We　propose　a　data　analysis　method　that　combines　the　objectives　of　nonlinear　principal　component　analysis　and　nonlinear　discriminant　analysis　with　the　kernel　method　in　a　reproducing　kernel　Hilbert　space.　This　method　addresses　nonlinear　data　analysis　problems　in　high-dimensional　spaces,　specifically　the　reproducing　kernel　Hilbert　space,　through　the　use　of　the　kernel　trick.　Our　proposed　method　can　be　considered　as　a　semi-supervised　data　analysis　approach.　We　evaluate　our　proposed　method　using　various　kernel　functions　and　datasets,　both　visually　and　quantitatively.　The　evaluation　results　demonstrate　that　our　proposal　outperforms　kernel　principal　component　analysis　and　generalized　discriminant　analysis　in　terms　of　classification　performance.　This　indicates　the　advantages　and　originality　of　our　proposed　method.　Furthermore,　we　analyze　and　discuss　our　findings　based　on　the　evaluation　results,　and　highlight　potential　areas　for　further　research　and　future　work　related　to　our　proposal.　©　2023　IEEE.