Symmetry Based Automatic Evolution of Clusters: A New Approach to Data Clustering

Algorithm 1

Point assignment based on proposed line symmetry distance.

Procedure: Point assignment based on proposed line symmetry distance( )

for = 1 to do

 for = 1 to do

  Find the first and the second symmetrical points and of relative to a

  projected point on line of cluster /To ensure the closure property /

  Calculate the line symmetry-based distance

 end for

 Find =

 if , where , = 1, …, and then

  Assign the point to the cluster

  Else

    Assign the point to the cluster based on the Euclidean distance measure, =

 end if

end for

Compute new cluster centers of the clusters as follows:

                 ,

where is the number of data points belonging to the cluster and is set of data

points which have been assigned to the cluster center .