VIASCKDE Index: A Novel Internal Cluster Validity Index for Arbitrary-Shaped Clusters Based on the Kernel Density Estimation

Algorithm 1

VIASCKDE Index.

	Input; X, labels
	Output; VIASCKDE
	KDE_X←Gaussian_KDE(X.T)
	for k = 1 to size (unique (labels)) do
	data_of_Cluster_k←X[labels = k]   ►data belongs to cluster k
	data_not_belong_k_X[labels ≠ k]   ►data not belongs to cluster k
	kde_k←MinMaxNormalization (KDE_X [labels = k]) ►KDE of each
	►data of cluster k and normalize them
	for i = 1 to size (data_of_k)do
	ai ← closed_data (data_of_cluster_k)  ►distance from i^thdata
	►to closed one in Cluster k
	bi ← closed_data (k_ait_olmagan_verileri)  ►distance from i^th
	►data to closest one that does not in the cluster k
	CoSeDi = kde_k[i][(bi−ai)/max(ai, bi0)]  ►Compactness and
	►Separation of data i
	CoSeCk = mean (CoSeDk)   ►Compactness-separation of Cluster k
	VIASCKDE =    ►Overall VIASCKDE value of Clustering