$$Given G_{i} = \Bigg(\frac{g_{ii}}{ (\sum\limits_{k=1}^m g_{ik}) - min e_{i}} \Bigg)$$
$$CLUMPY = \Bigg[ \frac{G_{i} - P_{i}}{P_{i}} for G_{i} < P_{i} \& P_{i} < .5; else \\ \frac{G_{i} - P_{i}}{1 -P_{i}} \Bigg] $$
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.
Behaviour
Equals -1 for maximally disaggregated, 0 for randomly distributed
and 1 for maximally aggregated classes.