The　nonnegative　matrix　factorization　(NMF)　has　been　widely　used　because　it　can　accomplish　both　feature　representation　learning　and　dimension　reduction.　However,　there　are　two　critical　and　challenging　issues　affecting　the　performance　of　NMF　models.　One　is　the　selection　of　matrix　factorization　rank,　while　most　of　the　existing　methods　are　based　on　experiments　or　experience.　For　tackling　this　issue,　an　adaptive　and　stable　NMF　model　is　constructed　based　on　an　adaptive　factorization　rank　selection　(AFRS)　strategy,　which　skillfully　and　simply　integrates　a　row　constraint　similar　to　the　generalized　elastic　net.　The　other　is　the　sensitivity　to　the　initial　value　of　the　iteration,　which　seriously　affects　the　result　of　matrix　factorization.　This　issue　is　alleviated　by　complementing　NMF　and　deep　learning　each　other　and　avoiding　complex　network　structure.　The　proposed　NMF　model　is　called　deep　AFRS-NMF　model　for　short,　and　the　corresponding　optimization　solution,　convergence　and　stability　are　analyzed.　Moreover,　the　statistical　consistency　is　discussed　between　the　rank　obtained　by　the　proposed　model　and　the　ideal　rank.　The　performance　of　the　proposed　deep　AFRS-NMF　model　is　demonstrated　by　applying　in　genetic　data-based　tumor　recognition.　Experiments　show　that　the　factorization　rank　obtained　by　the　deep　AFRS-NMF　model　is　stable　and　superior　to　classical　and　state-of-the-art　methods.