A Novel Hierarchical Clustering Approach Based on Universal Gravitation

Algorithm 1

CreateGravGraph (X, k, γ).

	Input: X: the data set. k: the number of data points with top k gravitational force. γ: the cutoff distance used to determine the mass of each point.
	Output: G: the sparse gravitational graph.
(1)	Scale the data set X using a feature transformation technique;
(2)	Calculate the Euler distance between any two data points i and j in the data set X;
(3)	Calculate the mass of any data point i in the data set X by equation (3);
(4)	Calculate the data gravitational force between any two data points i and j in the data set X;
(5)	Initialize the sparse gravitational graph . And set and ;
(6)	for each data point x in X do
(7)	Assign the mass of x as the weight of the corresponding vertex in V;
(8)	Select data points with the top k data gravitation exerted on data point x;
(9)	for to k do
(10)	Insert the edges into the set E;
(11)	Assign the data gravitational force of x and as the weight of the edge ;
(12)	end
(13)	Calculate the gravitational resultant force of data point x by equation (4) as the corresponding vertex in V;
(14)	end
(15)	return the sparse gravitational graph G;