We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 December 2024
Reseach Article

Spatial Distance Preservation based Methods for Non-Linear Dimensionality Reduction

by Rashmi Gupta, Pooja Pandey, Rajiv Kapoor
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 69 - Number 20
Year of Publication: 2013
Authors: Rashmi Gupta, Pooja Pandey, Rajiv Kapoor
10.5120/12090-8281

Rashmi Gupta, Pooja Pandey, Rajiv Kapoor . Spatial Distance Preservation based Methods for Non-Linear Dimensionality Reduction. International Journal of Computer Applications. 69, 20 ( May 2013), 37-41. DOI=10.5120/12090-8281

@article{ 10.5120/12090-8281,
author = { Rashmi Gupta, Pooja Pandey, Rajiv Kapoor },
title = { Spatial Distance Preservation based Methods for Non-Linear Dimensionality Reduction },
journal = { International Journal of Computer Applications },
issue_date = { May 2013 },
volume = { 69 },
number = { 20 },
month = { May },
year = { 2013 },
issn = { 0975-8887 },
pages = { 37-41 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume69/number20/12090-8281/ },
doi = { 10.5120/12090-8281 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:30:51.126299+05:30
%A Rashmi Gupta
%A Pooja Pandey
%A Rajiv Kapoor
%T Spatial Distance Preservation based Methods for Non-Linear Dimensionality Reduction
%J International Journal of Computer Applications
%@ 0975-8887
%V 69
%N 20
%P 37-41
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The preservation of the pairwise distances measured in a data set ensures that the low dimensional embedding inherits the main geometric properties of the data like the local neighborhood relationships. In this paper, distance preserving technique namely, Sammons nonlinear mapping (Sammon's NLM) and Curvilinear Component Analysis (CCA) have been discussed and compared for non-linear dimensionality reduction. Basic principle in both the technique is that local neighborhood relationship is maintained. The results have beencompared for both the techniques on artificially generated data set using MATLAB software.

References
  1. L. J. P. van der Maaten, E. O. Postma, and H. J. van den Herik, 2007 Dimensionality reduction: A comparative review. IEEE Transactions on Pattern Analysis and Machine Intelligence (submitted)
  2. R. N. Shepard, 1962the analysis of proximities: Multidimensional scaling with an unknown distance function (parts 1 and 2). Psychometrika, 27:125-140, 219-249.
  3. H. Robins and S. Monro. 22:400-407, 1951 A stochastic approximation methods. Annals of Mathematical Statistics.
  4. E. Pekalska, D. de Ridder, R. P. W. Duin, and M. A. Kraaijveld,1999 A new method of generalizing Sammon mapping with application to algorithm speed-up. In M. Boasson, J. A. Kaandorp, J. F. M. Tonino, and M. G. Vosselman, editors, Proceedings of ASCI'99, 5th Annual Conference of Advanced School for Computing and Imaging, pages 221-228. ASCI, Delft, the Netherlands, June
  5. J. W. Sammon. 1969 A nonlinear mapping algorithm for data structure analysis. IEEE Transactions on Computers, CC-18(5):401-409.
  6. P. Dermatines and J. Herault, September 1995 CCA: Curvilinear component analysis. In 15th Workshop GRETSI, Juan-les-Pins (France).
  7. P. Dermatines and J. Herault. January 1984 Curvilinear component analysis. A self-organizing neutral network for nonlinear mapping of data sets. IEEE Transactions on Neutral Networks, 8(1):148-154.
  8. P. Dermatines and J. Herault, 1993. Vector quantization and projection neural network. Volume 686 of Lecture Notes in Computer Science, pages 328-333. Springer-Verlag, New York,
  9. Gray, R. M, Stanford university, Stanford, CA, U. S. A, April 1984. Vector Quantization, Volume:1 Issue:2 ASSP Magazine, IEEE, Volume:1 Issue:2.
  10. Rashmi Gupta and Rajiv Kapoor, August-2012, Extension and Analysis of Local Nonlinear Techniques, vol. 51-No. 13.
  11. Lu Xu, Yang Xu, Tommy W. S. Chow, Pattern Recognition (43),2010, Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong,Elsevier Ltd.
  12. Jigang Sun, Malcolm Crowe, Colin Fyfe, 2013. Incorporating visualization quality measures to curvilinear component analysis, 2012, Information Science 223, 75-101.
  13. Rashmi Gupta, Rajiv Kapoor, 2012 Comparison of graph based methods for nonlinear dimensionality reduction,IJSISE, vol. 5,No. 2,pp. 101-109.
Index Terms

Computer Science
Information Sciences

Keywords

MDS Dimensionality Reduction Nonlinear Mapping Vector Quantization Quasi Newton Optimization Gradient Descent