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Manifold Guided Tensor Completion under Low-rank Structure

We make a breakthrough in two limited cases of current tensor completion methods!
  • Very sparse observations (missing data rate>90%); and
  • The desired tensor is not of exactly low-rank.

......Solving tensor completion is closely related to ubiquitous missing data problems if we represent our data by tensor. Existing methods assume the desired tensor's rank is low to circumvent the ill-posed problem. By contrast, 
  • We leverage rank minimization technique to estimate the tensor's rank in Tucker decomposition.  
  • We advocate using manifold priors, which come from the relation of data semantics and can be formally characterized by Tucker model factors, to guide the optimal solution.