Association Plots: visualizing cluster-specific associations in high-dimensional correspondence analysis biplots

Abstract

In molecular biology, just as in many other fields of science, data often come in the form of matrices or contingency tables with many observations (rows) for a set of variables (columns). While projection methods like principal component analysis or correspondence analysis (CA) can be applied for obtaining an overview of such data, in cases where the matrix is very large the associated loss of information upon projection into two or three dimensions may be dramatic. However, when the set of variables can be grouped into clusters, this opens up a new angle on the data. We focus on the question of which observations are associated to a cluster and distinguish it from other clusters. CA employs a geometry geared towards answering this question. We exploit this feature in order to introduce Association Plots for visualizing cluster-specific observations in complex data. Regardless of the data matrix dimensionality Association Plots are two-dimensional and depict the observations associated to a cluster of variables. We demonstrate our method on two small data sets and then use it to study a challenging genomic data set comprising >10,000 samples. We show that Association Plots can clearly highlight those observations which characterise a cluster of variables.