Lower　bounded　correlation　clustering　problem　is　a　generalization　of　the　classical　correlation　clustering　problem,　which　has　many　applications　in　protein　interaction　networks,　cross-lingual　link　detection,　and　communication　networks,　etc.　In　the　lower　bounded　correlation　clustering　problem,　we　are　given　a　complete　graph　and　an　integer　L.　Each　edge　is　labelled　either　by　a　positive　sign　+　or　a　negative　sign　-　whenever　the　two　endpoints　of　the　edge　are　similar　or　dissimilar　respectively.　The　goal　of　this　problem　is　to　partition　the　vertex　set　into　several　clusters,　subject　to　an　lower　bound　L　on　the　sizes　of　clusters　so　as　to　minimize　the　number　of　disagreements,　which　is　the　total　number　of　the　edges　with　positive　labels　between　clusters　and　the　edges　with　negative　labels　within　clusters.　In　this　paper,　we　propose　the　lower　bounded　correlation　clustering　problem　and　formulate　the　problem　as　an　integer　program.　Furthermore,　we　provide　two　polynomial　time　algorithms　with　constant　approximate　ratios　for　the　lower　bounded　correlation　clustering　problem　on　some　special　graphs.