Topological　Data　Analysis　(TDA)　is　a　rising　and　burgeoning　field　of　data　science,　which　provides　a　set　of　new　topological　and　geometric　tools　to　extract　relevant　features　out　of　complex　high-dimensional　data.　In　this　paper,　we　mainly　study　two　papers:　Topological　Data　Analysis　of　Time　Series　Data　for　B2B　Customer　Relationship　Management　[1];　An　Introduction　to　a　New　Text　Classification　and　Visualization　for　Natural　Language　Processing　Using　Topological　Data　Analysis　[2].　We　briefly　introduce　the　topological　concepts　involved　in　the　two　cases,　then　compare　and　analyze　the　corresponding　topological　solutions.　Accordingly,　we　summarize　the　advantages　of　TDA　and　finally　draw　a　conclusion　with　some　improvements　to　optimize　them.　©　Published　under　licence　by　IOP　Publishing　Ltd.