In　this　paper,　we　consider　the　Bregman　k-means　problem　(BKM)　which　is　a　variant　of　the　classical　k-means　problem.　For　an　n-point　set　S　and　k　＜=　n　with　respect　to　mu-similar　Bregman　divergence,　the　BKM　problem　aims　first　to　find　a　center　subset　C　subset　of　S　with　vertical　bar　C　vertical　bar=　k　and　then　separate　S　into　k　clusters　according　to　C,　such　that　the　sum　of　mu-similarBregman　divergence　from　each　point　in　S　to　its　nearest　center　is　minimized.　We　propose　a　mu-similar　BregMeans++　algorithm　by　employing　the　local　search　scheme,　and　prove　that　the　algorithm　deserves　a　constant　approximation　guarantee.　Moreover,　we　extend　our　algorithm　to　solve　a　variant　of　BKM　called　noisy　mu-similar　Bregman　k-means++　(noisy　mu-BKM++)　which　is　BKM　in　the　noisy　scenario.　For　the　same　instance　and　purpose　as　BKM,　we　consider　the　case　of　sampling　a　point　with　an　imprecise　probability　by　a　factor　between　1-　epsilon(1)　and　1+　epsilon(2)　for　epsilon(1)　is　an　element　of　epsilon[0,　1)　and　epsilon(2)　＞=　0,　and　obtain　an　approximation　ratio　of　O(log(2)　k)　in　expectation.