Data　representation　aims　at　learning　an　efficient　low-dimensional　representation,　which　is　always　a　challenging　task　in　machine　learning　and　computer　vision.　It　can　largely　improve　the　performance　of　specific　learning　tasks.　Unsupervised　methods　are　extensively　applied　to　data　representation,　which　considers　the　internal　connection　among　data.　Most　of　existing　unsupervised　models　usually　use　a　specific　norm　to　favor　certain　distributions　of　the　input　data,　leading　to　an　unsustainable　encouraging　performance　for　given　learning　tasks.　In　this　paper,　we　propose　an　efficient　data　representation　method　to　address　large-scale　feature　representation　problems,　where　the　deep　random　walk　of　unitary　invariance　is　exploited　for　learning　discriminative　features.　First,　the　data　representation　is　formulated　as　deep　random　walk　problems,　where　unitarily　invariant　norms　are　employed　to　capture　diverse　beneficial　perspectives　hidden　in　the　data.　It　is　embedded　into　a　state　transition　matrix　model,　where　an　arbitrary　number　of　transition　steps　is　available　for　an　accurate　affinity　evaluation.　Second,　data　representation　problems　are　then　transformed　as　high-order　matrix　factorization　tasks　with　unitary　invariance.　Third,　a　closed-form　solution　is　proved　for　the　formulated　data　representation　problem,　which　may　provide　a　new　perspective　for　solving　high-order　matrix　factorization　problems.　Finally,　extensive　comparative　experiments　are　conducted　in　publicly　available　real-world　data　sets.　In　addition,　experimental　results　demonstrate　that　the　proposed　method　achieves　better　performance　than　other　compared　state-of-the-art　approaches　in　terms　of　data　clustering.　(C)　2020　Elsevier　Inc.　All　rights　reserved.