Hopkins statistic
The Hopkins statistic is a way of measuring the cluster tendency of a data set. It belongs to the family of sparse sampling tests. It acts as a statistical hypothesis test where the null hypothesis is that the data is generated by a Poisson point process and are thus uniformly randomly distributed. A value close to 1 tends to indicate the data is highly clustered, random data will tend to result in values around 0.5, and uniformly distributed data will tend to result in values close to 0.Preliminaries
A typical formulation of the Hopkins statistic follows.Definition
With the above notation, if the data is dimensional, then the Hopkins statistic is defined as:
