IN: a series of th order tensors, ,   .
OUT: Matrices ( ,   ) with orthogonal column vectors.
 (1) Initial values: and whose columns are determined as the first
leading eigenvectors of the matrices .
 (2) Iterate for until convergence
  (i) Maximize ,  
   Solution: whose columns are determined as the first leading
   eigenvectors of
   Set .
  (ii) Maximize ,  
      Solution: whose columns are determined as the first leading
      eigenvectors of
      Set .
      
  (iii) Maximize ,
      
      Solution: whose columns are determined as the first leading
      eigenvectors of
      Set .
      
  (iv) Maximize ,  
      Solution: whose columns are determined as the first leading
      eigenvectors of
      Set .
  
 (3) Set ,   .
Algorithm 1: GND-PCA.