Quantile map: Simultaneous visualization of patterns in many distributions with application to tandem mass spectrometry

High-throughput experiments have become more and more prevalent in biomedical research. The resulting high-dimensional data have brought new challenges. Effective data reduction, summarization and visualization are important keys to initial exploration in data mining. In this paper, we introduce a visualization tool, namely a quantile map, to present information contained in a probabilistic distribution. We demonstrate its use as an effective visual analysis tool through the application of a tandem mass spectrometry data set. Information of quantiles of a distribution is presented in gradient colors by concentric doughnuts. The width of the doughnuts is proportional to the Fisher information of the distribution to present unbiased visualization effect. A parametric empirical Bayes (PEB) approach is shown to improve the simple maximum likelihood estimate (MLE) approach when estimating the Fisher information. In the motivating example from tandem mass spectrometry data, multiple probabilistic distributions are to be displayed in two-dimensional grids. A hierarchical clustering to reorder rows and columns and a gradient color selection from a Hue-Chroma-Luminance model, similar to that commonly applied in heatmaps of microarray analysis, are adopted to improve the visualization. Both simulations and the motivating example show superior performance of the quantile map in summarization and visualization of such high-throughput data sets.