High　dimensionality　is　quite　commonly　encountered　in　data　mining　problems,　and　hence　dimensionality　reduction　becomes　an　important　task　in　order　to　improve　the　efficiency　of　learning　algorithms.　As　a　widely　used　technique　of　dimensionality　reduction,　feature　selection　is　about　selecting　a　feature　subset　being　guided　by　certain　criterion.　In　this　paper,　three　unsupervised　feature　selection　algorithms　are　proposed　and　addressed　from　the　viewpoint　of　sparse　graph　embedding　learning.　First,　using　the　self-characterization　of　the　given　data,　we　view　the　data　themselves　as　a　dictionary,　conduct　sparse　coding　and　propose　the　sparsity　preserving　feature　selection　(SPFS)　algorithm.　Second,　considering　the　locality　preservation　of　neighborhoods　for　the　data,　we　study　a　special　case　of　the　SPFS　problem,　namely,　neighborhood　preserving　feature　selection　problem,　and　come　up　with　a　suitable　algorithm.　Third,　we　incorporate　sparse　coding　and　feature　selection　into　one　unified　framework,　and　propose　a　neighborhood　embedding　feature　selection　(NEFS)　criterion.　Drawing　support　from　nonnegative　matrix　factorization,　the　corresponding　algorithm　for　NEFS　is　presented　and　its　convergence　is　proved.　Finally,　the　three　proposed　algorithms　are　validated　with　the　use　of　eight　publicly　available　real-world　datasets　from　machine　learning　repository.　Extensive　experimental　results　demonstrate　the　superiority　of　the　proposed　algorithms　over　four　compared　state-of-the-art　unsupervised　feature　selection　methods.