Several biplot methods applied to gene expression data

DNA microarray experiments result in enormous amount of data, which need careful interpretation. Biplot approaches show simultaneous display of genes and samples in low-dimensional graphs and thus can be used to represent the relationships between genes and samples. There are several different types of biplots, and these methods need to be evaluated because each plot provides different result.     

A robust biplot

This paper introduces a robust biplot which is related to multivariate M-estimates. The n × p data matrix is first considered as a sample of size n from some p-variate population, and robust M-estimates of the population location vector and scatter matrix are calculated. In the construction of the biplot, each row of the data matrix is assigned a weight determined in the preliminary robust estimation. In a robust biplot, one can plot the variables in order to represent characteristics of the robust variance-covariance matrix: the length of the vector representing a variable is proportional to its robust standard deviation, while the cosine of the angle between two variables is approximately equal to their robust correlation. The proposed biplot also permits a meaningful representation of the variables in a robust principal-component analysis. The discrepancies between least-squares and robust biplots are illustrated in an example.