TABLE 2.

Six indices for determining cluster size.

Indices	Temporal profiles	Proposed cluster size	Criteria
Fuzzy hyper volume (FHV)	PH	2	Minimum value of the index. Small FHV indicates presence of compact clusters based on concepts of hyper volume and density (Gath and Geva, 1989).
	CRPH	2
	AGRPH	2
Partition density (PD)	PH	2	Maximum value of the index. PD is the general partition density. According to the physical definition of density; larger value of PD indicates better clustering (Gath and Geva, 1989).
	CRPH	2
	AGRPH	2
Xie-Beni (XB)	PH	2	Minimum value of the index. XB measures the average intra-cluster fuzzy compactness against the minimum inter-cluster separation. The optimal cluster size is reached when the minimum of XB is found (Xie and Beni, 1991).
	CRPH	2
	AGRPH	2
Fukuyama-Sugeno (FS)	PH	2	Minimum value of the index. Small FS indicates compact and well-separated clusters (Zanaty, 2012).
	CRPH	2
	AGRPH	2
Partition coefficient (PC)	PH	2	Maximum value of the index. The closer the index is to 1.0, the crisper the clustering. When PC is close to 1/C, no clustering trend exists in the data (Zanaty, 2012).
	CRPH	2
	AGRPH	2
Partition entropy (PE)	PH	2	Minimum value of the index. Ranges over the interval [0, logC]. When a PE is close to upper bound, and no clustering trend exits in the data (Krawczyk and Cyganek, 2017).
	CRPH	2
	AGRPH	4

PH, plant height; AGRPH; the average growth rate of plant height; CRPH, the contribution rate of plant height.