in this talk, i will present several works related to tensor data analysis. firstly, hypergraph matching (hgm) is a popular tool in establishing corresponding relationship between two sets of points, which becomes a central problem in computer vision. we reformulate hgm as a sparse constrained model, and show its relaxation problem can also recover the global optimizer. a quadratic penalty method is presented to solve the relaxation model. secondly, the analytic connectivity (ac) is an important quantity in spectral hypergraph theory. the definition of ac involves a series of polynomial optimization problem (pop). the number of pops can be reduced by the structure of hypergraphs. further, we proposed a simplex constrained model, a equality constrained model and a sparse constrained model for computing ac under different situations. thirdly, identifying new indications for known drugs, i.e., drug repositioning (dr), attracts a lot of attentions in bioinformatics. we develop a novel method for dr based on projection onto convex sets.