  In this paper, we ask if it is possible to increase the interpretability in
multivariate analysis by aligning and projecting covariates onto comparative
subspaces. We demonstrate our method as well as the interpretative power of PLS
decomposed models and how robust interpretability can lead to quantitative
insights.
  We discuss the statistical properties of the PLS weights, $p$-values
associated with specific axes, as well as their alignment properties.
  The applicability of this approach within life science is also demonstrated
by applying it to three use cases of publically available datasets.
  Further we present hierarchical pathway enrichment results stemming from
aligned $p$-values, which are compared with results derived from enrichment
analysis, as an external validation of our method.
  We find that the method can uncover known results from genomics for all of
the studied use cases, i.e. microarray data from multiple sclerosis and
diabetes patients as well as RNA sequencing data from breast cancer patients.
