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Reseach Article

Extensions and Analysis of Local Non-linear Techniques

by Rashmi Gupta, Rajiv Kapoor
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 51 - Number 13
Year of Publication: 2012
Authors: Rashmi Gupta, Rajiv Kapoor
10.5120/8099-1687

Rashmi Gupta, Rajiv Kapoor . Extensions and Analysis of Local Non-linear Techniques. International Journal of Computer Applications. 51, 13 ( August 2012), 1-6. DOI=10.5120/8099-1687

@article{ 10.5120/8099-1687,
author = { Rashmi Gupta, Rajiv Kapoor },
title = { Extensions and Analysis of Local Non-linear Techniques },
journal = { International Journal of Computer Applications },
issue_date = { August 2012 },
volume = { 51 },
number = { 13 },
month = { August },
year = { 2012 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume51/number13/8099-1687/ },
doi = { 10.5120/8099-1687 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:50:16.238215+05:30
%A Rashmi Gupta
%A Rajiv Kapoor
%T Extensions and Analysis of Local Non-linear Techniques
%J International Journal of Computer Applications
%@ 0975-8887
%V 51
%N 13
%P 1-6
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The techniques Conformal Eigenmap and Neighborhood Preserving Embedding (NPE) have been proposed as extensions of local non-linear techniques. Many of the commonly used non-linear dimensionality reduction, such as Local Linear Embedding (LLE) and Laplacian eigenmap are not explicitly designed to preserve local features such as distances or angles. In first proposed Conformal Eigenmap technique, a low dimensional embedding is constructed that maximally preserves angles between nearby data points. The embedding is derived from the bottom eigenvectors of LLE by solving an additional problem in Semidefinite Programming (SDP). In second proposed method, NPE minimizes the cost function of a local nonlinear technique for dimensionality reduction under the constraint that the mapping from the high-dimensional to the low-dimensional data representation is linear. The idea is to modify the LLE by introducing a linear transform matrix. The effectiveness of the proposed methods is demonstrated on synthetic datasets. Experimental results on several data sets demonstrate the merits of proposed techniques.

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Index Terms

Computer Science
Information Sciences

Keywords

Dimension reduction Manifold Learning Conformal Eigenmap Neighborhood Preserving Embedding Local Linear Embedding Laplacian Eigenmap