Abstract
Multidimensional Scaling (MDS) is a powerful dimension reduction technique for embedding high-dimensional data into a low-dimensional target space. Thereby, the distance relationships in the source are reconstructed in the target space as best as possible according to a given embedding criterion. Here, a new stress function with intuitive properties and a very good convergence behavior is presented. Optimization is combined with an efficient implementation for calculating dynamic distance matrix correlations, and the implementation can be transferred to other related algorithms. The suitability of the proposed MDS for high-throughput data (HiT-MDS) is studied in applications to macroarray analysis for up to 12,000 genes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Basalaj, W.: Proximity Visualization of Abstract Data. PhD thesis, Computer Lab, Univ. of Cambridge(2001), URL: http://www.pavis.org/essay/pavis.pdf
Buja, A., Swayne, D., Littman, M., Dean, N., Hofmann, H.: Interactive Data Visualization with Multidimensional Scaling. Report, University of Pennsylvania (2004), URL: http://www-stat.wharton.upenn.edu/~buja/
Cook, D., Buja, A., Cabrera, J.: Grand tour and projection pursuit. Journal of Computational and Graphical Statistics 4(3), 155–172 (1995)
Gansner, E., Koren, Y., North, S.: Graph drawing by stress majorization. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 239–250. Springer, Heidelberg (2005)
Gower, J.: Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika 53, 325–338 (1966)
Taguchi, Y.h., Oono, Y.: Relational patterns of gene expression via non-metric multidimensional scaling analysis. Bioinformatics 21(6), 730–740 (2005)
Hyvärinen, A., Karhunen, J., Oja, E.: Independent component analysis, 1st edn. John Wiley & Sons, Chichester (2001)
Kaski, S.: Dimensionality reduction by random mapping: Fast similarity computation for clustering. In: Proc. of the International Joint Conf. on Neural Networks (IJCNN 1998), vol. 1, pp. 413–418. IEEE Service Center, Piscataway (1998)
Kohonen, T.: Self-Organizing Maps, 3rd edn. Springer, Berlin (2001)
Kruskal, J., Wish, M.: Multidimensional Scaling. Sage Publications, New Park (1978)
Naud, A., Duch, W.: Visualization of large data sets using MDS combined with LVQ. In: Rutkowski, L., Kacprzyk, J. (eds.) Advances in Soft Computing, pp. 632–637. Physica Verlag, Heidelberg (2002)
Pekalska, E., de Ridder, D., Duin, R., Kraaijveld, M.: A new method of generalizing Sammon mapping with application to algorithm speed-up. In: Boasson, M., Kaandorp, J., Tonino, J., Vosselman, M. (eds.) Proc. 5th Annual Conf. of the Advanced School for Computing and Imaging, pp. 221–228. ASCI (1999)
Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)
Strickert, M., Teichmann, S., Sreenivasulu, N., Seiffert, U.: DiPPP Online Self-Improving Linear Map for Distance-Preserving Macro-Array Data Analysis. To appear at WSOM (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Strickert, M., Teichmann, S., Sreenivasulu, N., Seiffert, U. (2005). High-Throughput Multi-dimensional Scaling (HiT-MDS) for cDNA-Array Expression Data. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds) Artificial Neural Networks: Biological Inspirations – ICANN 2005. ICANN 2005. Lecture Notes in Computer Science, vol 3696. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11550822_97
Download citation
DOI: https://doi.org/10.1007/11550822_97
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28752-0
Online ISBN: 978-3-540-28754-4
eBook Packages: Computer ScienceComputer Science (R0)