As　one　of　the　fundamental　research　issues,　feature　selection　plays　a　critical　role　in　machine　learning.　By　the　removal　of　irrelevant　features,　it　attempts　to　reduce　computational　complexities　of　upstream　tasks,　usually　with　computation　accelerations　and　performance　improvements.　This　paper　proposes　an　auto-encoder　based　scheme　for　unsupervised　feature　selection.　Due　to　the　inherent　consistency,　this　framework　can　solve　traditional　constrained　feature　selection　problems　approximately.　Specifically,　the　proposed　model　takes　non-negativity,　orthogonality,　and　sparsity　into　account,　whose　internal　characteristics　are　exploited　sufficiently.　It　can　also　employ　other　loss　functions　and　flexible　activation　functions.　The　former　can　fit　a　wide　range　of　learning　tasks,　and　the　latter　has　the　ability　to　play　the　role　of　regularization　terms　to　impose　regularization　constraints　on　the　model.　Thereinafter,　the　proposed　model　is　validated　on　multiple　benchmark　datasets,　where　various　activation　and　loss　functions　are　analyzed　for　finding　better　feature　selectors.　Finally,　extensive　experiments　demonstrate　the　superiority　of　the　proposed　method　against　other　compared　state-of-the-arts.　©　2021　Elsevier　B.V.