Massive　volumes　of　high-dimensional　data　that　evolve　over　time　are　continuously　collected　by　contemporary　information　processing　systems,　which　bring　up　the　problem　of　organizing　these　data　into　clusters,　i.e.　achieving　the　purpose　of　dimensional　reduction,　and　meanwhile　learning　their　temporal　evolution　patterns.　In　this　paper,　a　framework　for　evolutionary　subspace　clustering,　referred　to　as　LSTM-ESCM,　is　introduced,　which　aims　at　clustering　a　set　of　evolving　high-dimensional　data　points　that　lie　in　a　union　of　low-dimensional　evolving　subspaces.　In　order　to　obtain　the　parsimonious　data　representation　at　each　time　step,　we　propose　to　exploit　the　so-called　self-expressive　trait　of　the　data　at　each　time　point.　At　the　same　time,　LSTM　networks　are　implemented　to　extract　the　inherited　temporal　patterns　behind　data　in　the　overall　time　frame.　An　efficient　algorithm　has　been　proposed.　Numerous　experiments　are　carried　out　on　real-world　datasets　to　demonstrate　the　effectiveness　of　our　proposed　approach.　The　results　show　that　the　suggested　algorithm　dramatically　outperforms　other　known　similar　approaches　in　terms　of　both　run　time　and　accuracy.