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 1 The cophenetic correlation coefficient values for $μ = 0$ , $σ^{2} = 1$ (without 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	*0.7552*	0.6358	0.6009	*0.7255*	0.6017	0.5753	*0.6922*	0.5728	0.5339
	Centroid	0.6927	*0.6393*	*0.6038*	0.6463	*0.6028*	*0.5557*	0.5829	*0.5759*	*0.5605*
	Complete	0.6858	0.4940	0.4313	0.6397	0.4135	0.3386	0.5920	0.3439	0.2640
	Median	0.7309	0.5600	0.4797	0.6897	0.5412	0.4605	0.6220	0.5338	0.4989
	Single	0.7034	0.6033	0.5947	0.6633	0.5663	0.5577	0.6157	0.5332	0.5295
	Ward	0.6832	0.4956	0.4422	0.6384	0.4124	0.3496	0.5895	0.3367	0.2664
	Weighted	0.7367	0.5428	0.4692	0.7064	0.5024	0.4105	0.6749	0.4791	0.3941
Squared Euclidean	Average	*0.7381*	0.6352	0.5978	*0.7090*	0.5974	0.5546	*0.6792*	0.5700	0.5315
	Centroid	0.7285	*0.6402*	*0.6056*	0.6874	*0.6085*	*0.5765*	0.6254	*0.5831*	*0.5632*
	Complete	0.6565	0.4826	0.4271	0.6128	0.4014	0.3325	0.5659	0.3318	0.2586
	Median	0.7102	0.5538	0.4745	0.6679	0.5386	0.4553	0.6013	0.5344	0.5039
	Single	0.6874	0.6038	0.5950	0.6453	0.5656	0.5578	0.6009	0.5324	0.5301
	Ward	0.6533	0.4830	0.4350	0.6093	0.3995	0.3421	0.5661	0.3264	0.2589
	Weighted	0.7191	0.5351	0.4615	0.6904	0.4978	0.4054	0.6623	0.4768	0.3969
Mahalanobis	Average	*0.6957*	0.6276	0.5950	*0.6176*	0.5865	0.5469	*NaN*	0.5591	0.5284
	Centroid	0.6749	*0.6325*	*0.6010*	0.5864	*0.5993*	*0.5723*	*NaN*	*0.5789*	*0.5630*
	Complete	0.5627	0.4578	0.4121	0.3958	0.3625	0.3097	*NaN*	0.2711	0.2270
	Median	0.6587	0.5426	0.4719	0.5762	0.5320	0.4538	*NaN*	0.5385	0.5106
	Single	0.6565	0.6032	0.5956	0.5642	0.5655	0.5589	*NaN*	0.5293	0.5317
	Ward	0.5541	0.4621	0.4235	0.3876	0.3539	0.3147	*NaN*	0.2495	0.2155
	Weighted	0.6760	0.5202	0.4549	0.6078	0.4843	0.3963	*NaN*	0.4869	0.4013
Cityblock	Average	*0.7427*	0.6228	0.5844	*0.7120*	0.5810	0.5349	*0.6787*	0.5484	0.5076
	Centroid	0.7372	*0.6280*	*0.5944*	0.6983	*0.5902*	*0.5557*	0.6343	*0.5579*	*0.5368*
	Complete	0.6716	0.4780	0.4229	0.6247	0.3976	0.3272	0.5771	0.3285	0.2502
	Median	0.7194	0.5460	0.4710	0.6799	0.5233	0.4455	0.6129	0.5117	0.4774
	Single	0.6876	0.5839	0.5756	0.6443	0.5410	0.5324	0.5975	0.5037	0.5009
	Ward	0.6728	0.4869	0.4348	0.6281	0.4052	0.3427	0.5823	0.3322	0.2596
	Weighted	0.7244	0.5290	0.4546	0.6936	0.4878	0.3969	0.6615	0.4601	0.3824
Minkowski	Average	*0.7552*	0.6393	0.6009	*0.7255*	0.6017	0.5557	*0.6922*	0.5728	0.5339
	Centroid	0.7497	*0.6447*	*0.6087*	0.7099	*0.6124*	*0.5791*	0.6450	*0.5833*	*0.5629*
	Complete	0.6858	0.4940	0.4313	0.6397	0.4135	0.3386	0.5920	0.3439	0.2640
	Median	0.7309	0.5600	0.4797	0.6897	0.5412	0.4605	0.6220	0.5338	0.4989
	Single	0.7034	0.6033	0.5947	0.6633	0.5663	0.5577	0.6157	0.5332	0.5295
	Ward	0.6832	0.4956	0.4422	0.6384	0.4124	0.3496	0.5895	0.3367	0.2664
	Weighted	0.7367	0.5428	0.4692	0.7064	0.5024	0.4105	0.6749	0.4791	0.3941
Cosine	Average	*0.7590*	*0.6277*	*0.5839*	*0.6994*	*0.5143*	*0.4524*	*0.6441*	*0.4152*	*0.3413*
	Centroid	0.7518	0.6045	0.5478	0.6866	0.4711	0.3894	0.6097	0.3242	0.2312
	Complete	0.7230	0.5782	0.5320	0.6501	0.4518	0.3929	0.5808	0.3428	0.2700
	Median	0.7340	0.5530	0.5040	0.6681	0.4273	0.3546	0.5911	0.3004	0.2146
	Single	0.6931	0.4695	0.3898	0.6034	0.3070	0.2202	0.5211	0.2017	0.1275
	Ward	0.7381	0.6142	0.5730	0.6716	0.4979	0.4418	0.6083	0.3974	0.3280
	Weighted	0.7433	0.5786	0.5336	0.6854	0.4711	0.4093	0.6311	0.3834	0.3069
Correlation	Average	*0.8217*	*0.7470*	*0.7226*	*0.7229*	*0.5581*	*0.5065*	*0.6507*	*0.4268*	*0.3542*
	Centroid	0.8169	0.7358	0.7037	0.7124	0.5245	0.4594	0.6212	0.3441	0.2518
	Complete	0.7979	0.7083	0.6775	0.6791	0.4987	0.4514	0.5893	0.3545	0.2855
	Median	0.7982	0.6886	0.6621	0.6952	0.4754	0.4128	0.6028	0.3177	0.2324
	Single	0.7939	0.6715	0.6285	0.6389	0.3624	0.2781	0.5307	0.2124	0.1355
	Ward	0.8069	0.7388	0.7155	0.6974	0.5429	0.4938	0.6170	0.4099	0.3426
	Weighted	0.8052	0.7061	0.6816	0.7075	0.5105	0.4534	0.6379	0.3916	0.3185
Spearman	Average	*0.8207*	0.7600	0.7441	*0.7240*	*0.5636*	*0.5163*	*0.6487*	*0.4274*	*0.3567*
	Centroid	0.8116	0.7413	0.7199	0.7132	0.5336	0.4715	0.6184	0.3452	0.2511
	Complete	0.8094	*0.7788*	*0.7780*	0.6815	0.5337	0.4966	0.5884	0.3572	0.2896
	Median	0.7903	0.7162	0.7114	0.6958	0.4818	0.4235	0.5990	0.3175	0.2329
	Single	0.6854	0.6737	0.6738	0.6397	0.4010	0.1830	0.5287	0.2198	0.1427
	Ward	0.7892	0.7358	0.7275	0.6973	0.5488	0.5030	0.6145	0.4093	0.3434
	Weighted	0.8118	*0.7788*	*0.7780*	0.7086	0.5154	0.4672	0.6357	0.3916	0.3194
Chebychev	Average	*0.7375*	0.6183	0.5804	*0.6933*	0.5595	0.5141	*0.6448*	0.4958	0.4523
	Centroid	0.7317	*0.6241*	*0.5870*	0.6811	*0.5693*	*0.5334*	0.6100	*0.5067*	*0.4805*
	Complete	0.6647	0.4780	0.4235	0.6035	0.3824	0.3164	0.5423	0.2962	0.2281
	Median	0.7140	0.5431	0.4630	0.6625	0.5036	0.4287	0.5928	0.4628	0.4249
	Single	0.6833	0.5792	0.5695	0.6223	0.5199	0.5084	0.5536	0.4468	0.4405
	Ward	0.6680	0.4852	0.4317	0.6128	0.3949	0.3341	0.5595	0.3140	0.2423
	Weighted	0.7189	0.5255	0.4494	0.6759	0.4734	0.3878	0.6294	0.4249	0.3525

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