Multi-view　clustering　aims　to　exploit　information　from　data　described　by　various　views　to　optimize　clustering　performance.　Multi-view　clustering　methods　based　on　deep　matrix　factorization　are　capable　of　extracting　intrinsic　category　information　from　data　that　contains　a　variety　of　knowledge.　And　the　optimization　process　of　deep　matrix　factorization　suffers　from　several　constraints.　To　address　these　issues,　this　paper　proposes　a　multi-view　clustering　model　via　deep　matrix　factorization　smoothed　by　local　geometrical　loss.　Based　on　the　assumption　that　samples　close　in　original　space　are　more　likely　to　be　in　the　same　category,　the　local　geometrical　information　is　preserved　during　the　training　process　of　deep　matrix　factorization　by　maximizing　the　conditional　distribution　on　the　graphs　built　by　different　views.　Then,　inspired　by　the　connection　between　deep　auto-encoder　and　deep　matrix　factorization,　we　leverage　a　deep　auto-encoder　based　solution　to　handle　the　optimization　of　the　objective　function.　By　adding　an　activation　function　to　each　layer　of　deep　auto-encoders,　the　nonnegativity　of　features　output　from　layers　in　deep　matrix　factorization　is　strictly　guaranteed　during　the　training　process.　Finally,　we　conduct　extensive　experiments　on　four　datasets　to　validate　that　the　proposed　method　is　superior　to　state-of-the-arts.　©　2022　IEEE.