Out-of-sample embedding of spherical manifold based on constrained least squares

Yongpeng Zhang, Zenggang Lin, Rui Yao, Yu Zhu, Haisen Li

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

All of the current state-of-the-art nonlinear dimensionality reduction methods attempt to seek the low-dimensional manifold structure by preserving global or local properties of the original data, but without considering the constraint of the manifold structure, thus, there may be a big contrast between the manifold structure result obtained by the nonlinear techniques and the result that we expected. Therefore, it is necessary for us to study the constrained nonlinear dimensionality reduction. In this paper, we study the embedding of a hidden manifold onto a unit sphere by using SMACOF algorithm and propose a method to solve the out-of-sample problem which usually arises in the manifold learning. By converting it into a constrained least squares problem with the spherical structure information, this method avoids reconstructing the neighborhood graph. The application results of 3-D object pose estimation show the effectiveness of our propose method.

Original languageEnglish
Title of host publicationIntelligent Science and Intelligent Data Engineering - Second Sino-Foreign-Interchange Workshop, IScIDE 2011, Revised Selected Papers
Pages562-570
Number of pages9
DOIs
StatePublished - 2012
Event2nd Sino-Foreign-Interchange Workshop on Intelligent Science and Intelligent Data Engineering, IScIDE 2011 - Xi'an, China
Duration: 23 Oct 201125 Oct 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7202 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference2nd Sino-Foreign-Interchange Workshop on Intelligent Science and Intelligent Data Engineering, IScIDE 2011
Country/TerritoryChina
CityXi'an
Period23/10/1125/10/11

Keywords

  • constrained least squares
  • manifold learning
  • out-of-sample embedding
  • SMACOF
  • spherical MDS

Fingerprint

Dive into the research topics of 'Out-of-sample embedding of spherical manifold based on constrained least squares'. Together they form a unique fingerprint.

Cite this