In　wireless　sensor　network　(WSN),　the　centralized　learning　method　by　transmitting　all　training　samples　scattered　across　different　sensor　nodes　to　a　centralized　data　center　to　train　classifier　will　significantly　increase　the　communication　cost.　To　decrease　the　communication　cost　in　transmitting　training　samples,　a　distributed　learning　method　for　kernel　minimum　squared　error　(KMSE)　by　incorporating　L1　regularized　term　was　studied,　which　just　relies　on　in-network　processing　between　single-hop　neighboring　nodes.　Each　node　obtains　its　local　optimum　sparse　model　by　constructing　the　optimization　problem　of　L1　regularized　KMSE　based　on　its　local　training　samples　and　solving　it　using　parallel　projections　and　alternating　the　direction　method　of　multipliers,　then　a　consistent　model　is　achieved　on　all　nodes　by　using　the　global　average　consensus　algorithm.　For　carrying　out　this　method,　a　new　distributed　training　algorithm　for　L1-regularized　kernel　minimum　squared　error　based　on　parallel　projections　(L1-DKMSE-PP)　was　proposed.　Simulations　show　that　L1-DKMSE-PP　can　obtain　almost　the　same　prediction　accuracy　as　that　of　the　centralized　counterpart　and　a　sparser　model,　and　more　importantly,　it　can　significantly　reduce　the　communication　cost.　©　2016,　Editorial　Department　of　Journal　of　Beijing　University　of　Posts　and　Telecommunications.　All　right　reserved.