Heat map

What is a heat map in an OMICS context?

While exploring individuals/features matrices in an OMICS framework, it is interesting to examine how correlated features (i.e. genes, proteins, metabolites) correspond to similar individuals (i.e. samples). For example, a cluster of diseased kidney tissue samples may be characterized by a high expression of a group of genes, compared to other samples. The heat map tool in XLSTAT allows performing such explorations.

Drawing a heat map in XLSTAT

Both features and individuals are clustered independently using ascendant hierarchical clustering based on Euclidian distances, optionally preceded by the k-means algorithm depending on the matrix’s size. The data matrix’s rows and columns are then permuted according to corresponding clusterings, which brings similar columns closer to each other and similar lines closer to each other. A heat map is then displayed, reflecting data in the permuted matrix (data values are replaced by corresponding color intensities).

Non-specific filtering

Before launching the analyses, it is interesting to filter out features with very poor variability across individuals. In heat map analysis, non-specific filtering has two major advantages:

• It allows computations to focus less on features which are very likely to be not differentially expressed thus saving computation time.
• It improves the readability of the heat map chart. 

Two methods are available in XLSTAT:

• The user specifies a variability threshold (interquartile range or standard deviation), and features with lower variability are eliminated prior to analyses.
• The user specifies a percentage of features with low variability (interquartile range or standard deviation) to be removed prior to analyses.

Heat map in XLSTAT results

Summary statistics: The tables of descriptive statistics show the simple statistics for all individuals. The number of observations, missing values, the number of non-missing values, the mean and the standard deviation (unbiased) are displayed.

heat map: The features dendrogram is displayed vertically (rows) and the individuals dendrogram is displayed horizontally (columns). A heat map is added to the chart, reflecting data values.

Similarly expressed features are characterized by horizontal rectangles of homogeneous color along the map.

Similar individuals are characterized by vertical rectangles of homogeneous color along the map.

Clusters of similar individuals characterized by clusters of similarly expressed features can be detected by examining rectangles or squares of homogeneous color at the intersection between feature clusters and individual clusters inside the map.

References

Hahne F., Huber W., Gentleman R. and Falcon S. (2008). Bioconductor Case Studies. Springer.