Statistical Implicative Analysis of DNA microarrays

This chapter presents an application of the Statistical Implicative Analysis to microarray gene expression data. The specificity of these data requires an adaptation of the concept of intensity of implication. More specifically, we propose to study the rankings of observations instead of the measurements themselves. This method makes our analysis more robust and insensitive to any monotonic transformation of gene expression. We introduce the concept of rank interval and show that the integration of the implicative method in this framework is more efficient than correlation techniques. Our method is applied to the most challenging problems encountered in gene expression analysis, namely the discovery of gene coregulation, gene selection and tumour classification. We compare our method with performing algorithms that are dedicated to gene expression data or that are well-suited to high-dimensional variable space.