Mathematical Problems in Engineering / 2016 / Article / Proc 1

Research Article

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.

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