In　machine　learning　and　data　mining　applications,　clustering　is　a　critical　task　for　knowledge　discovery　that　attract　attentions　from　large　quantities　of　researchers.　Generally,　with　the　help　of　label　information,　supervised　learning　methods　have　more　flexible　structure　and　better　result　than　unsupervised　learning.　However,　supervised　learning　is　infeasible　for　clustering　task.　In　this　paper,　to　fill　the　gap　between　clustering　and　supervised　learning,　the　proposed　clustering　methods　introduce　the　exemplars　discriminative　information　into　a　supervised　learning.　To　build　the　effective　objective　function,　a　strategy　for　reducing　intracluster　distance　and　increasing　intercluster　distance　is　introduced　to　form　a　unified　optimization　objective　function.　With　initially　setting　the　clustering　centers,　the　data　that　near　the　centers　are　selected　as　exemplars　to　indicate　the　ground　truth　of　different　classes.　Discriminative　learning　is　then　introduced　to　learn　the　partition　hyperplane　and　classify　all　the　data　into　different　classes.　New　clustering　centers　are　calculated　for　selecting　new　exemplars　alternately.　Using　the　proposed　algorithms,　the　unsupervised　K-means　clustering　problem　is　effectively　solved　from　the　perceptive　of　optimization.　Feature　mapping　is　also　introduced　to　improve　the　performance　by　reducing　the　intercluster　distance.　A　novel　framework　for　exploring　discriminative　information　from　unsupervised　data　is　provided.　The　proposed　algorithms　outperform　the　state-of-the-art　approaches　on　a　wide　range　of　benchmark　datasets　in　terms　of　accuracy.