In　wireless　sensor　networks,　classification　and　regression　are　very　fundamental　tasks.　To　reduce　and　balance　the　energy　consumption　of　nodes　during　training　classifiers　or　regression　machines,　a　distributed　incremental　learning　problem　of　kernel　machine　by　using　1-norm　regularization　is　studied,　and　an　energy-balanced　distributed　learning　algorithm　for　the　sparse　kernel　machine　is　proposed.　In　this　proposal,　a　novel　incremental　learning　algorithm　and　an　energy-balanced　node　selection　strategy　that　takes　into　account　the　residual　energy　of　node,　the　number　of　been　accessed　and　the　neighbors　number　of　node　are　used.　Simulation　results　show　that　this　proposal　can　obtain　pretty　consistent　prediction　correct　rate　with　the　batch　learning　algorithm,　and　it　can　get　a　very　simple　model.　Meanwhile,　it　has　significant　advantages　with　respect　to　the　communication　costs　and　the　iterations.　Moreover,　it　can　reduce　and　balance　the　energy　consumption　of　nodes.