Sectorization and Configuration Transition in Airspace Design

Procedure 1

Procedures of the method based on the NSCA.

()   Input , and desired cluster number, .

()   Prune and by deleting rows and columns where . Define the pruned matrices

     as and . Define the set of deleted vertices as where and the set of

     remained vertices as . Define the dimension of and as .

()   Calculate the Laplacian matrix, .

()   Compute the normalized Laplacian matrix, .

()   Compute the eigenvector corresponding to the smallest eigenvalues of .

()   Construct a matrix , each of its column corresponds to the eigenvector of one of the

      smallest eigenvalue.

()   Normalize every row of , meaning normalizing into ,

     , where and stand for the th row of and respectively,

     is the element at the th row and th column of .

()   For each row of , set a corresponding vector   .

()   Cluster vectors into clusters using k-means cluster. The index of the

      cluster for each row is the index of the sector for the th vertex of .

() For any vertex in , assign it to the sector to which its nearest vertex in belongs.