In　this　paper,　the　phase　space　reconstruction　of　time　series　produced　by　different　instruments　is　discussed　based　on　the　nonlinear　dynamic　theory.　The　dense　ratio,　a　novel　quantitative　recurrence　parameter,　is　proposed　to　describe　the　difference　of　wind　instruments,　stringed　instruments　and　keyboard　instruments　in　the　phase　space　by　analyzing　the　recursive　property　of　every　instrument.　Furthermore,　a　novel　supervised　learning　algorithm　for　automatic　classification　of　individual　musical　instrument　signals　is　addressed　deriving　from　the　idea　of　supervised　non-negative　matrix　factorization　(NMF)　algorithm.　In　our　approach,　the　orthogonal　basis　matrix　could　be　obtained　without　updating　the　matrix　iteratively,　which　NMF　is　unable　to　do.　The　experimental　results　indicate　that　the　accuracy　of　the　proposed　method　is　improved　by　3%　comparing　with　the　conventional　features　in　the　individual　instrument　classification.