L'image couleur pour visualiser des données multidimensionnelles

L'image couleur pour visualiser des données multidimensionnelles

Color Image to Visualize Multidimensional Data

Frédéric Blanchard Michel Herbin 

CReSTIC, Université de Reims, LERI, IUT, rue des Crayères, BP 1035, 51687 Reims Cedex 2

Corresponding Author Email: 
15 June 2004
31 October 2004
| Citation



Image is often considered as the fundamental perceptual unit of a visualization. In this paper, we suggest using one color image to allow an immediate and synthetic visualization of data. The color permits to exhibit the main structures of dataset. After reducing the dimensionality of the dataset, we generate color pixel using a transformation deduced from the work of Ohta et al. The last step consists in sorting and arranging pixel into a squared image to provides the final color image that summurizes initial data.


La visualisation de données multidimensionnelles est un problème important. Nous proposons dans cet article d'utiliser l'image couleur pour obtenir une visualisation immédiate et synthétique des données initiales. L'apport de la couleur permet d'exhiber les principales structures de ces données complexes. Après avoir réduit la dimension du problème, notre méthode génére des pixels couleur en utilisant une transformation non triviale inspirée des travaux d'Ohta et al. Une dernière étape de tri et d'arrangement de ces pixels dans une image nous permet alors de visualiser nos données multidimensionnelles sur une image couleur.


Color image, multimensional data, visualization

Mots clés

Image couleur, données multidimensionnelles, visualisation

1. Introduction
2. Réduction De Dimensionalité
3. Les Couleurs D'un Ensemble De Données
4. Construction D'une Image
5. Applications
6. Discussion Et Conclusion

[Aggarwal] C. C. AGGARWAL, A. HINNEBURG, and D. A. KEIM, "On the surprising behavior of distance metrics in high dimensional space''. In Proceedings of the 8th International Conference on Database Theory. Springer-Verlag, 2001.

[Asimov] D. ASIMOV, "The grand tour: a tool for viewing multidimensional data'', Journal on Scientific and Statistical Computing, Vol. 6, #1, p.128-143, 1985.

[Buja] A. BUJA, D. COOK, and D. F. SWAYNE, "Interactive high-dimensional data visualization'', Journal of Computational and Graphical Statistics, Vol. 5, p.78-99, 1996.

[Bellman] R. BELLMAN, "Adaptive control processes : a guide tour''. Princeton University Press, 1961.

[Bonnet] N. BONNET, M. HERBIN, and P. VAUTROT, "Extension of the scatterplot approach to multiple images'', Ultramicroscopy, Vol. 60, 1995.

[Blake] C.L. BLAKE and C.J. MERZ, UCI repository of machine learning databases, 1998.

[Debacker] A. DE BACKER, A. NAUD, and P. SCHEUDERS, "Non linear dimensionality reduction techniques for unsupervised feature extraction'', Pattern Recognition Letters, Vol. 19, p.711-720, 1998.

[Camastra] F. CAMASTRA, "Data dimensionality estimation methods: a survey'', Pattern Recognition, Vol. 36, p.2945-2954, 2003.

[Comon] P. COMON, "Independant component analysis, a new concept?'', Signal Processing, Vol. 36, #2, p.287-314, 1994.

[Demartines] P. DEMARTINES and J. HERAULT, "Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets'', IEEE Transactions on Neural Networks, Vol. 8, p.148-154, 1997.

[Devijver] P.J. DEVIJVER and J. KITTLER, "Pattern Recognition : A statistical Approach'', Prentice-Hall, Englewood Cliffs, NJ, 1982.

[Donoho] D. L. DONOHO, "High-dimensional data analysis: The curses and blessings of dimensionality'', Aide-Mémoire, 2000.

[Grinstein] G. GRINSTEIN, M. TRUTSCHL, and U. CVEK, "High-dimensional visualizations''. In Proceedings of the Visual Data Mining workshop, KDD'2001, San Francisco, California, 2001.

[Healey1] C. G. HEALEY and J. T. ENNS, "Large datasets at a glance: Combining textures and colors in scientific visualization'', IEEE Transactions on Visualization and Computer Graphics, 5(2):145-167, 1999.

[Healey2] C. G. HEALEY, "Choosing effective colours for data visualization''. In 7th IEEE Visualization '96 Conference, p. 263, 1996.

[Hyvären] A. HYVAREN, J. KARHUNEN, and E. OJA, "Independant Component Analysis'', John Wiley and Sons, 2001.

[Hughes] D.F. HUGHES, "On the mean accuracy of statistical pattern recognition'', IEEE Transaction on Information Theory, Vol. 14, #1, p.55-63, 1968.

[Herbin] M. HERBIN, P. VAUTROT, and N. BONNET, "Estimation of the number of clusters and influence zones'', Pattern Recognition Letters, Vol. 22, p.1557-1562, 2001.

[Keim] D. A. KEIM, "Pixel-oriented visualization techniques for exploring very large databases'', Journal of Computational and Graphical Statistics, Vol. 5, #1, p.58-77, 1996.

[Kohonen] T. KOHONEN, "Self-Organizing Maps'', Springer, Berlin, 1995.

[Landgrebe] D. LANDGREBE, "On information extraction principles for hyperspectral data''. In 4th International Conference on GeoComputation, Fredericksburg, Virginia, USA, p.25-28, 1999.

[Lennon] M. LENNON, «Méthodes d'analyse d'images hyperspectrales. Exploitation du capteur aéroporté CASI pour des applications de cartographie agro-environnemantale en Bretagne », PhD thesis, Université de Renne I, 2002.

[Lebart] L. LEBART, A. MORINEAU, and M. PIRON.,«Statistique exploratoire multidimensionnelle », Dunod, 2002.

[Moon] B. MOON, H. V. JAGADISH, C. FALOUTSOS, and J. H. SALTZ, "Analysis of the clustering properties of the hilbert space-filling curve'', IEEE Transactions on Knowledge and Data Engineering, Vol. 13, #1, p.124-141, 2001.

[Minnotte] M.C. MINNOTTE and R. W. WEST, "The data image: a tool for exploring high dimensional data sets''. In Proceedings of the ASA Section on Statistical Graphics, Dallas, Texas, USA, 1998.

[Nason] G. NASON, "Three-dimensional projection pursuit'', Applied Statistics, Vol. 44, #4, p.411-430, 1995.

[Ohta] Y. OHTA, T. KANADE, and T. SAKAI, "Color information for region segmentation'', Computer Graphics and Image Processing, Vol. 13, p.222-241, 1980.

[Rao] C.R. RAO, "The use and interpretation of principal component analysis in applied research.'', Sankya serie A, Vol. 26, 1964.

[Sasov] A. SASOV, "Non-raster isotropic scanning for analytical instruments'', Journal of Microscopy, Vol. 165, 1992.

[Verveer] P. J. VERVEER and R. P.W. DUIN, "Estimators for the intrinsic dimensionality evaluated and applied'', IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, #1, 1995.

[Verleysen] M. VERLEYSEN, "Machine learning of high-dimensional data: Local artificial neural networks and the curse of dimensionality'', Thesis, UCL University Catholique Louvain, Belgium, 2000.

[Wekemans] B. WEKEMANS, K. JANSSENS, L. VINCZE, A. AERTS, and J. HEERTOGEN, "Automated segmentation of µ-xrf image sets'', X-ray Spectrometry, Vol. 26, p.333-346, 1997.