3.2.2 Frequency-Based Selection and Retention of Sparse Centers . . . 19 3.3 Phase II: Center Grouping and Initialization . . . . . . . . . . . . 21 3.3.1 Construction of Structural Cores . . . . . . . . . . . . . . . . . 21 3.3.2 Adjusting for Allocation Bias under Density Heterogeneity . . . 22 3.4 Phase III: Depth-Adapted Bagdistance Assignment . . . . . . . . 24 3.4.1 Definition of Depth-Adapted Bagdistance . . . . . . . . . . . . . 26 3.4.2 Depth Function Selection and Local Subspace Projection . . . . 27 3.5 Phase IV: Global Refinement . . . . . . . . . . . . . . . . . . . . 29 3.5.1 Minimizing Depth-Adapted Bagdistance . . . . . . . . . . . . . 29 3.5.2 Fixing Local Reference Regions . . . . . . . . . . . . . . . . . . 30 Chapter 4 Simulation Study 31 4.1 Simulation Settings and Scenarios . . . . . . . . . . . . . . . . . . 31 4.2 Competitors and Implementation Details . . . . . . . . . . . . . . 33 4.3 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.4 Simulation Results and Discussion . . . . . . . . . . . . . . . . . 36 4.4.1 Discussion of Algorithmic Properties . . . . . . . . . . . . . . . 41 Chapter 5 Conclusion 43 References 46 | - |
| dc.language.iso | en | - |
| dc.subject | 分群 | - |
| dc.subject | 深度函數 | - |
| dc.subject | 袋形距離 | - |
| dc.subject | 密度異質性 | - |
| dc.subject | Clustering | - |
| dc.subject | Depth Functions | - |
| dc.subject | Bagdistance | - |
| dc.subject | Density Heterogeneity | - |
| dc.title | 應用一般化袋形距離於深度局部中心分群之框架研究 | zh_TW |
| dc.title | A Depth-Based Local Center Clustering Framework with Generalized Bagdistance | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 114-1 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 黃世豪;張馨文;藍俊宏 | zh_TW |
| dc.contributor.oralexamcommittee | Shih-Hao Huang;Hsin-Wen Chang;Jakey Blue | en |
| dc.subject.keyword | 分群,深度函數袋形距離密度異質性 | zh_TW |
| dc.subject.keyword | Clustering,Depth FunctionsBagdistanceDensity Heterogeneity | en |
| dc.relation.page | 49 | - |
| dc.identifier.doi | 10.6342/NTU202600688 | - |
| dc.rights.note | 未授權 | - |
| dc.date.accepted | 2026-02-11 | - |
| dc.contributor.author-college | 共同教育中心 | - |
| dc.contributor.author-dept | 統計碩士學位學程 | - |
| dc.date.embargo-lift | N/A | - |
| 顯示於系所單位： | 統計碩士學位學程 | |
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| ntu-114-1.pdf 未授權公開取用 | 4.36 MB | Adobe PDF |
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