Comparison of hierarchical cluster analysis methods by cophenetic correlation

Saraçli, Sinan; Doğan, Nurhan; Doğan, İsmet

doi:10.1186/1029-242X-2013-203

Journal of Inequalities and Applications

Table 2 The cophenetic correlation coefficient values for $μ = 0$ , $σ^{2} = 1$ (with outliers)

From: Comparison of hierarchical cluster analysis methods by cophenetic correlation

Distance measure	Clustering method	Cophenetic correlation coefficient
		$x = 3$			$x = 5$			$x = 10$
		$n = 10$	$n = 50$	$n = 100$	$n = 10$	$n = 50$	$n = 100$	$n = 10$	$n = 50$	$n = 100$
Euclidean	Average	*0.8478*	*0.8065*	0.7848	*0.8280*	*0.7818*	0.7629	*0.8102*	*0.7647*	0.7488
	Centroid	0.8188	0.8061	*0.7875*	0.7872	0.7816	*0.7704*	0.7484	0.7638	*0.7606*
	Complete	0.8095	0.7273	0.7006	0.7808	0.6865	0.6551	0.7535	0.6494	0.6136
	Median	0.8342	0.7644	0.7262	0.8073	0.7509	0.7182	0.7661	0.7432	0.7311
	Single	0.8168	0.7836	0.7774	0.7903	0.7582	0.7578	0.7653	0.7400	0.7426
	Ward	0.8064	0.7278	0.7050	0.7801	0.6869	0.6606	0.7531	0.6464	0.6161
	Weighted	0.8382	0.7551	0.7185	0.8182	0.7352	0.6918	0.8006	0.7197	0.6835
Squared Euclidean	Average	*0.8434*	0.8088	0.7859	*0.8239*	0.7837	0.7636	*0.8087*	0.7663	0.7490
	Centroid	0.8386	*0.8107*	*0.7900*	0.8123	*0.7880*	*0.7730*	0.7768	*0.7695*	*0.7629*
	Complete	0.8022	0.7331	0.7027	0.7724	0.6937	0.6580	0.7505	0.6550	0.6166
	Median	0.8289	0.7652	0.7275	0.8017	0.7525	0.7177	0.7637	0.7417	0.7313
	Single	0.8142	0.7838	0.7774	0.7865	0.7584	0.7575	0.7633	0.7397	0.7424
	Ward	0.7996	0.7337	0.7070	0.7725	0.6929	0.6645	0.7506	0.6532	0.6191
	Weighted	0.8333	0.7592	0.7197	0.8141	0.7358	0.6956	0.7997	0.7192	0.6824
Mahalanobis	Average	*0.8103*	*0.8565*	0.8315	*0.6965*	0.8239	0.8053	*NaN*	0.7705	0.7782
	Centroid	0.7976	0.8570	*0.8333*	0.6701	*0.8276*	*0.8113*	*NaN*	*0.7770*	*0.7882*
	Complete	0.6966	0.8051	0.7787	0.4529	0.7575	0.7380	*NaN*	0.6480	0.6848
	Median	0.7895	0.8219	0.7843	0.6695	0.7875	0.7600	*NaN*	0.7453	0.7309
	Single	0.7908	0.8220	0.8030	0.6633	0.7841	0.7680	*NaN*	0.7510	0.7515
	Ward	0.7313	0.8018	0.7755	0.5497	0.7523	0.7350	*NaN*	0.6442	0.6839
	Weighted	0.7980	0.8181	0.7848	0.6899	0.7824	0.7531	*NaN*	0.7230	0.7173
Cityblock	Average	*0.8404*	0.7982	0.7767	*0.8206*	0.7707	0.7518	*0.8027*	0.7522	0.7352
	Centroid	0.8367	*0.7997*	*0.7805*	0.8113	*0.7741*	*0.7611*	0.7739	*0.7552*	*0.7482*
	Complete	0.7995	0.7226	0.6935	0.7727	0.6761	0.6484	0.7464	0.6418	0.6059
	Median	0.8267	0.7566	0.7196	0.8018	0.7412	0.7074	0.7623	0.7306	0.7174
	Single	0.8077	0.7737	0.7676	0.7804	0.7448	0.7447	0.7533	0.7248	0.7269
	Ward	0.8004	0.7243	0.7003	0.7744	0.6817	0.6568	0.7493	0.6446	0.6131
	Weighted	0.8305	0.7507	0.7114	0.8111	0.7241	0.6867	0.7936	0.7102	0.6718
Minkowski	Average	*0.8478*	0.8065	0.7848	*0.8280*	0.7818	0.7629	*0.8102*	0.7647	0.7488
	Centroid	0.8441	*0.8088*	*0.7883*	0.8179	*0.7860*	*0.7721*	0.7797	*0.7695*	*0.7628*
	Complete	0.8095	0.7273	0.7006	0.7808	0.6865	0.6551	0.7535	0.6494	0.6136
	Median	0.8342	0.7644	0.7262	0.8073	0.7509	0.7182	0.7661	0.7432	0.7311
	Single	0.8168	0.7836	0.7774	0.7903	0.7582	0.7578	0.7653	0.7400	0.7426
	Ward	0.8064	0.7278	0.7050	0.7801	0.6869	0.6606	0.7531	0.6464	0.6161
	Weighted	0.8382	0.7551	0.7185	0.8182	0.7352	0.6918	0.8006	0.7197	0.6835
Cosine	Average	*0.7689*	*0.6484*	*0.6138*	*0.7107*	*0.5463*	*0.4946*	*0.6596*	*0.4549*	*0.3908*
	Centroid	0.7618	0.6285	0.5866	0.6982	0.5106	0.4462	0.6270	0.3717	0.2936
	Complete	0.7320	0.5960	0.5568	0.6604	0.4773	0.4226	0.5977	0.3743	0.3064
	Median	0.7438	0.5702	0.5265	0.6802	0.4521	0.3862	0.6058	0.3286	0.2517
	Single	0.7082	0.4942	0.4287	0.6182	0.3484	0.2651	0.5429	0.2451	0.1693
	Ward	0.7467	0.6325	0.5991	0.6808	0.5240	0.4733	0.6213	0.4232	0.3521
	Weighted	0.7534	0.5961	0.5531	0.6961	0.4958	0.4296	0.6454	0.4104	0.3378
Correlation	Average	*0.8214*	*0.7466*	*0.7239*	*0.7213*	*0.5584*	*0.5060*	*0.6508*	*0.4269*	*0.3550*
	Centroid	0.8171	0.7330	0.7064	0.7117	0.5248	0.4587	0.6210	0.3434	0.2560
	Complete	0.7978	0.7102	0.6794	0.6770	0.4992	0.4457	0.5887	0.3561	0.2874
	Median	0.7984	0.6852	0.6596	0.6935	0.4756	0.4128	0.6027	0.3150	0.2328
	Single	0.7931	0.6647	0.6319	0.6374	0.3624	0.2748	0.5293	0.2157	0.1354
	Ward	0.8069	0.7378	0.7162	0.6955	0.5431	0.4940	0.6161	0.4096	0.3428
	Weighted	0.8052	0.7017	0.6843	0.7059	0.5106	0.4557	0.6373	0.3914	0.3191
Spearman	Average	*0.8198*	0.7583	0.7455	*0.7233*	*0.5638*	*0.5159*	*0.6505*	*0.4267*	*0.3567*
	Centroid	0.8113	0.7396	0.7212	0.7133	0.5336	0.4729	0.6199	0.3429	0.2537
	Complete	0.8090	*0.7788*	*0.7762*	0.6802	0.5341	0.4983	0.5909	0.3558	0.2887
	Median	0.7887	0.7136	0.7140	0.6960	0.4819	0.4238	0.6021	0.3126	0.2304
	Single	0.6861	0.6736	0.6742	0.6404	0.4008	0.1821	0.5302	0.2190	0.1404
	Ward	0.7881	0.7364	0.7273	0.6963	0.5488	0.5037	0.6170	0.4081	0.3425
	Weighted	0.8112	*0.7788*	*0.7762*	0.7076	0.5157	0.4687	0.6366	0.3926	0.3197
Chebychev	Average	*0.8373*	0.7945	0.7740	*0.8094*	0.7588	0.7398	*0.7824*	0.7246	0.7059
	Centroid	0.8338	*0.7966*	*0.7774*	0.8008	*0.7627*	*0.7483*	0.7601	*0.7280*	*0.7181*
	Complete	0.7965	0.7182	0.6953	0.7581	0.6707	0.6424	0.7262	0.6226	0.5951
	Median	0.8244	0.7546	0.7195	0.7913	0.7315	0.6996	0.7510	0.7061	0.6907
	Single	0.8044	0.7700	0.7640	0.7663	0.7329	0.7324	0.7289	0.6940	0.6951
	Ward	0.7978	0.7216	0.6996	0.7647	0.6761	0.6495	0.7351	0.6345	0.6038
	Weighted	0.8279	0.7470	0.7135	0.8007	0.7171	0.6783	0.7745	0.6895	0.6557

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