(38-4) 32 * << * >> * Russian * English * Content * All Issues

The choice of a method for feature space decomposition for non-linear dimensionality reduction
E.V. Myasnikov

 

Samara State Aerospace University,

Image Processing Systems Institute, Russian Academy of Sciences

PDF, 585 kB

Full text of article: Russian language.

DOI: 10.18287/0134-2452-2014-38-4-790-793

Pages: 790-793.

Abstract:
This paper considers two approaches to the hierarchical decomposition of the feature space to improve the efficiency of the non-linear dimensionality reduction method. The first approach suggested by the author of the paper is based on the decomposition of the original feature space using hierarchical clustering. The second original approach is based on a hierarchical decomposition of the target space by using a KD-Tree. The approaches analyzed are evaluated in terms of the efficiency of the non-linear dimensionality reduction method.

Key words:
dimensionality reduction, decomposition of the feature space, hierarchical clustering, KD-trees.

Citation:
Myasnikov EV. The choice of a method for feature space decomposition for non-linear dimensionality reduction. Computer Optics 2014; 38(4): 790-793. DOI: 10.18287/0134-2452-2014-38-4-790-793.

References:

  1. Hiroike, A. Visualization of information spaces to retrieve and browse image data / A. Hiroike, Y. Musha, A. Sugimoto, Y. Mori // Proceedings of the Third International Conference on Visual Information and Information Systems (VISUAL'99). Lecture Notes in Computer Science. – Springer, 1999. – Vol. 1614. – P. 155-162.
  2. Myasnikov, E.V. Digital image collection navigation based on automatic classification methods / E.V. Myasnikov // Internet-Mathematics 2007: Collected papers. – Ekaterinburg, Russia, 2007. – P. 144-152. – (In Russian).
  3. Rodden, K. Evaluating Similarity-Based Visualisations As Interfaces For Image Browsing / K. Rodden. – Technical Report. – University of Cambridge, Computer Laboratory, 2002. – 248 p.
  4. Rose, T. ANVIL: a system for the retrieval of captioned images using NLP techniques / T. Rose, D. Elworthy, A. Kotcheff, A. Clare, P. Tsonis // The Challenge of Image Retrieval. Electronic Workshops in Computing, 2000.
  5. Rubner, Y. Adaptive color-image embeddings for database navigation / Y. Rubner, C. Tomasi, L.J. Guibas // Proceedings of the IEEE Asian Conference on Computer Vision, 1998. – P. 104-111.
  6. Kruskal, J.B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis / J.B. Kruskal // Psychometrika. – 1964. – Vol. 29. – P. 1-27.
  7. Sammon, J.W., Jr. A nonlinear mapping for data structure analysis / J.W. Sammon, Jr. // IEEE Transactions on Computers. – 1969. – Vol. C-18, Issue 5. – P. 401-409.
  8. Calvert, T.W. Randomly Generated Nonlinear Transformations for Pattern Recognition / T.W. Calvert, T.Y. Young // IEEE Transactions on Systems Science and Cybernetics. – 1969. – Vol. 5. – P. 266-273.
  9. De Leeuw, J. Applications of convex analysis to multidimensional scaling / J. De Leeuw, J.R. Barra, F. Brodeau, G. Romie [et al.] // Recent developments in statistics. – 1977. – P. 133-145.
  10. Lee, J.A. Nonlinear Dimensionality Reduction / J.A. Lee, M. Verleysen. – Springer, 2007.
  11. Eades, P. A Heuristic for Graph Drawing / P. Eades // Congressus Numerantium. – 1984. – Vol. 42. – P. 149-160.
  12. Fruchterman, T. Graph Drawing by Force-directed Placement / T. Fruchterman, E. Reingold // Software – Practice and Experience. – 1991. – Vol. 21, Issue 11. – P. 1129-1164.
  13. Kamada, T. An Algorithm for Drawing General Undirected Graphs / T. Kamada, S. Kawai // Information Processing Letters. – 1989. – Vol. 31. – P. 7-15.
  14. Lee, R.C.T. A Triangulation Method for the Sequential Mapping of Points from N-Space to Two-Space / R.C.T. Lee, J.R. Slagle, H. Blum // IEEE Transactions on Computers. – 1977. – Vol. 26, Issue 3. – P. 288-292.
  15. Pekalska, E. A new method of generalizing Sammon mapping with application to algorithm speed-up / E. P"ekalska, D. de Ridder, R.P.W. Duin, M.A. Kraaijveld // Proc. ASCI'99, 5th Annual Conf. of the Advanced School for Computing and Imaging. – Heijen, The Netherlands: 1999, June 15-17. – P. 221-228.
  16. Chalmers, M. A Linear Iteration Time Layout Algorithm for Visualizing High–Dimensional Data / M. Chalmers // Proc. IEEE Visualization `96. – San Francisco, 1996. – P. 127-132.
  17. Morrison, A. Fast Multidimensional Scaling Through Sampling, Springs and Interpolation / A. Morrison, G. Ross, M. Chalmers // Information Visualization. – 2003. – Vol. 2. – P. 68-77.
  18. Myasnikov, E.V. A Nonlinear Method for Dimensionality Reduction of Data Using Reference Nodes / E.V. Myasnikov // Pattern Recognition and Image Analysis. – 2012. – Vol. 22, Issue 2. – P. 337-345.
  19. Quigley, A. FADE: Graph Drawing, Clustering, and Visual Abstraction / A. Quigley, P. Eades // Proceedings of the 8-th International Symposium on Graph Drawing. – 2001. – P. 197-210.
  20. Myasnikov, E.V. The study of dimensionality reduction methods in the task of browsing of digital image collections / E.V. Myasnikov // Computer Optics. – 2008. – Vol. 32(3). – P. 296-301. – (In Russian).
  21. Stricker, M. Similarity of color images / M. Stricker, M. Orengo // In Proc. SPIE Conf. on Vis. Commun. and Image Proc. - 1995.
  22. Swain, M. Color indexing / M. Swain, D. Ballard // International Journal of Computer Vision. – 1991. – Vol. 7(1).
  23. Haralick, R.M. Texture features for image classification / R.M. Haralick, K. Shanmugam, I. Dinstein // IEEE Transactions on Systems, Man and Cybernetics. – 1973. – SMC-3(6).
© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail:journal@computeroptics.ru; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20