Leland Wilkinson and Michael Friendly.
The History of the Cluster Heat Map.
In The American Statistician, vol. 63, no. 2, pp. 179--184, 2009.


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Abstract:

The cluster heat map is an ingenious display that simultaneously reveals row and column hierarchical cluster structure in a data matrix. It consists of a rectangular tiling with each tile shaded on a color scale to represent the value of the corresponding element of the data matrix. The rows (columns) of the tiling are ordered such that similar rows (columns) are near each other. On the vertical and horizontal margins of the tiling there are hierarchical cluster trees. This cluster heat map is a synthesis of several dierent graphic displays developed by statisticians over more than a century. We locate the earliest sources of this display in late 19th century publications. And we trace a diverse 20th century statistical literature that provided a foundation for this most widely used of all bioinformatics displays.

Bibtex:

@Article{        wilkinson:2009:HCHM,
  author = 	 {Leland Wilkinson and Michael Friendly},
  title = 	 {The History of the Cluster Heat Map},
  journal = 	 {The American Statistician},
  year = 	 {2009},
  volume = 	 {63},
  number = 	 {2},
  pages = 	 {179--184},
}

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References:

Andrade, M. (2008), "Heatmap," http://en.wikipedia.org/.
Andrich, D. (1978), "A rating formulation for ordered response categories," Psychometrika, 43, 357-74.
Bar-joseph, Z., Demaine, E. D., Giord, D. K., Hamel, A. M., Jaakkola, T. S., and Srebro, N. (2003), "K-ary clustering with optimal leaf ordering for gene expression data," Bioinformatics, 19, 506-520.
Bertin, J. (1967), S`emiologie Graphique, Paris: Editions GauthierVillars.
Brinton, W. C. (1914), Graphic Methods for Presenting Facts, New York: The Engineering Magazine Company.
Chen, C. H. (2002), "Generalized Association Plots: Information Visualization via Iteratively Generated Correlation Matrices," Statistica Sinica, 12, 7-29.
Climer, S. and Zhang, W. (2006), "Rearrangement Clustering: Pitfalls, Remedies, and Applications," Journal of Machine Learning Research, 7, 919-943.
Czekanowski, J. (1909), "Zur dierentialdiagnose der Neandertalgruppe," Korrespondenzblatt der Deutschen Gesellschaft fu r Anthropologie, Ethnologie und Urgeschichte, 40, 44-47.
Eisen, M., Spellman, P., Brown, P., and Botstein, D. (1998), "Cluster analysis and display of genome-wide expression patterns," Proceedings of the National Academy of Sciences, 95, 14863-14868.
Friendly, M. (2002), "Corrgrams: Exploratory Displays for Correlation Matrices," The American Statistician,56, 316-324.
Friendly, M. and Kwan, E. (2003), "Eect ordering for data displays," Computational Statistics & Data Analysis, 43, 509-539.
Gale, N., Halperin, W., and Costanzo, C. (1984), "Unclassed matrix shading and optimal ordering in hierarchical cluster analysis," Journal of Classification, 1, 75-92.
Goodman, L. (1975), "A new model for scaling response patterns: An application of the quasi-independence concept," Journal of the American Statistical Association, 70, 755-768.
Gower, J. and Digby, P. (1981), "Expressing complex relationships in two dimensions," in Interpreting Multivariate Data, ed. Barnett, V., Chichester, UK: John Wiley & Sons, pp. 83-118.
Gruvaeus, G. and Wainer, H. (1972), "Two additions to hierarchical cluster analysis," British Journal of Mathematical and Statistical Psychology, 25, 200-206.
Guttman, L. (1950), "The basis for scalogram analysis," in Measurement and Prediction. The American Soldier, ed. et al., S. S., New York: John Wiley & Sons, vol. IV.
Hage, P. and Harary, F. (1995), "Close-Proximity Analysis: Another Variation on the Minimum-Spanning-Tree Problem," Current Anthropology, 36, 677-683.
Hartigan, J. (1974), "BMDP3M: Block Clustering," in BMDP Biomedical Computer Programs, ed. Dixon,
W., Berkeley, CA: University of California Press.
- (1975), Clustering Algorithms, New York: John Wiley & Sons.
Hubert, L. (1974), "Some applications of graph theory and related non-metric techniques to problems of approximate seriation: The case for symmetric proximity measures," The British Journal of Mathematical and Statistical Psychology, 27, 133-153.
- (1976), "Seriation using asymmetric proximity measures," The British Journal of Mathematical and Statistical Psychology, 29, 32-52.
Kendall, D. (1963), "A statistical approach to Flinders Petries sequence dating," Bulletin of the International Statistical Institute, 40, 657-680.
Kettenring, J. (2006), "The Practice of Cluster Analysis," Journal of Classification, 23, 3-30.
Lenstra, J. (1974), "Clustering a data array and the Traveling Salesman Problem," Operations Research, 22,413-414.
Liiv, I. (2008), "Pattern discovery using seriation and matrix reordering: A unified view," Ph.D. thesis, Tallinn University of Technology, Department of Informatics, Tallinn, Estonia.
Ling, R. (1973), "A computer generated aid for cluster analysis," Communications of the ACM, 16, 355-361. Liu, L., Hawkins, D., Ghosh, S., and Young, S. (2003), "Robust singular value decomposition analysis of microarray data," Proceedings of the National Academy of Sciences, 100, 13167-13172.
Loua, T. (1873), Atlas statistique de la population de Paris, Paris: J. Dejey. McCormick, W. T., Schweitzer, P. J., and White, T. W. (1972), "Problem decomposition and data reorga- nization by a clustering technique," Operations Research, 20, 993-1009.
Morris, S. A., Asnake, B., and Yen, G. G. (2003), "Dendrogram seriation using simulated annealing," Information Visualization, 2, 95-104.
Nie, N. H., Bent, D. H., and Hull, C. H. (1970), SPSS: Statistical Package for the Social Sciences, New York, NY: McGraw-Hill Book Company.
Petrie, W. (1899), "Sequences in Prehistoric Remains," The Journal of the Anthropological Institute of Great Britain and Ireland, 29, 295-301.
PNAS (2008), "Most-Cited Articles as of July 1, 2008 - updated monthly," http://www.pnas.org/reports/ most-cited.
Robinson, W. (1951), "A method for chronologically ordering archaeological deposits," American Antiquity, 16, 293-301.
Rondinelli, D. A. (1980), Spatial analysis for regional development, Tokyo, Japan: The United Nations University.
Siirtola, H. and M akinen, E. (2005), "Constructing and reconstructing the reorderable matrix," Information Visualization, 4, 32-48.
Sneath, P. (1957), "The application of computers to taxonomy," Journal of General Microbiology, 17, 201- 226.
Weinstein, J. (2008), "A Postgenomic Visual Icon," Science, 319, 1772-1773.
Wilkinson, L. (1979), "Permuting a matrix to a simple pattern," in Proceedings of the Statistical Computing Section of the American Statistical Association, Washington, DC: The American Statistical Association, pp. 409-412.
- (1984), SYSTAT, Version 2, Evanston, IL: SYSTAT Inc.
- (1994), SYSTAT for DOS: Advanced Applications, Version 6, Evanston, IL: SYSTAT Inc. - (2005), The Grammar of Graphics, New York: Springer-Verlag, 2nd ed.
Wishart, D. (1997), "ClustanGraphics: Interactive Graphics for Cluster Analysis," Computing Science and Statistics, 29, 48-51.