Skewness-Kurtosis Model-Based Projection Pursuit with Application to Summarizing Gene Expression Data

Abstract

Non-normality is a usual fact when dealing with gene expression data. Thus, flexible models are needed in order to account for the underlying asymmetry and heavy tails of multivariate gene expression measures. This paper addresses the issue by exploring the projection pursuit problem under a flexible framework where the underlying model is assumed to follow a multivariate skew-t distribution. Under this assumption, projection pursuit with skewness and kurtosis indices is addressed as a natural approach for data reduction. The work examines its properties giving some theoretical insights and delving into the computational side in regards to the application to real gene expression data. The results of the theory are illustrated by means of a simulation study; the outputs of the simulation are used in combination with the theoretical insights to shed light on the usefulness of skewness-kurtosis projection pursuit for summarizing multivariate gene expression data. The application to gene expression measures of patients diagnosed with triple-negative breast cancer gives promising findings that may contribute to explain the heterogeneity of this type of tumors.