The　great　advances　in　mobile　devices　make　it　critical　to　exploit　multiple　auxiliary　information　for　efficient　point　-of-interest　(POI)　recommendations.　However,　most　existing　methods　can　neither　effectively　address　the　extreme　data　sparsity　encountered　in　temporal-aware　recommendation　nor　reasonably　deal　with　implicit　feedback.　Furthermore,　previous　methods,　including　those　relying　on　similarity　measurement,　cannot　capture　the　intrinsic　data　correlations　exhibited　in　the　sparse　data.　To　remedy　these　drawbacks,　this　paper　proposes　a　temporal-aware　personalized　recommendation　framework　called　Temporal　Spatial　Popularity　and　Temporal-aware　Matrix　Factorization　(TeSP-TMF).　In　TeSP-TMF,　we　present　the　potential　preferences　model　and　temporal-aware　matrix　factorization　model.　Specifically,　users＇　potential　preferences　that　incorporate　temporal,　spatial,　and　popularity　information　are　investigated　to　learn　a　set　of　potential　POIs　for　each　user,　which　are　filled　into　the　original　matrix　for　further　matrix　factorization,　owing　to　the　sparse　nature　of　the　rating　matrix.　On　this　basis,　we　develop　a　new　approach　using　a　combination　of　grey　relational　analysis　and　matrix　factorization,　which　not　only　relieves　data　scarcity　caused　by　dividing　the　matrix　with　time　slots　but　also　strategically　mines　inherent　temporal　relation-ships.　Finally,　we　implement　extensive　experiments　on　two　public　datasets　collected　from　Foursquare　and　Yelp.　Experimental　results　demonstrate　that　our　proposed　method　yields　competitive　quality　compared　to　several　state-of-the-art　methods.　Theoretically,　our　work　contributes　promising　insights　for　mitigating　data　sparsity.　In　practice,　our　results　can　enhance　personalized　temporal-aware　POI　recommendation　services　for　location-based　social　networks.