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Open AccessArticle

Robust Hessian Locally Linear Embedding Techniques for High-Dimensional Data

by 1,*, 2 and 1,*
1
College of Automation, Harbin Engineering University, Harbin 150001, China
2
School of Electronic Science and Engineering, Nanjing University, Nanjing 210046, China
*
Authors to whom correspondence should be addressed.
Academic Editor: Stephan Chalup
Algorithms 2016, 9(2), 36; https://doi.org/10.3390/a9020036
Received: 26 November 2015 / Revised: 14 May 2016 / Accepted: 16 May 2016 / Published: 26 May 2016
(This article belongs to the Special Issue Manifold Learning and Dimensionality Reduction)
Recently manifold learning has received extensive interest in the community of pattern recognition. Despite their appealing properties, most manifold learning algorithms are not robust in practical applications. In this paper, we address this problem in the context of the Hessian locally linear embedding (HLLE) algorithm and propose a more robust method, called RHLLE, which aims to be robust against both outliers and noise in the data. Specifically, we first propose a fast outlier detection method for high-dimensional datasets. Then, we employ a local smoothing method to reduce noise. Furthermore, we reformulate the original HLLE algorithm by using the truncation function from differentiable manifolds. In the reformulated framework, we explicitly introduce a weighted global functional to further reduce the undesirable effect of outliers and noise on the embedding result. Experiments on synthetic as well as real datasets demonstrate the effectiveness of our proposed algorithm. View Full-Text
Keywords: manifold learning; nonlinear dimensionality reduction; tangent coordinates; outlier removal; noise reduction; robust statistics manifold learning; nonlinear dimensionality reduction; tangent coordinates; outlier removal; noise reduction; robust statistics
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Xing, X.; Du, S.; Wang, K. Robust Hessian Locally Linear Embedding Techniques for High-Dimensional Data. Algorithms 2016, 9, 36.

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