With　the　rapid　development　of　information　technology,　a　large　amount　of　unlabeled　high-dimensional　data　has　been　generated.　To　be　able　to　better　handle　these　data,　we　propose　a　new　self-supervised　feature　selection　algorithm　for　spectral　embedding　based　on　block　HSIC　lasso　(FSSBH).　It　innovatively　applies　the　HSIC　theoretical　approach　to　unlabeled　scenarios　for　feature　importance　assessment,　and　performs　feature　selection　by　self-supervised　learning　with　the　pseudo-label　matrix　formed　by　the　spectral　embedding.　The　algorithm　is　compared　with　five　popular　algorithms　for　classification　experiments　on　seven　publicly　available　datasets.　The　results　show　the　superior　performance　of　the　FSSBH　algorithm.　©　Published　under　licence　by　IOP　Publishing　Ltd.