A new formulation of principal component analysis (PCA) that considers group structure in the data is proposed as a variable down-selection method. Optimization of electrode channels is a key problem in brain-computer interfaces (BCI). BCI experiments generate large feature spaces compared to the sample size due to time limitations in EEG sessions. It is essential to understand the importance of the features in terms of physical electrode channels in order to design a high performance yet realistic BCI. The proposed algorithm produces a ranked list of original variables (electrode channels or features), according to their ability to discriminate movement imagery tasks. A linear discrimination analysis (LDA) classifier is applied to the selected variable subset. Evaluation of the down-selection method using synthetic datasets selected more than 83% of relevant variables. Classification of imagery tasks using real BCI datasets resulted in less than 19% classification error. Across-Group Variance (AGV) showed the best classification performance with the largest dimensionality reduction in comparison with other algorithms in common use.