Moran's I and Geary's C have good statistical characteristics to describe global spatial autocorrelation, but they do not have the ability to identify different types of spatial aggregation patterns, such as cold spots and hot spots.

General G:

The General G statistic of overall spatial association is given as

\( G=\frac{\sum_{i=1}^{n}w_{ij}x_ix_j}{\sum_{i=1}^{n}x_ix_j} \)

where \( x_i \) and \( x_j \) are observations for features i and j, and \( w_{ij} \) is the spatial weight between feature i and j. n is the number of elements and \( x_i \) couldn’ t be the same as \( x_j \).

Meanwhile the expection of General G is E(G), \( E(G)=\frac{\sum_{i=1}^{n}\sum_{j=1}^{n}w_{ij}}{n(n-1)} \).So When the General G value is higher than the observed E(G) value, there is a high value aggregation.When the General G value is lower than the observed value of E(G), there is address aggregation.As Genera G approaches E(G) the observed values are randomly distributed in space.

Local G:

The local G-exponent can be expressed as

\( G_i^*=\frac{\sum_{j=1}^nw_{ij}x_j-x_{average}\sum_{j=1}^nw_{ij}}{s\sqrt{\frac{[n\sum_{j=1}^nw_{ij}^2-(\sum_{j=1}^nw_{ij})^2]}{n-1}}} \)

where \( x_p=\frac{\sum_{j=1}^{n}x_j}{n} \) and \( s=\sqrt{\frac{\sum_{j=1}^{n}x_j^2}{n}-x_{average}^2} \).This index can be used to identify spatial clusters of high and low values (hot spots) of statistical significance and to tell us where the high and low values are clustered.