The　emerging　low　rank　matrix　approximation　(LRMA)　method　provides　an　energy　efficient　scheme　for　data　collection　in　wireless　sensor　networks　(WSNs)　by　randomly　sampling　a　subset　of　sensor　nodes　for　data　sensing.　However,　the　existing　LRMA　based　methods　generally　underutilize　the　spatial　or　temporal　correlation　of　the　sensing　data,　resulting　in　uneven　energy　consumption　and　thus　shortening　the　network　lifetime.　In　this　paper,　we　propose　a　correlated　spatio-temporal　data　collection　method　for　WSNs　based　on　LRMA.　In　the　proposed　method,　both　the　temporal　consistence　and　the　spatial　correlation　of　the　sensing　data　are　simultaneously　integrated　under　a　new　LRMA　model.　Moreover,　the　network　energy　consumption　issue　is　considered　in　the　node　sampling　procedure.　We　use　Gini　index　to　measure　both　the　spatial　distribution　of　the　selected　nodes　and　the　evenness　of　the　network　energy　status,　then　formulate　and　resolve　an　optimization　problem　to　achieve　optimized　node　sampling.　The　proposed　method　is　evaluated　on　both　the　simulated　and　real　wireless　networks　and　compared　with　state-of-the-art　methods.　The　experimental　results　show　the　proposed　method　efficiently　reduces　the　energy　consumption　of　network　and　prolongs　the　network　lifetime　with　high　data　recovery　accuracy　and　good　stability.