Classification of mental tasks from electroencephalogram (EEG) signals has important applications in brain-computer interfacing (BCI). However, classification of the highly redundant and high-dimensional EEG signal, with high spatial and spectral correlations, is quite challenging. Therefore, the discriminant information, especially that of the first and second data moments, need to be extracted in the form of uncorrelated features. This work addresses this need by approximating a linear minimal-dimension sufficient statistic of the EEG matrix data in both spatial and spectral domains. As a result of the two-dimensional spatio-temporal approach and the generalized sufficiency approximation, a significant improvement on the classification accuracy is achieved.