In　wireless　sensor　networks,　centralized　learning　methods　have　very　high　communication　costs　and　energy　consumption.　These　are　caused　by　the　need　to　transmit　scattered　training　samples　from　various　sensor　nodes　to　the　central　fusion　center　where　a　classifier　or　a　regression　machine　is　trained　by　batch　learning　with　all　training　samples.　To　decrease　the　communication　costs　and　energy　consumption,　a　distributed　learning　problem　of　kernel　machine　by　incorporating　1　norm　regularization　is　investigated,　and　a　novel　distributed　incremental　learning　algorithm　for　the　1regularized　kernel　minimum　mean　squared　error　(KMSE)　machine　is　proposed.　The　proposed　algorithm　relies　on　the　incremental　learning　method　and　the　collaboration　between　single-hop　neighboring　nodes　based　on　Markov　Chains　Theory.　This　paper　evaluates　the　proposed　algorithm　with　respect　to　the　prediction　accuracy,　the　sparse　rate　of　model　and　the　communication　costs　on　synthetic　and　real　datasets.　The　simulation　results　show　that　the　proposed　algorithm　can　obtain　approximately　the　same　prediction　accuracy　as　that　obtained　by　the　batch　learning　method　and　the　current　state-of-the-art　distributed　algorithms.　Moreover,　it　is　significantly　superior　in　terms　of　the　sparse　rate　of　model　and　communication　costs.　©　2017　ACM.