As　a　widely　used　method　in　signal　processing,　Principal　Component　Analysis　(PCA)　performs　both　the　compression　and　the　recovery　of　high　dimensional　data　by　leveraging　the　linear　transformations.　Considering　the　robustness　of　PCA,　how　to　discriminate　correct　samples　and　outliers　in　PCA　is　a　crucial　and　challenging　issue.　In　this　paper,　we　present　a　general　model,　which　conducts　PCA　via　a　non-decreasing　concave　regularized　minimization　and　is　termed　PCA-NCRM　for　short.　Different　from　most　existing　PCA　methods,　which　learn　the　linear　transformations　by　minimizing　the　recovery　errors　between　the　recovered　data　and　the　original　data　in　the　least　squared　sense,　our　model　adopts　the　monotonically　non-decreasing　concave　function　to　enhance　the　ability　of　model　in　distinguishing　correct　samples　and　outliers.　To　be　specific,　PCA-NCRM　enlarges　the　attention　to　samples　with　smaller　recovery　errors　and　diminishes　the　attention　to　samples　with　larger　recovery　errors　at　the　same　time.　The　proposed　minimization　problem　can　be　efficiently　addressed　by　employing　an　iterative　re-weighting　optimization.　Experimental　results　on　several　datasets　show　the　effectiveness　of　our　model.