sentence1: mean supervectors motivate us to perform discriminant analysis on the unit hypersphere rather than in the euclidean space , which leads to a novel dimensionality reduction technique .
sentence2: motivated by the directional scattering patterns of the gmm mean supervectors , we peroform discriminant analysis on the unit hypersphere rather than in the euclidean space , leading to a novel dimensionality reduction technique ¡°sda¡± .