Our　paper　proposes　a　new　feature　extraction　method,　named　as　robust　discriminant　analysis　(RDA),　for　data　classification　tasks.　Based　on　linear　discriminant　analysis　(LDA),　RDA　integrates　the　feature　selection　and　feature　extraction　into　a　unified　framework.　The　transformation　matrix　with　l2,1-norm　constraint　is　introduced　to　map　original　data　feature　into　a　discriminative　low-dimensional　subspace,　in　which　the　l2,1　sparsity　regularizer　can　endow　the　feature　selection　with　better　interpretability.　And,　we　use　two　different　matrices　(i.e.,　transformation　matrix　P　and　reconstruction　matrix　Q)　for　better　data　reconstruction,　which　can　provide　more　freedom　to　ensure　that　the　learned　data　representation　holds　the　main　variance　and　hence　improve　robustness　to　noises.　To　ensure　that　the　learned　features　are　optimal　for　classification,　the　structurally　incoherent　learning　is　introduced　to　add　additional　discriminant　ability　by　minimizing　the　correlation　of　different　classes.　In　other　hand,　the　between-classes　structural　incoherence　term　is　also　equivalent　to　cosine　distance　metric,　which　is　robust　to　noises　and　outliers.　An　efficient　optimization　algorithm　is　designed　to　solve　the　proposed　optimization　model.　Extensive　experiments　conducted　on　all　kinds　of　benchmark　databases　confirm　the　superiority　of　the　proposed　method.(c)　2022　Elsevier　Inc.　All　rights　reserved.