Background: The combination of gene expression profiling with linkage analysis has become a powerful paradigm for mapping gene expression quantitative trait loci (eQTL). To date, most studies have searched for eQTL by analyzing gene expression traits one at a time. As thousands of expression traits are typically analyzed, this can reduce power because of the need to correct for the number of hypothesis tests performed. In addition, gene expression traits exhibit a complex correlation structure, which is ignored when analyzing traits individually. Results: To address these issues, we applied two different multivariate dimension reduction techniques, the Singular Value Decomposition (SVD) and Independent Component Analysis (ICA) to gene expression traits derived from a cross between two strains of Saccharomyces cerevisiae. Both methods decompose the data into a set of meta-traits, which are linear combinations of all the expression traits. The meta-traits were enriched for several Gene Ontology categories including metabolic pathways, stress response, RNA processing, ion transport, retro-transposition and telomeric maintenance. Genome-wide linkage analysis was performed on the top 20 meta-traits from both techniques. In total, 21 eQTL were found, of which 11 are novel. Interestingly, both cis and trans-linkages to the meta-traits were observed. Conclusion: These results demonstrate that dimension reduction methods are a useful and complementary approach for probing the genetic architecture of gene expression variation.