Functional connectivity between brain regions is modulated by cognitive states or experimental conditions. Such connectivity variations can be appreciated in covariance or correlation matrices obtained from fMRI data. A multivariate methodology that can capture fMRI connectivity maps in light of different experimental conditions would be of primary importance to learn about the specific roles of the different brain areas involved in the observed connectivity variations. Here we introduce Spatial Patterns for Discriminative Estimation (SP♠DE), a supervised dimensionality reduction model that provides a full multivariate characterization by achieving optimal discriminative linear spatial filters in terms of variance and provides interpretable spatial maps directly reflecting the brain areas involved in the accounted connectivity changes. We demonstrate the strength of SPADE using fMRI data from the Human connectome project to show that the model provides close to perfect discrimination between different fMRI tasks at low dimensionality. Additionally, the straightforward interpretability of the model is demonstrated by the obtained linear filters relating to anatomical areas well known to be involved in each considered fMRI task. Further, we also show that such an approach provides an alternative view to traditional task fMRI analyses by looking at changes in the covariance structure as a substitute to changes in the mean signal as the general linear model (GLM) analyses. We use 2-back and 0-back working memory task fMRI data from the Human connectome project to show that SPADE discovers connectivity changes in memory related areas during the 2-back periods, while attention network areas are involved during the 0-back task periods. We conclude that SPADE is a robust tool to investigate brain connectivity alterations across induced cognitive changes and has the potential to be used in pathological or pharmacological cohort studies.