Clumpiness index (Aggregation metric)
Details
$$Given G_{i} = \Bigg(\frac{g_{ii}}{ (\sum\limits_{k=1}^m g_{ik}) - min e_{i}} \Bigg)$$ $$CLUMPY = \Bigg[ \frac{G_{i} - P_{i}}{P_{i}} for G_{i} < P_{i} \& P_{i} < .5; else \\ \frac{G_{i} - P_{i}}{1 -P_{i}} \Bigg] $$
where \(g_{ii}\) is the number of like adjacencies, \(g_{ik}\) is the classwise number of all adjacencies including the focal class, \(min e_{i}\) is the minimum perimeter of the total class in terms of cell surfaces assuming total clumping and \(P_{i}\) is the proportion of landscape occupied by each class.
CLUMPY is an 'Aggregation metric'. It equals the proportional deviation of the proportion of like adjacencies involving the corresponding class from that expected under a spatially random distribution. The metric is based on he adjacency matrix and the the double-count method.