流形學習回顧

A Review of Manifold Learning Algorithms

黃毅平(Yi-Ping Huang)

指導教授 ： 王藹農

國立臺灣大學/理學院/數學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201903104

摘要

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。

關鍵字

流形學習

並列摘要

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.

並列關鍵字

Manifold Learning

參考文獻

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