流形學習回顧

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。

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.