A Fusion Scheme of Local Manifold Learning Methods ( Manifolds - Current Research Areas )

Publication series : Manifolds - Current Research Areas

Author: Xianglei Xing Kejun Wang and Weixing Feng  

Publisher: IntechOpen‎

Publication year: 2017

E-ISBN: INT6313866303

P-ISBN(Paperback): 9789535128717

P-ISBN(Hardback):  9789535128724

Subject: O18 geometric topology

Keyword: 几何、拓扑

Language: ENG

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A Fusion Scheme of Local Manifold Learning Methods

Description

Spectral analysis‐based dimensionality reduction algorithms, especially the local manifold learning methods, have become popular recently because their optimizations do not involve local minima and scale well to large, high‐dimensional data sets. Despite their attractive properties, these algorithms are developed based on different geometric intuitions, and only partial information from the true geometric structure of the underlying manifold is learned by each method. In order to discover the underlying manifold structure more faithfully, we introduce a novel method to fuse the geometric information learned from different local manifold learning algorithms in this chapter. First, we employ local tangent coordinates to compute the local objects from different local algorithms. Then, we utilize the truncation function from differential manifold to connect the local objects with a global functional and finally develop an alternating optimization‐based algorithm to discover the low‐dimensional embedding. Experiments on synthetic as well as real data sets demonstrate the effectiveness of our proposed method.

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