請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/21330完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王藹農(Ai-Nung Wang) | |
| dc.contributor.author | Yi-Ping Huang | en |
| dc.contributor.author | 黃毅平 | zh_TW |
| dc.date.accessioned | 2021-06-08T03:31:16Z | - |
| dc.date.copyright | 2019-08-16 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-08-12 | |
| dc.identifier.citation | [1] M. Belkin and P. Niyogi. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15(6):1373–1396, 2003.
[2] X. He and P. Niyogi. Locality preserving projections. In S. Thrun, L. K. Saul, and B. Schölkopf, editors, Advances in Neural Information Processing Systems 16, pages 153–160. MIT Press, 2004. [3] E. Kokiopoulou and Y. Saad. Orthogonal neighborhood preserving projections. In Proceedings of the Fifth IEEE International Conference on Data Mining, ICDM ’05, pages 234–241, Washington, DC, USA, 2005. IEEE Computer Society. [4] E. Kokiopoulou and Y. Saad. Orthogonal neighborhood preserving projections: A projectionbased dimensionality reduction technique. IEEE Trans. Pattern Anal. Mach. Intell., 29(12):2143–2156, Dec. 2007. [5] S. T. Roweis and L. K. Saul. Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500):2323–2326, 2000. [6] J. B. Tenenbaum, V. d. Silva, and J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500):2319–2323, 2000. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/21330 | - |
| dc.description.abstract | 流形學習是降低資料維度的方法，可分為線性以及非線性的。非線性的方法有 Laplacian eigenmaps 和 locally linear embeddings 等。線性的方法有 MDS、ISOMAP、LPP 以及他們的衍生。這些方法的解可由跡數最小化問題得來，並等價於特徵值問題。我們給一個通用的架構並討論他們之間的關係。 | zh_TW |
| dc.description.abstract | Manifold learning algorithms are techniques utilized to reduce the dimen sion of data sets. These methods includes the nonlinear (implicit) ones, and the linear (projective) ones. Among the nonlinear are Laplacian eigenmaps and locally linear embeddings (LLE); and among the linear are metric multi dimensional scaling (MDS), ISOMAP, locally preserving projections (LPP) and derivatives of them. All these methods give rise to trace minimization problems and, as a result, eigenvalue problems. We give a common frame work for them and discuss their relationships. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T03:31:16Z (GMT). No. of bitstreams: 1 ntu-108-R03221024-1.pdf: 3006596 bytes, checksum: 5a60c79d0ab720e381b97fa99e7515db (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | 口試委員會審定書 iii
誌謝 v Acknowledgements vii 摘要 ix Abstract xi 1 Preliminaries 1 1.1 Covariance 1 1.2 Frobenius Norm of a Matrix 3 1.3 Principle Components 5 1.4 Optimal Properties of PCA 8 1.4.1 PCA as Minimizing the Square Distances 11 2 Problem Statement, Conventions and the Relevant 13 2.1 Problem Statement 13 2.2 Data Matrix 14 2.3 Gramian Matrix 14 2.4 The Trace Minimizing Problems 16 2.5 Graph Construction 17 3 Classical Linear Methods 19 3.1 PCA, Reinterpreted 19 3.2 Multidimensional Scaling 20 3.2.1 Distance Matrix 20 3.2.2 Gramian matrix 21 3.2.3 Embedding 23 3.3 ISOMAP 25 4 GraphBased Nonlinear Methods 27 4.1 Laplacian Eigenmaps 27 4.1.1 Objective Function 28 4.1.2 Embeddings 29 4.2 Locally Linear Embedding 29 4.2.1 Reconstruction of a Single Point 30 4.2.2 Weight Matrix 32 4.2.3 Finding Weight 32 4.2.4 Find the Embedding 33 4.3 Connection between Laplacian Eigenmaps and LLE 34 5 GraphBased Methods with Linear Assumptions 37 5.1 Locally Preserving Projections 37 5.2 Orthogonal Locality Preserving Projections 38 5.3 Neighborhood Preserving Projection 38 5.4 Orthogonal Neighborhood Preserving Projection 39 6 The Unifying Framework 41 Bibliography 43 | |
| dc.language.iso | en | |
| dc.title | 流形學習回顧 | zh_TW |
| dc.title | A Review of Manifold Learning Algorithms | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 107-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 梁惠禎(Fei-tsen Liang),謝春忠(Chun-Chung Hsieh) | |
| dc.subject.keyword | 流形學習, | zh_TW |
| dc.subject.keyword | Manifold Learning, | en |
| dc.relation.page | 43 | |
| dc.identifier.doi | 10.6342/NTU201903104 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2019-08-13 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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