In　the　Intelligent　Transportation　System　(ITS),　loss　of　traffic　data　seriously　influences　the　accuracy　of　decision-making　of　urban　traffic　planning　and　management.　To　solve　this　vital　challenge,　we　introduce　a　new　algebraic　framework　for　tensor　decompositions　with　different　representation　of　tensor　rank　for　traffic　missing　data　imputation.　We　propose　a　novel　tensor　completion　algorithm　by　using　tensor　factorization　and　introduce　a　spatial-Temporal　regularized　constraint　into　the　algorithm　to　improve　the　imputation　performance.　The　simulation　results　with　real　traffic　dataset　demonstrate　that　the　proposed　algorithm　can　significantly　improve　the　performance　in　terms　of　recovery　accuracy　compared　with　other　tensor　completion　algorithms　under　different　data　missing　patterns　at　all　data　loss　rates.　This　also　indicates　that　the　proposed　algorithm　is　more　efficient　for　missing　traffic　data　imputation　by　exploiting　such　an　algebraic　framework　than　the　traditional　multilinear　algebraic　framework　for　tensor　decompositions.　©　2018　IEEE.