Features:
1. Spatial validation
https://geodacenter.github.io/pygeoda/generated/pygeoda.spatial_validation.html
Spatial validation provides a collection of validation measures including (1) fragmentations (entropy, simpson), (2) join count ratio, (3) compactness (isoperimeter quotient) and (4) diameter.
**Fragmentation** is a measure of spatial validation of clusters. It includes:
1. entropy, which measures the fraction of observations in each cluster
2. entropy*, which is the standardized entropy measure
3. simpson, which is an index for diversity measure in each cluster
4. simpson*, which is the standardized simpson measure
> For non-spatially constrained clusters, the validation also reports cluster_fragmentation, which is a list of Fragmentation objects for each cluster, or None for spatially constrained clusters.
**JoinCountRatio** is measure of join counts (the number of times a category is surrounded by neighbors of the same category) over the total number of neighbors after converting each category to a dummy variable. It includes:
1. neighbors, the total number of neighbors of elements in a cluster
2. join count, the total join count of elements in a cluster
3. ratio: the ratio of total join count over total neighbors
**Compactness** is a measure of isoperimeter quotient for each spatially constrained cluster. It includes:
1. area, the area of a cluster. For points, the convex hull is used to compute the area.
2. perimeter, the perimeter of a cluster. For points, the convex hull is used to compute the perimeter
3. isoperimeter_quotient, (4 * pi * area) / (perimeter^2)
**Diameter** is a measure of the longest shortest distance between any pairs in a cluster. It includes:
1. steps, the longest shortest distance between any pairs
2. ratio, the ratio of steps over the number of elements in the cluster
2. Make Spatial
https://geodacenter.github.io/pygeoda/generated/pygeoda.make_spatial.html
Make spatially constrained clusters from spatially non-constrained clusters using the contiguity information from the input weights
3. Bivariate Local Moran
https://geodacenter.github.io/pygeoda/generated/pygeoda.local_bimoran.html
The bivariate Local Moran’s I captures the relationship between the value for one variable at location i, and the average of the neighboring values for another variable. Please note this statistic needs to be interpreted with caution, since it ignores in-situ correlation between the two variables. The most meaningful application of the bivariate Local Moran statistic is comparing the same variable at two time periods.