The　long-term　safe　operation　of　rotating　machinery　is　closely　related　to　the　stability　of　rolling　bearings.　This　paper　proposes　a　rolling　bearing　fault　diagnosis　method　based　on　refined　composite　multiscale　fuzzy　entropy　(RCMFE),　topology　learning　and　out-of-sample　embedding　(TLOE),　and　the　marine　predators　algorithm　based-support　vector　machine　(MPA-SVM).　First,　the　RCMFE　algorithm　is　used　to　extract　the　features　of　the　original　rolling　bearing　fault　signal　and　to　construct　the　original　high-dimensional　fault　feature　set.　Then,　TLOE　is　used　to　reduce　the　dimensionality　of　the　high-dimensional　fault　feature　set.　The　low-dimensional　sensitive　fault　features　are　extracted　to　construct　a　low-dimensional　fault　feature　subset.　Finally,　fault-type　discrimination　is　performed　using　the　MPA-SVM.　The　Case　Western　Reserve　University　dataset　and　data　from　fault　diagnosis　experiments　performed　on　1210　self-aligning　ball　bearings　were　used　to　verify　the　proposed　method.　The　results　demonstrate　the　effectiveness　of　the　fault　diagnosis　method,　which　can　diagnose　bearing　faults　with　up　to　100%　accuracy.　©　2021　Elsevier　Ltd