Next Article in Journal
A New Multi-Step Iterative Algorithm for Approximating Common Fixed Points of a Finite Family of Multi-Valued Bregman Relatively Nonexpansive Mappings
Previous Article in Journal
Application of the Energy-Conserving Integration Method to Hybrid Simulation of a Full-Scale Steel Frame
Previous Article in Special Issue
Alternating Direction Method of Multipliers for Generalized Low-Rank Tensor Recovery
Article Menu

Export Article

Open AccessArticle
Algorithms 2016, 9(2), 36; doi:10.3390/a9020036

Robust Hessian Locally Linear Embedding Techniques for High-Dimensional Data

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
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)
View Full-Text   |   Download PDF [5064 KB, uploaded 2 June 2016]   |  

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Xing, X.; Du, S.; Wang, K. Robust Hessian Locally Linear Embedding Techniques for High-Dimensional Data. Algorithms 2016, 9, 36.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top