A Rank-Constrained Matrix Representation for Hypergraph-Based Subspace Clustering

Algorithm 1

Rank-constrained matrix representation.

Input: Data matrix   , desired rank   , parameter  

Output: ,

Initialization: , , , , ,

While! (  and  ) and   do

Step  1. low-rank part update

   ,

   For    do

    , ,

    If  , return  ;

      ;

   End For

Step  2. sparse part update

   set ;

   shrink each column of with soft-threshold

   where is the th column of .

Step  3. dictionary update

   Equation (10);

  ;

End While