Due　to　limited　resources　in　wireless　sensor　nodes,　energy　efficiency　is　considered　as　one　of　the　primary　constraints　in　the　design　of　the　topology　of　wireless　sensor　networks　(WSNs).　Since　data　that　are　collected　by　wireless　sensor　nodes　exhibit　the　characteristics　of　temporal　association,　data　fusion　has　also　become　a　very　important　means　of　reducing　network　traffic　as　well　as　eliminating　data　redundancy　as　far　as　data　transmission　is　concerned.　Another　reason　for　data　fusion　is　that,　in　many　applications,　only　some　of　the　data　that　are　collected　can　meet　the　requirements　of　the　sink　node.　In　this　paper,　we　propose　a　method　to　calculate　the　number　of　cluster　heads　or　data　aggregators　during　data　fusion　based　on　the　rate-distortion　function.　In　our　discussion,　we　will　first　establish　an　energy　consumption　model　and　then　describe　a　method　for　calculating　the　number　of　cluster　heads　from　the　point　of　view　of　reducing　energy　consumption.　We　will　also　show　through　theoretical　analysis　and　experimentation　that　the　network　topology　design　based　on　the　rate-distortion　function　is　indeed　more　energy-efficient.