Clustering　plays　a　crucial　role　in　the　field　of　data　mining,　where　deep　non-negative　matrix　factorization　(NMF)　has　attracted　significant　attention　due　to　its　effective　data　representation.　However,　deep　matrix　factorization　based　on　autoencoder　is　typically　constructed　using　multi-layer　matrix　factorization,　which　ignores　nonlinear　mapping　and　lacks　learning　rate　to　guide　the　update.　To　address　these　issues,　this　paper　proposes　an　autoencoder-like　deep　NMF　representation　learning　(ADNRL)　algorithm　for　clustering.　First,　according　to　the　principle　of　autoencoder,　construct　the　objective　function　based　on　NMF.　Then,　decouple　the　elements　in　the　matrix　and　apply　the　nonlinear　activation　function　to　enforce　non-negative　constraints　on　the　elements.　Subsequently,　the　gradient　values　corresponding　to　the　elements　update　guided　by　the　learning　rate　are　transformed　into　the　weight　values.　This　weight　values　are　combined　with　the　activation　function　to　construct　the　ADNRL　deep　network,　and　the　objective　function　is　minimized　through　the　learning　of　the　network.　Finally,　extensive　experiments　are　conducted　on　eight　datasets,　and　the　results　demonstrate　the　superior　performance　of　ADNRL.　©　2024　Elsevier　B.V.