Peculiarity　oriented　mining　(POM),　aiming　to　discover　peculiarity　rules　hidden　in　a　dataset,　is　a　new　data　mining　method.　In　the　past　few　years,　many　results　and　applications　on　POM　have　been　reported.　However,　there　is　still　a　lack　of　theoretical　analysis.　In　this　paper,　we　prove　that　the　peculiarity　factor　(PF),　one　of　the　most　important　concepts　in　POM,　can　accurately　characterize　the　peculiarity　of　data　with　respect　to　the　probability　density　function　of　a　normal　distribution,　but　is　unsuitable　for　more　general　distributions.　Thus,　we　propose　the　concept　of　local　peculiarity　factor　(LPF).　It　is　proved　that　the　LPF　has　the　same　ability　as　the　PF　for　a　normal　distribution　and　is　the　so-called　ν-sensitive　peculiarity　description　for　general　distributions.　To　demonstrate　the　effectiveness　of　the　LPF,　we　apply　it　to　outlier　detection　problems　and　give　a　new　outlier　detection　algorithm　called　LPF-Outlier.　Experimental　results　show　that　LPF-Outlier　is　an　effective　outlier　detection　algorithm.　©　2008　ACM.