Journal of Inequalities and Applications

Table 3 Comparisons of clustering methods and Rand’s C statistics

From: Performance of Rand’s C statistics in clustering analysis: an application to clustering the regions of Turkey

Clustering method	Distance measure
	Squared Euclidean distance				Cosine
	Together in both	Separate in both	Mixed	Rand’s C	Together in both	Separate in both	Mixed	Rand’s C
Between-Nearest	4	10	7	0.67	4	14	3	0.86
Between-Within	5	16	0	1.00	4	13	4	0.81
Between-Furthest	5	16	0	1.00	5	16	0	1.00
Between-Centroid	5	16	0	1.00	5	16	0	1.00
Between-Median	5	16	0	1.00	5	16	0	1.00
Between-Ward’s	5	16	0	1.00	5	16	0	1.00
Nearest-Within	4	10	7	0.67	4	12	5	0.76
Nearest-Furthest	4	10	7	0.67	4	14	3	0.86
Nearest-Centroid	4	10	7	0.67	4	14	3	0.86
Nearest-Median	4	10	7	0.67	4	14	3	0.86
Nearest-Ward’s	4	10	7	0.67	4	14	3	0.86
Within-Furthest	5	16	0	1.00	4	13	4	0.81
Within-Centroid	5	16	0	1.00	4	13	4	0.81
Within-Median	5	16	0	1.00	4	13	4	0.81
Within-Ward’s	5	16	0	1.00	4	13	4	0.81
Furthest-Centroid	5	16	0	1.00	5	16	0	1.00
Furthest-Median	5	16	0	1.00	5	16	0	1.00
Furthest-Ward’s	5	16	0	1.00	5	16	0	1.00
Centroid-Median	5	16	0	1.00	5	16	0	1.00
Centroid-Ward’s	5	16	0	1.00	5	16	0	1.00
Median-Ward’s	5	16	0	1.00	5	16	0	1.00

Clustering method	Distance measure
	Pearson correlation				Customized
	Together in both	Separate in both	Mixed	Rand’s C	Together in both	Separate in both	Mixed	Rand’s C
Between-Nearest	4	16	1	0.95	4	10	7	0.67
Between-Within	4	16	1	0.95	5	16	0	1.00
Between-Furthest	4	16	1	0.95	5	16	0	1.00
Between-Centroid	4	16	1	0.95	4	10	7	0.67
Between-Median	4	16	1	0.95	5	16	0	1.00
Between-Ward’s	4	16	1	0.95	5	16	0	1.00
Nearest-Within	5	16	0	1.00	4	10	7	0.67
Nearest-Furthest	5	16	0	1.00	4	10	7	0.67
Nearest-Centroid	5	16	0	1.00	10	11	0	1.00
Nearest-Median	5	16	0	1.00	4	10	7	0.67
Nearest-Ward’s	5	16	0	1.00	4	10	7	0.67
Within-Furthest	5	16	0	1.00	5	16	0	1.00
Within-Centroid	5	16	0	1.00	4	10	7	0.67
Within-Median	5	16	0	1.00	5	16	0	1.00
Within-Ward’s	5	16	0	1.00	5	16	0	1.00
Furthest-Centroid	5	16	0	1.00	4	10	7	0.67
Furthest-Median	5	16	0	1.00	5	16	0	1.00
Furthest-Ward’s	5	16	0	1.00	5	16	0	1.00
Centroid-Median	5	16	0	1.00	4	10	7	0.67
Centroid-Ward’s	5	16	0	1.00	4	10	7	0.67
Median-Ward’s	5	16	0	1.00	5	16	0	1.00

Clustering method	Distance measure
	Minkowski				Block
	Together in both	Separate in both	Mixed	Rand’s C	Together in both	Separate in both	Mixed	Rand’s C
Between-Nearest	4	10	7	0.67	4	10	7	0.67
Between-Within	5	16	0	1.00	5	16	0	1.00
Between-Furthest	5	16	0	1.00	5	16	0	1.00
Between-Centroid	4	10	7	0.67	5	16	0	1.00
Between-Median	5	16	0	1.00	5	16	0	1.00
Between-Ward’s	5	16	0	1.00	5	16	0	1.00
Nearest-Within	4	10	7	0.67	4	10	7	0.67
Nearest-Furthest	4	10	7	0.67	4	10	7	0.67
Nearest-Centroid	10	11	0	1.00	4	10	7	0.67
Nearest-Median	4	10	7	0.67	4	10	7	0.67
Nearest-Ward’s	4	10	7	0.67	4	10	7	0.67
Within-Furthest	5	16	0	1.00	5	16	0	1.00
Within-Centroid	4	10	7	0.67	5	16	0	1.00
Within-Median	5	16	0	1.00	5	16	0	1.00
Within-Ward’s	5	16	0	1.00	5	16	0	1.00
Furthest-Centroid	4	10	7	0.67	5	16	0	1.00
Furthest-Median	5	16	0	1.00	5	16	0	1.00
Furthest-Ward’s	5	16	0	1.00	5	16	0	1.00
Centroid-Median	4	10	7	0.67	5	16	0	1.00
Centroid-Ward’s	4	10	7	0.67	5	16	0	1.00
Median-Ward’s	5	16	0	1.00	5	16	0	1.00
Within-Median	4	10	7	0.67	4	10	7	0.67
Within-Ward’s	5	16	0	1.00	5	16	0	1.00
Furthest-Centroid	4	10	7	0.67	5	16	0	1.00
Furthest-Median	5	16	0	1.00	5	16	0	1.00
Furthest-Ward’s	5	16	0	1.00	5	16	0	1.00
Centroid-Median	4	10	7	0.67	5	16	0	1.00
Centroid-Ward’s	4	10	7	0.67	5	16	0	1.00
Median-Ward’s	5	16	0	1.00	5	16	0	1.00

Clustering method	Distance measure
	Chebychev
	Together in both	Separate in both	Mixed	Rand’s C
Between-Nearest	4	10	7	0.67
Between-Within	4	10	7	0.67
Between-Furthest	5	16	0	1.00
Between-Centroid	4	10	7	0.67
Between-Median	4	10	7	0.67
Between-Ward’s	5	16	0	1.00
Nearest-Within	10	11	0	1.00
Nearest-Furthest	4	10	7	0.67
Nearest-Centroid	10	11	0	1.00
Nearest-Median	10	11	0	1.00
Nearest-Ward’s	4	10	7	0.67
Within-Furthest	4	10	7	0.67
Within-Centroid	10	11	0	1.00
Within-Median	10	11	0	1.00
Within-Ward’s	4	10	7	0.67
Furthest-Centroid	4	10	7	0.67
Furthest-Median	4	10	7	0.67
Furthest-Ward’s	5	16	0	1.00
Centroid-Median	10	11	0	1.00
Centroid-Ward’s	4	10	7	0.67
Median-Ward’s	4	10	7	0.67

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