Dimensionality　reduction　aims　at　reducing　redundant　information　in　big　data　and　hence　making　data　analysis　more　efficient.　Resource-constrained　enterprises　or　individuals　often　outsource　this　time-consuming　job　to　the　cloud　for　saving　storage　and　computing　resources.　However,　due　to　inadequate　supervision,　the　privacy　and　security　of　outsourced　data　have　been　a　serious　concern　to　data　owners.　In　this　paper,　we　propose　a　privacy　preserving　and　verifiable　outsourcing　scheme　for　data　dimension　reduction,　based　on　incremental　Non-negative　Matrix　Factorization　(NMF)　method.　We　emphasize　the　importance　of　incremental　data　processing,　exploiting　the　properties　of　NMF　to　enable　data　dynamics　in　consideration　of　data　updating　in　reality.　Besides,　our　scheme　can　also　maintain　data　confidentiality　and　provide　verifiability　of　the　computation　result.　Experiment　evaluation　has　shown　that　the　proposed　scheme　achieves　high　efficiency,　saving　about　more　than　80%　computation　time　for　clients.　(c)　2021　Elsevier　Inc.　All　rights　reserved.