Matrix Visualization

  • Han-Ming Wu
  • ShengLi Tzeng
  • Chun-houh Chen
Part of the Springer Handbooks Comp.Statistics book series (SHCS)


The graphical exploration of quantitative/qualitative data is an initial but essential step inmodern statistical data analysis.Matrix visualization (Chen, 2002; Chen et al., 2004) is a graphical technique that can simultaneously explore the associations between thousands of subjects, variables, and their interactions, without needing to first reduce the dimensions of the data. Matrix visualization involves permuting the rows and columns of the raw data matrix using suitable seriation (reordering) algorithms, together with the corresponding proximity matrices.The permuted raw data matrix and two proximity matrices are then displayed as matrix maps via suitable color spectra, and the subject clusters, variable groups, and interactions embedded in the dataset can be extracted visually.


Exploratory Data Analysis Proximity Measure Proximity Matrix Hierarchical Cluster Tree Binary Data Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alon, U., Barkai, N., Notterman, D.A., Gish, K. Ybarra, S., Mack, D. and Levine, A.J. (1999). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays, Proc Natl Acad Sci USA., 96(12):6745–6750.CrossRefGoogle Scholar
  2. Asimov, D. (1985). The grand tour: a tool for viewing multidimensional data, SIAM Journal of Scientific and Statistical Computing, 6(1):128–143.zbMATHCrossRefMathSciNetGoogle Scholar
  3. Bar-Joseph, Z., Gifford, D.K. and Jaakkola, T.S. (2001). Fast optimal leaf ordering for hierarchical clustering, Bioinformatics, 17:S22–S29.Google Scholar
  4. Bertin, J. (1967). Semiologie Graphique, Paris: Editions gauthier-Villars. English translation by William J. Berg. as Semiology of Graphics: Diagrams, Networks, Maps. University of Wisconsin Press, Madison, WI, 1983.Google Scholar
  5. Carmichael, J.W. and Sneath, P.H.A. (1969). Taxometric maps, Systematic Zoology, 18:402–415.CrossRefGoogle Scholar
  6. Chang, S.C., Chen, C.H., Chi, Y.Y. and Ouyoung, C.W. (2002). Relativity and resolution for high dimensional information visualization with generalized association plots (GAP), Section for Invited Papers, Proceedings in Computational Statistics 2002 (Compstat 2002), Berlin, Germany, 55–66.Google Scholar
  7. Chen, C.H. (1996). The properties and applications of the convergence of correlation matrices. In 1996 Proceedings of the Section on Statistical Graphics of the American Statistical Association, 49–54.Google Scholar
  8. Chen, C.H. (1999). Extensions of generalized association plots, 1999 Proceedings of the Section on Statistical Graphics of the American Statistical Association, 111–116.Google Scholar
  9. Chen, C.H. (2002). Generalized association plots: information visualization via iteratively generated correlation matrices, Statistica Sinica, 12:7–29.zbMATHMathSciNetGoogle Scholar
  10. Chen, C.H., Hwu, H.G., Jang, W.J., Kao, C.H., Tien, Y.J., Tzeng, S. and Wu, H.M. (2004). Matrix visualization and information mining, Proceedings in Computational Statistics 2004 (Compstat 2004), pp. 85–100, Physika Verlag, Heidelberg.Google Scholar
  11. Eisen, M.B., Spellman, P.T., Brown, P.O. and Botstein, D. (1998). Cluster analysis and display of genome-wide expression patterns, Proc Natl Acad Sci USA, 95:14863–14868.CrossRefGoogle Scholar
  12. Fisher, R.A. (1936). The use of multiple measurements in taxonomic problems, Annals of Eugenics, 7:179–188.Google Scholar
  13. Friendly, M. (2002). Corrgrams: exploratory displays for correlation matrices. The American Statistician, 56(4):316-324.CrossRefMathSciNetGoogle Scholar
  14. Friendly, M. and Kwan, E. (2003). Effect ordering for data displays. Computational Statistics and Data Analysis, 43(4):509–539.CrossRefMathSciNetzbMATHGoogle Scholar
  15. Hartigan, J.A. (1972). Direct clustering of a data matrix. Journal of the American Statistical Association, 78:123–129.CrossRefGoogle Scholar
  16. Hurley, C.B. (2004). Clustering visualization of multidimensional data, Journal of Computational and Graphics Statistics, 13:788–806.CrossRefMathSciNetGoogle Scholar
  17. Inselberg, A. (1985). The plane with parallel coordinates, The Visual Computer, 1:69–91.zbMATHCrossRefGoogle Scholar
  18. Lenstra, J. (1974). Clustering a data array and the traveling salesman problem, Operations Research, 22:413–414.zbMATHCrossRefGoogle Scholar
  19. Ling, R.L. (1973). A computer generated aid for cluster analysis, Communications of the ACM, 16(6):355–361.CrossRefGoogle Scholar
  20. Marc, P., Devaux, F. and Jacq, C. (2001). yMGV: a database for visualization and data mining of published genome-wide yeast expression data, Nucleic Acids Research, 29(13):e63.CrossRefGoogle Scholar
  21. Marchette, D.J. and Solka, J.L. (2003). Using data images for outlier detection, Computational Statistics and Data Analysis, 43:541–552.CrossRefMathSciNetzbMATHGoogle Scholar
  22. Michailidis, G. and de Leeuw, J. (1998). The Gifi system for descriptive multivariate analysis, Statistical Science, 13:307–336.zbMATHCrossRefMathSciNetGoogle Scholar
  23. Minnotte, M. and West, W. (1998). The data image: a tool for exploring high dimensional data sets, in Proceedings of the ASA Section on Statistical Graphics, Dallas, TX, 25–33.Google Scholar
  24. Murdoch, D.J. and Chow, E.D. (1996). A graphical display of large correlation matrices, The American Statistician, 50:178–180.CrossRefGoogle Scholar
  25. Robinson, W.S. (1951). A method for chronologically ordering archaeological deposits, American Antiquity 16:293–301.CrossRefGoogle Scholar
  26. Slagle, J.R., Chang, C.L. and Heller, S.R. (1975). A clustering and data-reorganizing algorithm, IEEE Trans. Syst. Man Cybern, 5:125-128.zbMATHGoogle Scholar
  27. Streng, R. (1991). Classification and seriation by iterative reordering of a data matrix. In Classification, Data Analysis, and Knowledge Organization: Models and Methods with Applications (Edited by H.H. Bock and P. Ihm), 121-130. Springer, New York.Google Scholar
  28. Tenenbaum, J.B., de Silva, V. and Langford, J.C. (2000). A global geometric framework for nonlinear dimensionality reduction, Science, 290(5500):2319–2323.CrossRefGoogle Scholar
  29. Tibshirani, R., Hastie, T., Eisen, M., Ross, D., Botstein, D. and Brown, P. (1999). Clustering methods for the analysis of DNA microarray data. Technical Report, Stanford University, Oct. 1999.Google Scholar
  30. Tien, Y.J., Lee, Y.S, Wu, H.M. and Chen, C.H. (2006). Integration of clustering and visualization methods for simultaneously identifying coherent local clusters with smooth global patterns in gene expression profiles. Technical Report 2006-11, Institute of Statistical Science, Academia, Taiwan.Google Scholar
  31. Tukey, J.W. (1977). Exploratory Data Analysis. Addison-Wesley, Reading, MA.zbMATHGoogle Scholar
  32. Unwin, A.R., Hawkins, G., Hofmann, H. and Siegl, B. (1996). Interactive graphics for data sets with missing values – MANET, Journal of Computational and Graphical Statistics 5:113–122.CrossRefGoogle Scholar
  33. Unwin, A.R and Hofmann, H. (1998). New interactive graphics tools for exploratory analysis of spatial data. In Innovations in GIS 5, ed. S Carver, pp. 46–55. Taylor & Francis, London.Google Scholar
  34. Wegman, E.J. (1990). Hyperdimensional data analysis using parallel coordinates. Journal of the American Statistical Association. 85:664–675.CrossRefGoogle Scholar
  35. Wu, H.M. and Chen, C.H. (2005). Covariate adjusted matrix visualization. Technical Report. Institute of Statistical Science, Academia, Taiwan.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Han-Ming Wu
    • 1
  • ShengLi Tzeng
    • 1
  • Chun-houh Chen
    • 1
  1. 1.Institute of Statistical ScienceAcademia SinicaNangkangChina

Personalised recommendations