Feature　selection　plays　a　critical　role　in　many　machine　learning　applications　as　it　effectively　addresses　the　challenges　posed　by　“the　curse　of　dimensionality”　and　enhances　the　generalization　capability　of　trained　models.　However,　existing　approaches　for　multi-class　feature　selection　(MFS)　often　combine　sparse　regularization　with　a　simple　classification　model,　such　as　least　squares　regression,　which　can　result　in　suboptimal　performance.　To　address　this　limitation,　this　paper　introduces　a　novel　MFS　method　called　Sparse　Softmax　Feature　Selection　(S2FS).　S2FS　combines　a　l2,0-norm　regularization　with　the　Softmax　model　to　perform　feature　selection.　By　utilizing　the　l2,0-norm,　S2FS　produces　a　more　precise　sparsity　solution　for　the　feature　selection　matrix.　Additionally,　the　Softmax　model　improves　the　interpretability　of　the　model’s　outputs,　thereby　enhancing　the　classification　performance.　To　further　enhance　discriminative　feature　selection,　a　discriminative　regularization,　derived　based　on　linear　discriminate　analysis　(LDA),　is　incorporated　into　the　learning　model.　Furthermore,　an　efficient　optimization　algorithm,　based　on　the　alternating　direction　method　of　multipliers　(ADMM),　is　designed　to　solve　the　objective　function　of　S2FS.　Extensive　experiments　conducted　on　various　datasets　demonstrate　that　S2FS　achieves　higher　accuracy　in　classification　tasks　compared　to　several　contemporary　MFS　methods.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2024.