A heat map is a graphical representation of data where the values taken by a variable in a two-dimensional map are represented as colors. A very similar presentation form is a tree map. The term is also used to mean its thematic application as a choropleth map.

Heat maps originated in 2D displays of the values in a data matrix. Larger values were represented by small dark gray or black squares (pixels) and smaller values by lighter squares. Sneath (1957) displayed the results of a cluster analysis by permuting the rows and the columns of a matrix to place similar values near each other according to the clustering. Jacques Bertin used a similar representation to display data that conformed to a Guttman scale. The idea for joining cluster trees to the rows and columns of the data matrix originated with Robert Ling in 1973. Ling used overstruck printer characters to represent different shades of gray, one character-width per pixel. Leland Wilkinson developed the first computer program in 1994 (SYSTAT) to produce cluster heat maps with high-resolution color graphics. The Eisen et al. display shown in the figure is a replication of the earlier SYSTAT design.

Heat map generated from DNA microarray data reflecting gene expression values in several conditions

There are several different kinds of heat map:

• Web heat maps have been used for displaying areas of a Web page most frequently scanned by visitors.
• Biology heat maps are typically used in molecular biology to represent the level of expression of many genes across a number of comparable samples (e.g. cells in different states, samples from different patients) as they are obtained from DNA microarrays.
• The tree map is a 2D hierarchical partitioning of data that visually resembles a heat map.
• A mosaic plot is a tiled heat map for representing a two-way or higher-way table of data. As with treemaps, the rectangular regions in a mosaic plot are hierarchically organized. The means that the regions are rectangles instead of squares. Friendly (1994) surveys the history and usage of this graph.

[edit] References

• Bertin, J. (1967). Sémiologie Graphique. Les diagrammes, les réseaux, les cartes. Gauthier-Villars. 
• Eisen, M.B., Spellman, P.T., Brown, P.O. & Botstein, D. (1998). "Cluster analysis and display of genome-wide expression patterns". Proc. Natl. Acad. Sci. USA 95 (25): 14863–14868. doi:10.1073/pnas.95.25.14863. PMID 9843981. PMC 24541. http://www.pnas.org/cgi/content/full/95/25/14863. 
• Friendly, M. (1994). "Mosaic displays for multi-way contingency tables". Journal of the American Statistical Association 89: 190–200. doi:10.2307/2291215. http://www.math.yorku.ca/SCS/Papers/drew. 
• Ling, R.F. (1973). "A computer generated aid for cluster analysis". Communications of the ACM 16: 355–361. doi:10.1145/362248.362263. 
• Sneath, P.H.A. (1957). "The application of computers to taxonomy". Journal of General Microbiology 17: 201–226. 
• Wilkinson, L. (1994). Advanced Applications: Systat for DOS Version 6. SYSTAT Inc.. ISBN 9780134472850. 

[edit] External links

• The History of the Cluster Heat Map. Leland Wilkinson and Michael Friendly.

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