Robust Hessian locally linear embedding techniques for high-dimensional data
type: Item
instance of: scholarly article
title: Robust Hessian locally linear embedding techniques for high-dimensional data
zbMATH Open document ID: 1461.62075
author: Xianglei Xing
author: Sidan Du
author: Kejun Wang
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62G35
Mathematics Subject Classification ID: 62-08
Mathematics Subject Classification ID: 68T10
zbMATH DE Number: 7042345
zbMATH Keywords: manifold learning
zbMATH Keywords: nonlinear dimensionality reduction
zbMATH Keywords: tangent coordinates
zbMATH Keywords: outlier removal
zbMATH Keywords: noise reduction
zbMATH Keywords: robust statistics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a9020036
OpenAlex ID: W2407230345
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DOI: 10.3390/A9020036
description: scientific article; zbMATH DE number 7042345