Metric　learning　algorithms　have　been　widely　applied　for　hyperspectral　image　(HSI)　dimensionality　reduction　and　classification.　One　of　the　metric　learning　algorithms　proposed　recently　is　discriminative　locality　alignment　(DLA).　The　DLA　attacks　the　distribution　nonlinearity　of　samples,　and　preserves　the　discriminative　ability.　However,　the　DLA　needs　to　manually　adjust　a　parameter　called　scaling　factor　and　produce　mutually　correlated　discriminant　vectors　that　may　lead　to　unsatisfactory　classification　results.　In　this　letter,　a　modified　DLA　algorithm,　i.e.,　quotient　DLA　(QDLA),　is　proposed　to　solve　the　problems　outlined　previously.　Moreover,　we　extend　QDLA　to　a　novel　exponential　DLA　(EDLA)　algorithm,　which　can　achieve　a　more　effective　transformation　from　a　nonlinear　mapping　of　original　data　into　a　new　space.　The　classification　results　with　HSIs　demonstrate　that　the　performances　of　the　proposed　EDLA　are　better　than　other　related　methods.